GENERAL INTRODUCTION 1. THE MANY FACES OF THE FLOWER

The flower is a short axis bearing, from the center out, female reproductive organs consisting of ovules protected by carpels, male reproductive organs called stamens and a perianth [START_REF] Bateman | Morphological and molecular phylogenetic context of the angiosperms: contrasting the "top-down" and "bottom-up" approaches used to infer the likely characteristics of the first flowers[END_REF]. The flower is one of the most distinctive features of angiosperms, the clade of land plants with the highest diversity. "Diversity" is here used in the sense of having a large number of species, and is accompanied by a variety of flower forms that is exemplified in Figure I.1. The image that the word "flower" evokes to the layman probably greatly resembles the upper left picture of Figure I.1 and consists of reproductive organs of both sexes surrounded by a specialized two-whorl perianth in which the inner whorl is colorful and showy but delicate, while the outer whorl is more inconspicuous and stiff as it protects the developing bud; it will also probably have five petals and five sepals. That mental picture includes the organs being separate and those of a given category being the same size and shape.

Adaptation to pollinators, self-pollination, abiotic pollination or simply evolutionary history has led to the development among flowers of aspects that are radically different from that "layman's mental image". For instance, the "sepal and petal" perianth is not the only form of perianth that exists and is actually a derived state (see Figure I.3 and Chapter 3). Species from the early-diverging clades of angiosperms can have only one type of perianth part, or two types that are different in shape but of similar color, petal-like or sepal-like. Flowers from these earlydiverging clades can also have more than two perianth whorls or a spiral perianth, usually associated with a large number of perianth parts. While most species in such cases are found in early-diverging angiosperms, the above situations occasionally appear within clades in which the "sepal and petal" two-whorled perianth is otherwise the norm. The whorled flowers of magnoliids and monocots are mostly trimerous (three perianth parts per whorl) rather than pentamerous (five parts per whorl). Some flowers show variation in perianth part size and shape within the same whorl, which may result in a perianth with bilateral symmetry, disymmetry (two perpendicular planes of symmetry) or no symmetry at all, instead of the more common radial symmetry. Certain types of inflorescences (flower aggregations) are made of a large number of extremely small or simplified flowers. Simplified flowers can lose their perianth and consist only of reproductive organs, which themselves can be reduced to a very small number; there are flowers that effectively consist of a single carpel and/or a single stamen, such as members of Cryptocoryne (Araceae) and Sarcandra (Chloranthaceae). While we will be focusing on the perianth in this thesis, stamens and carpels can also be subject to variation in number, shape, differentiation, symmetry, and presence/absence. Some species of angiosperms have the two sexes separated in different flowers on the same individual (monoecy) or different individuals (dioecy). In such situations, the organs corresponding to the absent sex are either reduced or absent. All this variation in flower form has appeared via various changes in flower development across the evolutionary history of angiosperms. In the days before widespread gene sequencing, shared morphological features, including those of flowers when they were present, were used to classify species into groups. Molecular data broke up some of the families from the time, but confirmed that the members of others were indeed related. Clades in which most or all species share a given morphological attribute can be safely assumed to have inherited that attribute from a common ancestor. Some morphological attributes are encountered in more species than others, and are sometimes a characteristic shared by entire, very diverse (in terms of species number) clades. Because of this, it has been speculated that such attributes could be a cause of the high diversity of these clades.

A SERIES OF ABOMINABLE MYSTERIES

Charles Darwin strongly believed in gradual evolution. He found that the fossil record of several groups did not confirm this belief, with the rapid appearance of many different angiosperms being the most extreme example. Such groups were part of the "abominable mystery" mentioned in the letter written to Joseph Hooker in 1879. However, concerning angiosperms specifically, he suggested that fast appearance of multiple forms may have a biological explanation in the form of co-evolution with pollinators [START_REF] Friedman | The meaning of Darwin's "abominable mystery[END_REF]. A century and a half after these words were written, we now know that the diversity of the approximately 300,000 living species of angiosperms is unevenly distributed across the whole clade, that the five largest families, which account for 30% of that diversity, are not closely related to each other and that pollinator interaction is one of the probable causes of the large number of flower forms [START_REF] Armbruster | Floral specialization and angiosperm diversity: phenotypic divergence, fitness trade-offs and realized pollination accuracy[END_REF]). When we look at angiosperm families separately, we indeed find species diversity ranging from one (this is the known diversity of about 30 families, including Amborellaceae, sister to all other angiosperms) to more than 25,000 species in the Asteraceae.

However, rather than solving the mystery, this fact is closer to giving us several abominable mysteries to resolve instead of only one. Out of 424 families recognized today (APG IV, 2016), only five boast five-digit species diversity (Asteraceae, Orchidaceae, Fabaceae, Poaceae and Rubiaceae). Families with four-digit diversity, while much more frequent in comparison, can still be exceptionally diverse compared to their most closely related families (e.g. the 3460species strong Gesneriaceae are sister to the 260-species Calceolariaceae). A distribution of family diversities is shown in Figure I.2.

One of the proposed causal factors of this imbalance is the origin of key innovations, which are character states whose appearance in a clade results in higher diversification [START_REF] Hunter | Key innovations and the ecology of macroevolution[END_REF]). Several character states, which include the aforementioned bilateral symmetry and specialization of the perianth into sepals and petals, have been proposed as candidate key innovations [START_REF] Sargent | Floral symmetry affects speciation rates in angiosperms[END_REF][START_REF] Vamosi | Key innovations within a geographical context in flowering plants: towards resolving Darwin's abominable mystery[END_REF][START_REF] Endress | Evolutionary diversification of the flowers in angiosperms[END_REF][START_REF] Armbruster | Floral specialization and angiosperm diversity: phenotypic divergence, fitness trade-offs and realized pollination accuracy[END_REF][START_REF] Vos | Heterostyly accelerates diversification via reduced extinction in primroses[END_REF][START_REF] O'meara | Non-equilibrium dynamics and floral trait interactions shape extant angiosperm diversity[END_REF]. Following this initial definition, the flower can itself be considered a key innovation within land plants, which led to angiosperm diversification. However, since there have in reality probably been multiple bursts of diversification within angiosperms (Magallón et al. 2015;[START_REF] Tank | Nested radiations and the pulse of angiosperm diversification : increased diversification rates often follow whole genome duplications[END_REF], the causes must be multiple: a different cause for each outburst, the same cause appearing several times, or a mix of both. In fact, only cases in which a candidate morphological or environmental character state has appeared several times independently and is correlated with higher diversification rates can be potentially hypothesized to be key innovations. This extra requirement is due to a caveat in tests deducing key innovation properties in traits found only in a single subsection of the clade in which they are being tested [START_REF] Maddison | The unsolved challenge to phylogenetic correlation tests for categorical characters[END_REF]. Indeed, if a character state is present only in one clade that is extremely diverse, it is easy to assume that this character state is the cause of the higher diversity, the flower's presence in land plants being an example of this. In reality, the character state may be a neutral one that appeared in the clade before, after or at the same time as the actual cause of diversification and was never eliminated due to a lack of negative effects on the clade's fitness. For example, we could be attributing the higher diversification of angiosperms (compared to their closest living relatives, the gymnosperms, or to any other clade among land plants) to the presence of flowers when in reality, something else that is exclusive to angiosperms could have played a much bigger role in the higher diversity.

In such a case, the character state would be simply correlated to the higher diversification and hitchhiking on one or several of the character states that are the true factors responsible the higher diversification [START_REF] Vamosi | Factors influencing diversification in angiosperms: at the crossroads of intrinsic and extrinsic traits[END_REF]. Because of this, only character states that appear repeatedly and in several parts of the angiosperm tree will be considered as potential key innovations in this thesis. Figure I.3 shows a summary of the hypothesized origins of character states that could be considered as potential key innovations across the angiosperms: several of them have appeared several times, even on the scale of the order-level tree.

THE NEGLECTED FLIP SIDE OF THE ABOMINABLE MYSTERY

Character states that have the opposite effect of key innovations have been called "selfdestructive" [START_REF] Bromham | Detecting Macroevolutionary Self-Destruction from Phylogenies[END_REF]) and lineages that have very few species have been called "depauperons" [START_REF] Donoghue | Confluence, synnovation, and depauperons in plant diversification[END_REF]. Such character states have been encountered in various studies [START_REF] Gyllenberg | Necessary and sufficient conditions for evolutionary suicide[END_REF][START_REF] Literature Cited Agnarsson | Sociality in theridiid spiders: repeated origins of an evolutionary dead end[END_REF][START_REF] Rankin | Species-level selection reduces selfishness through competitive exclusion[END_REF][START_REF] Helanterä | Unicolonial ants: where do they come from, what are they and where are they going?[END_REF][START_REF] Schwander | Twigs on the tree of life? Neutral and selective models for integrating macroevolutionary patterns with microevolutionary processes in the analysis of asexuality[END_REF][START_REF] Beck | Do asexual polyploid lineages lead short evolutionary lives? A case study from the fern genus Astrolepis[END_REF][START_REF] Kokko | Prudent males, group adaptation, and the tragedy of the commons[END_REF][START_REF] Wright | Evolutionary consequences of self-fertilization in plants[END_REF][START_REF] Igic | Is self-fertilization an evolutionary dead end ?[END_REF][START_REF] Pruitt | A real-time eco-evolutionary dead-end strategy is mediated by the traits of lineage progenitors and interactions with colony invaders[END_REF][START_REF] Burin | Omnivory in birds is a macroevolutionary sink[END_REF]. Many self-destructive traits have been called evolutionary dead-ends, a term that has also been used to cover derived states that cannot revert to their ancestral state (without necessarily being detrimental to the lineage) and lineages with no present-day descendants [START_REF] Bromham | Detecting Macroevolutionary Self-Destruction from Phylogenies[END_REF]. They have received less focus than key innovations, perhaps due to having a negative connotation [START_REF] Donoghue | Confluence, synnovation, and depauperons in plant diversification[END_REF]. Being aware that self-destructive character states exist alongside key innovations is important. If one state of a binary character is found to be associated with higher species diversification than the other state, labelling it a "key innovation" implies that it is, indeed, an innovation and that the other state, associated with lower diversification, is the ancestral one. If the ancestral state of the clade is unknown or ambiguous, suggesting that the state associated with the most diverse subclade must be the derived one may at first seem valid; natural selection suggests that innovations that are advantageous are kept, while those that are harmful are "discarded" and thus unlikely to be observed. This rationale seems to have been followed for floral phyllotaxy. The notion that the spiral perianth is a "primitive" state seems to be at least as old as 1907, as an article from that year mentions it [START_REF] Arber | The origin of angiosperms[END_REF]. The spiral state is much less frequent that the whorled one, which is present in all hyperdiverse (extremely high diversity) clades. The ancestral character state was assessed as equivocal between whorled and spiral in the most recent common ancestor of all angiosperms in all recent optimizations using parsimony. While studies dating from the end of the 20 th century have found the ancestral state to be spiral [START_REF] Endress | Patterns of floral construction in ontogeny and phylogeny[END_REF][START_REF] Soltis | Basal lineages of angiosperms: relationships and implications for floral evolution[END_REF], later studies have consistently found the state to be equivocal [START_REF] De Craene | Evolution of floral structures in basal angiosperms[END_REF][START_REF] Zanis | Phylogenetic analyses and perianth evolution in basal angiosperms[END_REF][START_REF] Soltis | Phylogeny and evolution of angiosperms[END_REF]Endress andDoyle 2007, 2009). These results can legitimately be interpreted either as the angiosperm perianth being ancestrally spiral or ancestrally whorled, especially considering that all spiral lineages that are not in the orders Amborellales or Austrobaileyales tend to be reconstructed as being part of a larger clade that is either ancestrally whorled or equivocal. However, out of the five studies cited above, three make mention of transitions from the spiral to whorled state while discussing the results, and two are non-committal concerning the direction of the transition; this indicates that the idea of spiral flowers being ancestral is still quite strong, but that the possibility of whorled flowers being ancestral is starting to emerge. In the latter scenario, the whorled state would have been conserved by Nymphaeales and the common ancestor of Magnoliidae, while Amborellales and Austrobaileyales would have a derived spiral state. Figure I.4 illustrates the potential pitfall that the existence of self-destructive character states creates in the "most diverse clade equals key innovation" reasoning. If the most diverse clade has the derived state, this state is possibly a key innovation. However, if the most diverse clade exhibits the ancestral state, the less diverse one may have developed a self-destructive state. However, when the ancestral state is uncertain, such as the root of the largest clade in which it is possible to diagnose the character state at all being equivocal (e.g. floral phyllotaxy above), both situations are possible.

THE CRITICAL ROLE OF ANCESTRAL STATE RECONSTRUCTION IN THE STUDY OF CHARACTER EVOLUTION

Many studies of character evolution base their conclusions on ancestral state reconstructions that assume that the ancestral state reconstructed is reliable. However, there are several models available for ancestral state reconstruction, several methods for sampling species and several ways to take rate heterogeneity within the clade into account (or not). A change in any of these factors may have an impact on the ancestral state that will be reconstructed for a given node. In this thesis, I am mostly interested in ancestral state reconstruction as a step towards determining whether a given character state may be a key innovation or not. Because of this, what I look for in ancestral state reconstructions is confirmation that the character state I consider a potential key innovation is derived and has repeated origins. Demonstrating repeated origins of the potential key innovation states was one of the purposes of the trees presented in the supplementary material of Chapter 1. I also did a reconstruction for the same purpose for a study of Proteaceae symmetry, of which I am coauthor (Citerne et al 2016, Figure 1). However, ancestral state reconstruction has other applications, such as (i) establishing the evolutionary pattern of a character that had not been previously optimized on a phylogenetic tree, (ii) determining whether a given character state can be considered a synapomorphy of a given clade, and (iii) explaining the choice of study species in an evolution and development (evo-devo) study. Another application of ancestral state reconstruction is implied by [START_REF] Käfer | Standard sister clade comparison fails when testing derived character states[END_REF], who suggest that clades in a derived state had less time to diversify than their sister clades in the ancestral state. Using their proposed correction for this factor involves testing if a clade actually does present a derived state.

THESIS OBJECTIVES

This thesis focuses on floral characters in angiosperms and their impact on species diversification. It is part of the eFLOWER project, whose aims include reconstructing the morphology of flowers in the deep nodes of the angiosperm tree and finding out which floral innovations are linked with major increases in diversification rates. One of the means used for these objectives is the collaborative database of floral morphological traits PROTEUS [START_REF] Sauquet | PROTEUS: A database for recording morphological data and creating NEXUS matrices[END_REF]. Chapter 1 presents an initial test of the key innovation nature of two character states on a small clade, the family Proteaceae. The next step was to do a similar test on all angiosperms with five characters (symmetry, fusion, phyllotaxy, pentamery, differentiation). One of the essential elements for doing this was ancestral state reconstruction for all five characters, as I needed to know in which clades the derived state of each of these characters had appeared, and eventually reverted to the ancestral state. The ancestral state reconstruction done on my test characters provided interesting results in itself. In addition, the methods I had used on Proteaceae proved to be inapplicable at the scale of all angiosperms and were severely criticized in 2015 [START_REF] Maddison | The unsolved challenge to phylogenetic correlation tests for categorical characters[END_REF][START_REF] Rabosky | Model inadequacy and mistaken inferences of traitdependent speciation[END_REF]. This caused ancestral state reconstruction to become the primary focus of the following chapters, in which I experimented with a taxon sampling method that focused on ensuring the inclusion of as many putative character state transitions as I could find across angiosperms. In Chapter 2, the sampling method was used on one character, perianth symmetry. The ancestral states were reconstructed via parsimony, because the sampling method produced unusable results with maximum likelihood. In Chapter 3, we used the same sampling method, this time on five characters simultaneously (Figure I.5) instead of only one, which altered the species sampling sufficiently to be able to use a maximum likelihood approach. This enabled me to test several modifications of the maximum likelihood model and their impact on the states that were reconstructed on a selection of nodes. Aside from the objectives from the third chapter, the three studies have made me work on two taxonomic scales, use two different ancestral state reconstruction methods and test three different species samplings, which let me gain an overview of elements that affect ancestral state reconstruction. The discussion will explore the properties of the sampling method used in Chapters 2 and 3, discuss what is missing to better understand the diversification or angiosperms, and review other studies that are approaching the latter question. Many members of the flowering plant family Proteaceae are found in Mediterranean hotspots, which are known to have a very high species diversity. A previous article has found a correlation between presence in hotspots and high diversification rates in the family (Sauquet et al. 2009). Proteaceae also have many species with a perianth displaying bilateral symmetry (Figure I.6), a character trait that has been found to be correlated with higher diversification in angiosperms [START_REF] Sargent | Floral symmetry affects speciation rates in angiosperms[END_REF]. Two methods for analyzing species diversification were tested on the characters of surrounding climate and perianth symmetry to verify if presence in hotspots and bilateral perianth symmetry may have had an impact on species diversification in the family. The family was chosen for this test because the diversity of each genus and the relationships among the genera are well-known. The floral morphology of the species is also well known; flowers have a well-conserved groundplan (four tepals, four opposite stamens, a monocarpellous ovary; Figures I.6, V.1 in general discussion) despite the size of the family (1750 species). Bilateral symmetry, also known as monosymmetry or zygomorphy, is a character state that is characteristic of several large families of angiosperms, such as Fabaceae and Orchidaceae. Zygomorphy has been shown to be a key innovation across angiosperms [START_REF] Sargent | Floral symmetry affects speciation rates in angiosperms[END_REF]). The first method I used to analyze species diversification in the Proteaceae phylogenetic tree is MEDUSA [START_REF] Alfaro | Nine exceptional radiations plus high turnover explain species diversity in jawed vertebrates[END_REF], which detects shifts in diversification rate within a phylogenetic tree. The second is BiSSE [START_REF] Maddison | Estimating a binary character's effect on speciation and extinction[END_REF][START_REF] Fitzjohn | Estimating trait-dependent speciation and extinction rates from incompletely resolved phylogenies[END_REF], which is used to test if a given character state is correlated with higher diversification rates than the other.

The ideal situation to produce a phylogeny that most accurately reflects evolutionary history is a fully-resolved and completely sampled species level phylogeny. Getting to such a situation is rare and becomes more difficult as the study clade gets larger. Both BiSSE (used to search for correlations between character states and species diversification) and MEDUSA (used to find diversification rate shifts) can accommodate non-resolved higher clades (genera in my application) on several conditions. One is that the tree must be fully resolved outside of these unresolved clades. Another is that the tree needs to be dated. For each unresolved clade, BiSSE has the additional requirement that the proportion of species in each character state must be known. The tree published by Sauquet et al. (2009) was a completely resolved genus-level tree with presumably monophyletic genera of known diversity, which enabled me to fill the requirements common to both methods. Hotspot presence data collected from Sauquet et al. (2009), and availability of perianth symmetry data for a majority of Proteaceae species enabled me to meet the extra requirement from BiSSE.

The results of the MEDUSA analysis showed five locations in which a significant rate shift had occurred: four in which the diversification rate increased and one in which the rate decreased. These results, while giving an idea of which clades could have benefitted from a key innovation, are independent of the character state of the species and only show that shifts are present. The BiSSE results showed that species found in Mediterranean hotspots had a diversification rate significantly higher than that of species found only outside of these hotspots.

They also demonstrated that the transition rate from hotspot to non-hotspot is higher than the transition rate from non-hotspot to hotspot. These results confirmed, with more appropriate methods, what had been found in Sauquet et al. (2009) using the methods available at that time.

In addition to this, I observed that the diversification rate of non-hotspot clades was negative (r=-0.002) and the net transition rate from hotspot (1) to non-hotspot (0) climate had a value high enough to compensate for it (q10-q01= 0.0027). In other words, my results suggest that presence in a non-hotspot climate is globally a macroevolutionary sink for Proteaceae i.e., a character state that is correlated with extinction among the species that have it, but is acquired by new species frequently enough to compensate for the loss of those that go extinct [START_REF] Burin | Omnivory in birds is a macroevolutionary sink[END_REF]. The results for perianth symmetry showed that perianth zygomorphy has no discernible impact on diversification, but that there was a higher frequency of state change from actinomorphic to zygomorphic than from zygomorphic to actinomorphic. My conclusion was that Proteaceae are an exception to the rule and that some of the other morphological characteristics of the family could be of greater importance to account for species diversification than the zygomorphy of individual flowers. This article was published around the same time as two articles discrediting BiSSE and other methods derived from it. The first, [START_REF] Maddison | The unsolved challenge to phylogenetic correlation tests for categorical characters[END_REF], was accepted but not yet published at the time at which our manuscript was in review. From the perspective of my study, it was merely a warning against a potential caveat of the BiSSE method. That caveat was concluding that a character state has an impact on diversification even when it appears in only one clade that happens to have a high diversification rate. To give support to my results, I demonstrated via maximum likelihood ancestral state reconstruction that both species living in Mediterranean hotspots and species with perianth zygomorphy were found across several clades that were distributed in the entire family tree (Appendices II.S3, S7). I also used split-BiSSE (FitzJohn 2012), a form of BiSSE that allowed the rates for both traits to change in a chosen subclade. Here, I conducted five tests. In each one, the rates were allowed to change in a different subclade defined by one of the nodes at which MEDUSA had found a rate shift. In all of these tests, the portion allowed to have a different rate from the rest was too small to have enough statistical power; however, the remaining part of the tree consistently had results similar to those of the full tree (Table II.S5,S6). This showed that neither of the potential caveats mentioned by [START_REF] Maddison | The unsolved challenge to phylogenetic correlation tests for categorical characters[END_REF] applied to my data. In a later article, [START_REF] Rabosky | Model inadequacy and mistaken inferences of traitdependent speciation[END_REF] demonstrated that BiSSE and it variants had a tendency to conclude that neutral character states have an impact on diversification. In my case, however, perianth symmetry (which had no effect on diversification) was found to be neutral in Proteaceae and presence in a non-hotspot climate was found to be a macroevolutionary sink rather than simply causing species to not diversify as fast as hotspot species. These two results are hence likely to reflect a level of biological reality.

A derivative of this work, a species-level Proteaceae chronogram with sampling proportional to genus diversity on which the evolution of perianth symmetry was optimized (Figure V.1 in general discussion), later became part of part of [START_REF] Citerne | Characterization of CYCLOIDEA-like genes in Proteaceae, a basal eudicot family with multiple shifts in floral symmetry[END_REF], an article in which I am a co-author, as are my supervisors, Sophie Nadot and Hervé Sauquet. I built the species-level dataset with the help of Peter Weston and I was in charge of phylogenetic reconstruction and dating. The parsimony reconstruction found a minimum 10 origins and 12 reversals. The maximum likelihood reconstruction found 16 origins of zygomorphy and six reversals to actinomorphy.

INTRODUCTION

Species richness is notoriously unevenly distributed across taxonomic groups. This uneven distribution is a general feature of life that has been observed in insects, amphibians, birds, mammals, and plants [START_REF] Harmon | An inordinate fondness for eukaryotic diversity[END_REF]. In phylogenetic trees, the difference in numbers of species across groups manifests itself by what is often referred to as tree imbalancethe extent to which sister clades across a phylogeny have different numbers of species [START_REF] Colless | Phylogenetics: the theory and practice of phylogenetic systematics, by E. O. Wiley[END_REF][START_REF] Mooers | Inferring evolutionary process from phylogenetic tree shape[END_REF]. While tree imbalance has been documented across the Tree of Life, the processes driving this pattern are less clear. One of the most intuitive explanations for tree imbalance is that diversification rates depend on a heritable evolving trait [START_REF] Heard | Patterns in phylognetic tree balance with variable and evoloving speciation rates[END_REF]. While this explanation is widely accepted (although see Pigot et al., 2010 for possible 'neutral' explanations), the heritable trait(s) responsible for diversification rate variation are rarely known.

Proteaceae are a flowering plant family with more than 1700 species widely distributed throughout the Southern Hemisphere that provides a good illustration of uneven species distribution across genera: 25 out of 81 genera are monospecific and 12 have only two species, while the largest genus, Grevillea, contains 362 species and the second largest, Banksia, has 169 species. Although Proteaceae have been widely studied by botanists, ecologists and evolutionary biologists, both the evolutionary success of the family and the reason for the uneven distribution of species within genera remain poorly understood.

Proteaceae are found in a variety of habitats including tropical rainforests, sclerophyllous forests, and open shrublands. Yet, they are mostly concentrated in the Cape Floristic Region (CFR) of South Africa and Southwest Australia (SWA), both of which are Mediterranean-type regions characterized by dry summers, mild winters, nutrient-poor soils and frequent fires [START_REF] Cowling | Plant diversity in mediterranean-climate regions[END_REF]. These environments may seem inhospitable for plants, but Proteaceae have developed a number of adaptive traits such as serotiny and dense cluster roots [START_REF] Lambers | Root structure and functioning for efficient acquisition of phosphorus: matching morphological and physiological traits[END_REF][START_REF] He | Banksia born to burn[END_REF]. Hence, the species richness of Proteaceae in general, and of CFR and SWA lineages in particular, could conceivably be linked to their adaptation to the conditions of Mediterranean climates.

Various intrinsic features have played a role in the radiation of clades of angiosperms (flowering plants) and may have contributed to the high diversity of Proteaceae. For instance, self-incompatibility has been shown to be associated with higher long-term diversification [START_REF] Igic | Loss of self-incompatibility and its evolutionary consequences[END_REF][START_REF] Goldberg | Species selection maintains selfincompatibility[END_REF][START_REF] Vamosi | Factors influencing diversification in angiosperms: at the crossroads of intrinsic and extrinsic traits[END_REF] and fused carpels (syncarpy) have been proposed to be a key innovation in angiosperms [START_REF] Endress | Evolutionary diversification of the flowers in angiosperms[END_REF]. Flowers may have radial symmetry (actinomorphy), which is the ancestral state for angiosperms as a whole, or bilateral symmetry (zygomorphy), which evolved numerous times independently [START_REF] Citerne | The evolution of floral symmetry[END_REF].

Zygomorphy characterizes many species-rich plant families (e.g., Orchidaceae, Fabaceae) and zygomorphic clades tend to be more diverse than actinomorphic ones [START_REF] Sargent | Floral symmetry affects speciation rates in angiosperms[END_REF], suggesting that bilateral symmetry may favor diversification. Potential advantages of zygomorphy include an attractive visual signal for pollinators and a single access angle that maximizes the efficiency of pollen deposition [START_REF] Sargent | Floral symmetry affects speciation rates in angiosperms[END_REF]). In addition, zygomorphy could facilitate adjustment of the shape of the flower to that of the pollinating animal and thus enhance plant-pollinator specialization. In Proteaceae, floral symmetry is remarkably variable, despite a well-preserved floral groundplan of four tepals with opposite stamens and a single carpel [START_REF] Weston | The Families and Genera of Vascular Plants[END_REF]. Zygomorphy is expressed in various ways in the family, from differential curvature of a tubular perianth to pronounced shape differentiation among tepals (e.g., with one tepal longer or broader than the others). Therefore, we might expect that zygomorphy could have a positive effect on diversification rates in Proteaceae.

The objective of the present study was to identify shifts in diversification rates throughout Proteaceae and to test the impact of Mediterranean hotspots and/or zygomorphy on speciation and extinction rates in the family. Sauquet et al. (2009) assembled a fossil-calibrated, dated phylogenetic tree of Proteaceae including all genera. Analyses of this phylogeny suggested that some clades within the family diversified significantly faster than the family-wide background rate, and that clades present in Mediterranean-type hotspots diversified faster (Sauquet et al. 2009). However, the methodological tools available at the time of the study did not allow the authors to locate putative diversification rate shifts, nor to disentangle the separate effect on speciation and extinction rates of the occurrence in Mediterranean-type regions.

There has recently been fast development of phylogenetic methods for studying diversification [START_REF] Pennell | An integrative view of phylogenetic comparative methods: connections to population genetics, community ecology, and paleobiology[END_REF][START_REF] Stadler | Recovering speciation and extinction dynamics based on phylogenies[END_REF][START_REF] Pyron | Phylogenetic estimates of speciation and extinction rates for testing ecological and evolutionary hypotheses[END_REF][START_REF] Morlon | Phylogenetic approaches for studying diversification[END_REF]). These methods mostly stem from the original work of [START_REF] Nee | The reconstructed evolutionary process[END_REF], who showed that although molecular phylogenies contain information of only extant taxa, patterns in their branching times contain information about both speciation and extinction rates. Recently developed methods in particular allow us to study when shifts in diversification rates occurred during clade evolution [START_REF] Rabosky | Exceptional among-lineage variation in diversification rates during the radiation of Australia's most diverse vertebrate clade[END_REF][START_REF] Alfaro | Nine exceptional radiations plus high turnover explain species diversity in jawed vertebrates[END_REF][START_REF] Silvestro | A Bayesian framework to estimate diversification rates and their variation through time and space[END_REF][START_REF] Morlon | Reconciling molecular phylogenies with the fossil record[END_REF][START_REF] Rabosky | Automatic detection of key innovations, rate shifts, and diversitydependence on phylogenetic trees[END_REF], and how specific traits --such as the occurrence in Mediterraneantype hotspots or characters reflecting floral symmetry --affected the speciation and extinction rates of clades [START_REF] Fitzjohn | Estimating trait-dependent speciation and extinction rates from incompletely resolved phylogenies[END_REF][START_REF] Fitzjohn | Diversitree : comparative phylogenetic analyses of diversification in R[END_REF].

A complete species-level tree for Proteaceae would be desirable to answer our questions, but it does not exist yet for the entire family. Recent studies have addressed similar questions using well-sampled species-level phylogenies of two large genera of Proteaceae [START_REF] Valente | Diversification of the African genus Protea (Proteaceae) in the Cape biodiversity hotspot and beyond: equal rates in different biomes[END_REF][START_REF] Schnitzler | Causes of plant diversification in the Cape biodiversity hotspot of South Africa[END_REF][START_REF] Cardillo | Evolution of a hotspot genus: geographic variation in speciation and extinction rates in Banksia (Proteaceae)[END_REF]. Interestingly, these studies did not find support for increased diversification rates in Mediterranean-climate hotspots. However, it remains unknown whether their results can be generalized across the entire family. Thus, we chose here to use the genus-level tree of Sauquet et al. (2009) with methods that have been developed to specifically work on such backbones with tips representing large terminally unresolved clades [START_REF] Alfaro | Nine exceptional radiations plus high turnover explain species diversity in jawed vertebrates[END_REF][START_REF] Fitzjohn | Estimating trait-dependent speciation and extinction rates from incompletely resolved phylogenies[END_REF]. These methods analyze rates of speciation and extinction based on a combination of this backbone tree and standing diversity (total number of species) assigned to each terminal taxon. The same methods have recently been used on similar data to study the diversity dynamics of very large clades such as the vertebrates [START_REF] Alfaro | Nine exceptional radiations plus high turnover explain species diversity in jawed vertebrates[END_REF]) and the Malpighiales [START_REF] Xi | Phylogenomics and a posteriori data partitioning resolve the Cretaceous angiosperm radiation Malpighiales[END_REF].

Using the phylogeny of Sauquet et al. (2009) and these recently developed phylogenetic tools [START_REF] Maddison | Estimating a binary character's effect on speciation and extinction[END_REF][START_REF] Alfaro | Nine exceptional radiations plus high turnover explain species diversity in jawed vertebrates[END_REF][START_REF] Fitzjohn | Estimating trait-dependent speciation and extinction rates from incompletely resolved phylogenies[END_REF], we identify shifts in diversification rates in the history of Proteaceae, and analyze if and how the presence in Mediterranean-type regions and floral symmetry have influenced diversification in the family.

MATERIALS AND METHODS

Phylogeny

We used the dated phylogeny (chronogram) obtained by Sauquet et al. (2009), in which all of the Proteaceae genera recognized at that time (79) were represented. Two recently described genera, Lasjia (5 spp.) and Nothorites (1 sp.) (Mast et al. 2008) are not sampled in this tree. This phylogeny was constructed from eight molecular markers (the nuclear ITS and seven plastid markers: atpB, atpB-rbcL, matK, rbcL, rpl16 intron, trnL intron, trnL-trnF) using BEAST [START_REF] Drummond | BEAST: Bayesian evolutionary analysis by sampling 118 trees[END_REF] and 25 phylogenetically analyzed fossil calibration points; the tree was in general very well-supported. Specifically, we used the maximum clade credibility tree with mean ages from the posterior sample of 10 combined runs of BEAST (4 million generations each) as the main chronogram for our core analyses. In addition, we repeated our analyses with 4000 chronograms randomly sampled from this posterior (see below). We pruned all outgroup taxa. Two genera, Protea and Banksia, were represented by three and seven tips in the original tree, respectively. This corresponded to very low sampling fractions given the standing diversity of these two genera. Therefore, we preferred to treat both of them as terminally unresolved clades as we did for the rest of the genera in the tree. Thus, we also pruned two and six tips, respectively, from these two genera so that the final tree used in our analyses had exactly one tip per genus of Proteaceae.

Diversification rate shift analyses

In order to identify major diversification rate shifts, we used the MEDUSA approach of [START_REF] Alfaro | Nine exceptional radiations plus high turnover explain species diversity in jawed vertebrates[END_REF]. MEDUSA is a likelihood-based approach that identifies shifts in diversification and relative extinction rates using a stepwise approach based upon the Akaike Information Criterion (AIC). More specifically, we used the multiMEDUSA function, which applies the MEDUSA algorithm to each tree in a collection of chronograms and draws statistics from these results, such as the number of trees supporting a rate shift at a specific node. Other recently developed methods to detect diversification rate shifts such as the Bayesian approaches implemented in BayesRates and BAMM [START_REF] Silvestro | A Bayesian framework to estimate diversification rates and their variation through time and space[END_REF][START_REF] Rabosky | Automatic detection of key innovations, rate shifts, and diversitydependence on phylogenetic trees[END_REF] would be attractive alternatives to analyze our data but also have limitations. BayesRates does not yet handle higher-level trees where tips represent large clades with known diversity but unknown phylogeny (terminally unresolved clades), such as the genus-level phylogeny used here. On the other hand, BAMM does not yet handle multiple trees and therefore cannot take phylogenetic and dating uncertainty into account. Therefore, MEDUSA was the most suitable approach for our data. MEDUSA now provides the choice between three different models: Yule (pure birth), birth-death, or a mixed model, that is, a model with a combination of both Yule and birth-death processes within the same tree. We chose the birth-death model for our analyses because it is the most biologically appropriate for Proteaceae, but we also generated results with the other two models for comparison. Total numbers of species in each genus are provided in Table II.S1 and were taken from Sauquet et al. (2009). All analyses were performed in R using the multiMEDUSA function from package MEDUSA v0.93 4.33 (https://github.com/josephwb /turboMEDUSA).

Character-dependent analyses

In order to test the effect of Mediterranean-type regions and floral symmetry on diversification, we used the BiSSE (Binary-State Speciation and Extinction) approach of [START_REF] Maddison | Estimating a binary character's effect on speciation and extinction[END_REF]), extended by FitzJohn et al. (2009) to handle terminally unresolved trees, which corresponds to our situation of a tree resolved at the genus rather than at the species level.

For polymorphic genera, the proportion of species in each state was specified (see below). All BiSSE analyses were conducted using the diversitree package in R.

Should the possible states of a given character be named 0 and 1, the rates calculated by BiSSE are λ0 and λ1 (speciation rate of a lineage in state 0 and 1, respectively), µ0 and µ1 (extinction rate of a lineage in state 0 and 1, respectively), and q01 and q10 (transition rate from state 0 to state 1 and from state 1 to state 0, respectively). We fitted by maximum likelihood (ML) eight models of increasing complexity, ranging from a 3-parameter model in which speciation, extinction and transition rates did not depend on the character state (λ0 = λ1, µ0 = µ1, q01 = q10), to a 6-parameter model in which speciation, extinction and transition rates depended on the character state (λ0 ≠ λ1, µ0 ≠ µ1, q01 ≠ q10). We found that, for this data set, different initial parameter values led to different ML estimates of model parameters and, occasionally, a different best model based on AIC scores, suggesting multiple peaks in the likelihood surface.

Hence, we ran the full procedure (i.e., the ML fit of the 8 BiSSE models) multiple times for each analysis and present the results for which the highest maximum likelihood score was obtained. We then selected the best model based on the AIC criterion and ran an MCMC (Markov Chain Monte Carlo) algorithm to generate credibility intervals for the parameter estimates.

By using the BiSSE model, we are restricted to analyzing the effect of a binary trait on diversification, and on character changes happening along the branches of the trees (and not at cladogenetic events). Hence, a character state corresponding to species spanning both Mediterranean hotspots and non-Mediterranean regions cannot be accounted for, nor allopatric speciation, whereby a species spanning both regions would split into two species, one in each region. Other models, such as GeoSSE [START_REF] Goldberg | Phylogenetic inference of reciprocal effects between geographic range evolution and diversification[END_REF] or BiSSE-ness (Magnuson-Ford and Otto 2012) would allow taking such processes into account. However, GeoSSE is not yet implemented for unresolved clades and BiSSE-ness only allows binary traits without overlapping states. In addition, extant Proteaceae species spanning both Mediterranean hotspots and non-Mediterranean regions were rare (less than 10%), and for these species, most of the distribution was either clearly Mediterranean or not. Last, the recently developed Bayesian implementation of BiSSE (Silvestro et al. 2014) could be potentially useful to take into account phylogenetic uncertainty, but this approach cannot yet be applied to phylogenies with terminally unresolved clades such as ours (D. Silvestro, pers. comm.). Hence, the BiSSE model was the most appropriate to deal with our data.

As currently implemented, BiSSE does not accommodate unresolved clades of more than 200 species [START_REF] Fitzjohn | Estimating trait-dependent speciation and extinction rates from incompletely resolved phylogenies[END_REF]), which has proven to be a problem in other studies (e.g., [START_REF] Wiens | Re-evolution of lost mandibular teeth in frogs after more than 200 million years, and re-evaluating Dollo's law[END_REF][START_REF] Mcdaniel | Recurrent evolution of dioecy in bryophytes[END_REF]. This was problematic here for the genus Grevillea, which includes 359 species and for which there is currently no comprehensive phylogeny. Therefore, we used the morphological taxonomic classification of the genus to break this clade into four pseudoclades. [START_REF] Makinson | Flora of Australia volume 17A-Proteaceae 2 Grevillea[END_REF] recognized thirty-three subgroups, some of which were assumed to be more or less closely related to each other based on their morphology. Using these putative relationships, we assembled these subgroups into four clusters: "Grevillea1" (one species), "Grevillea2" (112 species), "Grevillea3" (90 species), and "Grevillea4" (156 species). To approximate a polytomy giving birth to all four clusters, they were arranged in a way so that the clusters diverged from each other early within a short time span (0.5 Ma): (Finschia:11.1947, ((Grevillea1:10.5, Grevillea4:10.5):0.5, (Grevillea2:10.5, Grevillea3:10.5):0.5): 0.1947). Divergence times within Grevillea are actually unknown.

However, the genus is the largest in the family, the majority of its species are in Mediterranean hotspots, and most of its species are zygomorphic (Table II.S1). We therefore chose the short divergence times above specifically to remain conservative with respect to the questions asked in our study. We acknowledge that this strategy might introduce an artificial short burst of diversification, but longer divergence times and therefore younger subclades would result in an even higher artificial increase of diversification rates in Grevillea. We then randomly resolved the relationships among these four clades and tested the robustness of our results to three alternative resolutions differing only in topology (same branch lengths): tree 1 = (Grevillea1, Grevillea4), (Grevillea2, Grevillea3); tree 2 = (Grevillea1, Grevillea2), (Grevillea3, Grevillea4); tree 3 = (Grevillea1, Grevillea3), (Grevillea2, Grevillea4). We also tested a different set of branch lengths in which divergences were more evenly distributed:

( Finschia:11.1947, ((Grevillea1:3.7316, Grevillea4:3.7316): 3.7315, (Grevillea2:3.7316, Grevillea3:3.7316):3.7315):3.7316).

To run the version of BiSSE that handles unresolved terminal clades, we needed the number of species in each state for each tip (here equivalent to a genus). The number of species in each genus that occur within or outside Mediterranean hotspots were taken from Sauquet et al. (2009) and revised for Grevillea based on a thorough review of the data in the Flora of Australia [START_REF] Makinson | Flora of Australia volume 17A-Proteaceae 2 Grevillea[END_REF]. Numbers of hotspot and non-hotspot species in each cluster were compiled using the maps from Flora of Australia and FloraBASE (Western Australia). Species with part of their distribution in SWA and the rest outside of SWA were treated as hotspot species. This gave us a total of 735 non-hotspot species and 1021 hotspot species. These numbers are provided in Table II.S1.

Floral symmetry data were found in the Flora of Australia and other sources for non-Australian species [START_REF] Rebelo | Proteas : A Field Guide to the Proteas of Southeren Africa[END_REF][START_REF] Weston | The Families and Genera of Vascular Plants[END_REF]. These data are also provided in Table II.S1.

Precise data on floral symmetry in the genus Banksia were not available. [START_REF] Weston | The Families and Genera of Vascular Plants[END_REF] stated that both Banksia and the formerly segregate genus Dryandra (now a subgroup of Banksia)

were polymorphic for floral symmetry (i.e., with actinomorphic species and zygomorphic species). As a consequence, Banksia was considered unknown in the general results, but we also tested the impact of assuming different ratios of actinomorphy vs. zygomorphy (100/0, 75/25, 50/50, 25/75, 0/100). This gave us a total of 643 actinomorphic species and 944 zygomorphic species when Banksia was considered unknown (812:944 when Banksia was assumed to be entirely actinomorphic and 1113:643 when Banksia was assumed to be entirely zygomorphic).

There is a possibility that our BiSSE analyses could spuriously identify an effect of the traits of interest on diversification rates when there is none. This could happen if there were heterogeneity in diversification rates across the tree linked to other factors, and if one (or potentially few) large clades coincidentally happened to contain many species with the trait in a given character state. This scenario is most likely to occur in cases with few transitions between character states, which results in a lack of (or pseudo) replication) [START_REF] Maddison | The unsolved challenge to phylogenetic correlation tests for categorical characters[END_REF]. To assess whether our analyses are likely subject to this potential pitfall, we mapped ancestral character states on the phylogeny (see Methods S1 for details). In addition, we carried out "split BiSSE" analyses, which allow different rates on different parts on the tree.

For each of the two studied traits, we conducted five split analyses, each with a "split" at one of the five nodes identified by MEDUSA as supporting a diversification rate shift. This procedure provides the model with an alternative to attributing the rate shifts to the trait of interest.

RESULTS

Our MEDUSA analyses of 4000 timetrees of Proteaceae with the birth-death model identified five to eleven rate shifts per tree, with a peak frequency of seven rate shifts (Fig. II.1).

Five diversification rate shifts were found in more than 50% of trees. Four of these shifts corresponded to an increase in net diversification rate, and one corresponded to a decrease in net diversification rate. MEDUSA analyses with a mixed model (e.g., the possibility of having both Yule and birth-death processes on the same tree) applied to the same set of trees found a number of rate shifts per tree ranging from seven to sixteen, with a peak frequency of 10 rate shifts, and seven shifts supported in more than 50% of trees. Interestingly, the difference between speciation and extinction rates (i.e., the net diversification rate) was found to be positive and significantly higher in Mediterranean hotspots than in other regions, where it was found to be negative (Fig. II.2a). In addition, the transition rate from nonhotspot to hotspot was estimated to be much lower than the hotspot to non-hotspot rate (Table II ). The results of the split BiSSE analyses corresponding to the main part of the tree were consistently similar to those of the main analyses, further supporting our results. The only exception was the analyses with a split at shift 2, which yielded a positive diversification rate instead of a negative one outside hotspots, but it was still less than a tenth of the diversification rate inside hotspots. We choose to not report results for the portions of the tree that were split off, as some results indicate that they may be too small to have decent statistical power.

Applied to floral symmetry, character-dependent analyses also identified the model with all parameters different as the best-supported model, suggesting that speciation and extinction rates differ between actinomorphic and zygomorphic species and that transition rates from/to actinomorphy and zygomorphy are significantly different ( Fig. S1b,d). Specifically, we found speciation and extinction rates to be higher for zygomorphic than actinomorphic species, and transitions to be more frequent from actinomorphy to zygomorphy than from zygomorphy to actinomorphy ( Because data on floral symmetry were missing or ambiguous for the genus Banksia, we initially treated it as unknown for this trait. The results were robust when we tested different ratios of actinomorphic vs. zygomorphic flowers in the genus (Figs. II.S4, S5, S6). Only when treating the entire genus as zygomorphic did we find a (non-significant) tendency for zygomorphic species to have higher net diversification rates than actinomorphic species (Fig. II.S4f). These results were robust to various subclade arrangements within Grevillea (results not shown) as well as when the splits within Grevillea were more evenly distributed (Table II.S6; Fig.

II.S2).

Similarly to the 'hotspot' analyses, the mapping of ancestral symmetry showed that zygomorphy appeared several times in Proteaceae, yielding confidence that the BiSSE results are not spurious (Fig. II.S7). The results of the split BiSSE analyses corresponding to the main part of the tree consistently show the zygomorphic species to have a diversification rate slightly higher than that of actinomorphic species. However, the difference between the two the diversification rates is small and similar to the ML results from the core BiSSE analysis, suggesting that they are not significantly different. We choose to not report results for the portions of the tree that were split off, as some results indicate that they may be too small to have decent statistical power.

DISCUSSION

Proteaceae diversification rates

The estimates of the background net diversification rate for Proteaceae are slightly lower, but similar to those previously reported for the family as a whole (Sauquet et al. 2009).

Diversification rates, however, are not homogeneous across the Proteaceae family (Fig. II.1).

Our analyses of rate shifts confirm results by Sauquet et al. (2009), which showed that some clades within Proteaceae have diversified much faster than others. Previous studies with the MEDUSA model have identified a similar number of significant shifts for clades much larger than Proteaceae. Among angiosperms, 13 diversification rate shifts have been found by [START_REF] Baker | Global biogeography and diversification of palms sheds light on the evolution of tropical lineages. II. Diversification history and origin of regional assemblages[END_REF] for palms (~2500 species) and six among the Malpighiales (~16,000 species) by [START_REF] Xi | Phylogenomics and a posteriori data partitioning resolve the Cretaceous angiosperm radiation Malpighiales[END_REF]. Among Metazoa, [START_REF] Moreau | Testing the museum versus cradle tropical biological diversity hypothesis: phylogeny, diversification, and ancestral biogeographic range evolution of the ants[END_REF] found ten shifts among 12,500 ant species, and the original [START_REF] Alfaro | Nine exceptional radiations plus high turnover explain species diversity in jawed vertebrates[END_REF] study on the approximately 60,000 gnathostome species found nine diversification rate shifts. Many more empirical studies will be required to assess whether there is a scale effect. Indeed, one shift was identified within mammals by [START_REF] Alfaro | Nine exceptional radiations plus high turnover explain species diversity in jawed vertebrates[END_REF] and 11 within the same clade by [START_REF] Rabosky | Clade age and species richness are decoupled across the eukaryotic tree of life[END_REF], but the two studies differed in the number of terminal unresolved clades used to represent the 5,279 mammals (4 and 149, respectively; see also [START_REF] Yu | A comparative study of mammalian diversification pattern[END_REF]. While these previous studies also show that finding several rate shifts is not exceptional, we note that the other known groups in which a similar number of shifts has been found so far have much higher diversity than Proteaceae.

Diversification within versus outside Mediterranean hotspots

Our results confirm that diversification of Proteaceae in the two Mediterranean biodiversity hotspots, the Cape Floristic Region and Southwest Australia, has been higher than in any other area of their wide distribution, as suggested in a previous study (Sauquet et al. 2009). This contradicts the idea that the great species diversity of SWA and the CFR could be the result of long-term accumulation of species rather than increased diversification rates, at least for certain clades [START_REF] Linder | Plant species radiations: where, when, why?[END_REF][START_REF] Schnitzler | Causes of plant diversification in the Cape biodiversity hotspot of South Africa[END_REF]. The character-dependent models we used here [START_REF] Maddison | Estimating a binary character's effect on speciation and extinction[END_REF][START_REF] Fitzjohn | Estimating trait-dependent speciation and extinction rates from incompletely resolved phylogenies[END_REF]) allowed a finer analysis than in Sauquet et al. (2009) in which we could disentangle the effect of Mediterranean-climate regions on both speciation and extinction rates. These analyses suggest that higher net diversification rates in Mediterranean hotspots result from significantly increased speciation rates, but not from decreased extinction rates, which instead appear to have also increased. Interestingly, they also suggest that other regions act as a sink of Proteaceae biodiversity, whereby extinction events exceed speciation events but species also migrate from the hotspots (see below). This is compatible with the observation of many species-poor genera, some of them very old, in tropical regions of the Proteaceae distribution, in particular the Australian Wet Tropics. This would be consistent with a "museum" interpretation of tropical rainforests for Proteaceae, a view also matched by the fossil record [START_REF] Dettmann | The early history of the Proteaceae in Australia: the pollen record[END_REF]. Specifically, negative net diversification rates would explain here why tropical Proteaceae are species-poor, while comparatively lower extinction rates would explain why old lineages of Proteaceae are more common in the Tropics than in Mediterranean hotspots. Last, all of our analyses estimated high relative extinction rates (close to 1), suggesting a high turnover of species during the evolutionary history of Proteaceae, a result at least compatible with the abundant fossil record known for the family. However, these results are to be taken with caution, especially due to the difficulty in accurately estimating extinction rates from molecular phylogenies [START_REF] Rabosky | Extinction rates should not be estimated from molecular phylogenies[END_REF][START_REF] Quental | Diversity dynamics: molecular phylogenies need the fossil record[END_REF]. These results are also conditional on the assumption of constant rates in each region, which might be incorrect if diversification experienced slowdowns, either due to adaptive radiations or other processes, in these new environments [START_REF] Moen | Why does diversification slow down?[END_REF].

Table II.2. Parameter estimates obtained in the BiSSE analysis of the impact of floral symmetry on diversification rates in Proteaceae (mean estimates followed with 95% confidence intervals). r = net diversification rate (λµ); ε = relative extinction rate (µ / λ); q = transition rate. Several factors have been proposed to explain higher net diversification rates of Proteaceae and other plant clades in Mediterranean hotspots, including edaphic specialization, microhabitats, adaptation to fire, and nutrient-poor soils [START_REF] Cowling | Plant diversity in mediterranean-climate regions[END_REF][START_REF] Linder | The radiation of the Cape flora, southern Africa[END_REF][START_REF] Barraclough | What can phylogenetics tell us about speciation in the Cape flora?[END_REF][START_REF] Lambers | Root structure and functioning for efficient acquisition of phosphorus: matching morphological and physiological traits[END_REF][START_REF] Verdú | Burning phylogenies: fire, molecular evolutionary rates, and diversification[END_REF]). However, establishing a causal link between these factors and diversification rates requires the timing of the onset of specific conditions of Mediterranean-climate regions to be consistent with the diversification of taxa in these regions. This question remains open for Proteaceae in general because too few specieslevel phylogenies are available to address it properly, therefore we prefer not to elaborate further on these factors here.

Our results at first glance seem to contradict those of similar analyses performed at a lower taxonomic scale in the South African genus Protea and the Australian genus Banksia [START_REF] Valente | Diversification of the African genus Protea (Proteaceae) in the Cape biodiversity hotspot and beyond: equal rates in different biomes[END_REF][START_REF] Cardillo | Evolution of a hotspot genus: geographic variation in speciation and extinction rates in Banksia (Proteaceae)[END_REF]. Indeed, BiSSE analyses of well-sampled specieslevel phylogenies of both genera revealed no significant differences in diversification rates for Mediterranean-climate lineages compared to other lineages. Two main reasons might explain this apparent contradiction. First, it is possible that the sample size of these two species-level studies is insufficient for detecting an impact on diversification rates with the BiSSE approach even if it existed [START_REF] Davis | Exploring power and parameter estimation of the BiSSE method for analyzing species diversification[END_REF]. In particular, both genera are inferred to have originated in the Mediterranean-climate regions and only one (Protea) and two (Banksia) subclades migrated to other regions, representing 17 (20%) out of 87 and 15 (9%) out of 158 total sampled species, respectively. For comparison, there are 735 (42%) non-hotspot species in Proteaceae and these are more widespread across the family tree than in these two genera (Fig. II.1). It remains uncertain whether the BiSSE approach has the power of detecting the effect of a trait on diversification rates with so few transitions and such small fractions of species in the nonhotspot state. Second, these two genera might represent exceptions to the general pattern seen in Proteaceae. Similar analyses carried out on a densely sampled species-level phylogeny of Proteaceae, when available, will help understand further this apparent contradiction [START_REF] Cardillo | Evolution of a hotspot genus: geographic variation in speciation and extinction rates in Banksia (Proteaceae)[END_REF]).

An interesting result found in our character-dependent analyses is that the mean rate estimated for the transition to a Mediterranean hotspot (q01 = 0.002; CI = 0-0.007) is about ten times lower than the mean rate for the transition to a non-Mediterranean region (q10 = 0.029 ; CI = 0.019-0.041; Table II .1;Fig. II.2c). This result may be due to the nature of prerequisites for moving from an area to the other: it may be easier for a species that is optimized for absorbing nutrients to thrive on a richer soil than it is for a species that usually grows on richer soils to move to poor soils (e.g., [START_REF] Lambers | Phosphorusmobilization ecosystem engineering: the roles of cluster roots and carboxylate exudation in young P-limited ecosystems[END_REF]. This tendency was confirmed in a recent study focusing on the genus Banksia [START_REF] Cardillo | Evolution of a hotspot genus: geographic variation in speciation and extinction rates in Banksia (Proteaceae)[END_REF], in which the authors suspect the more diverse portion of SWA to be a "biodiversity pump" for both its less diverse portion and the non-hotspot parts of Australia. In other words, the situation may closely resemble the biodiversity counterpart to a source-sink dynamic [START_REF] Pulliam | Sources, sinks and population regulation[END_REF]. Most new species would be emerging in the hotspot, but only a fraction of them would be able to last a significant amount of time in the region due to high competition. The non-hotspot regions, on the other hand, would be places where extinction is much more frequent than speciation and in which diversity would be maintained by a flux of species coming from the hotspots. It may seem strange for the nonhotspot regions to be a sink for Proteaceae when it appears that they should thrive in richer soils and less demanding environments. Our results show that extinction is lower outside hotspots, but that the phenomenon is even stronger for speciation, thus resulting in negative diversification. This could be due to Proteaceae having to compete with species that have had a longer time to adapt to non-hotspot environments.

Floral symmetry and diversification

Our results suggest that floral symmetry had no significant impact on Proteaceae net diversification rates, but that transitions from actinomorphy to zygomorphy are more likely to occur (i.e., have a higher rate) than their reversals in the family. Current developmental evidence on the genetic basis of floral symmetry would suggest instead that zygomorphy can be lost more easily than it is gained (e.g., by a single mutation in a CYCLOIDEA-like gene involved in dorsoventral asymmetry; [START_REF] Citerne | The evolution of floral symmetry[END_REF]. Thus, one interpretation of our result is that loss of zygomorphy is sufficiently disadvantageous when it occurs to be counter-selected at the microevolutionary level, perhaps because specialized pollinators would ignore or be less effective on actinomorphic mutant flowers. Nevertheless, our results do support both higher speciation and higher extinction rates for zygomorphic species in the family. Although we note that we should remain careful about interpretation of such analyses in terms of speciation and extinction rather than net diversification (e.g., [START_REF] Leslie | Explaining the distribution of breeding and dispersal syndromes in conifers[END_REF], these results are interesting from a biological point of view. Indeed, increased efficiency in pollen transfer allowed by zygomorphic flowers and increased pollinator specialization may increase speciation rates, but at the same time increased specialization may also make zygomorphic species more vulnerable to extinction.

However, the lack of impact of zygomorphy on net diversification in Proteaceae is inconsistent with the global pattern found by [START_REF] Sargent | Floral symmetry affects speciation rates in angiosperms[END_REF] in angiosperms. It is possible that the balance between speciation and extinction in zygomorphic Proteaceae is different from the one at the scale of angiosperms as a whole. Many Proteaceae species (e.g., Protea and Leucospermum) have zygomorphic flowers densely clustered in actinomorphic inflorescences, which are the primary visual signal to pollinators, making the possession of zygomorphic flowers less relevant than in other zygomorphic angiosperm clades with solitary flowers or loose inflorescences (e.g., Orchidaceae, Fabaceae, Lamiales). One of the characteristics of SWA Proteaceae, which are more diverse than the CFR Proteaceae, is that they are more likely to be pollinated by vertebrates (e.g., birds and mammals; [START_REF] Hopper | The Southwest Australian Floristic Region: evolution and conservation of a global hotspot of biodiversity[END_REF], while the visual and pollen deposition advantages for zygomorphy have only been confirmed with insect pollinators [START_REF] Citerne | The evolution of floral symmetry[END_REF].

Methodological limitations [START_REF] Maddison | Estimating a binary character's effect on speciation and extinction[END_REF] and Maddison and FitzJohn (2014) have noted that the BiSSE method can suffer from pseudoreplication. A character may seem to have an influence on speciation and extinction because it occurs in a clade that underwent a significant increase in diversification rate for reasons unrelated to the given character. This is unlikely to be the case for the two characters studied here, because hotspot as well as zygomorphic species occur in multiple replicates across the tree (Figs. II.S3, S7). In addition, our analyses isolating major shifts have confirmed that none of the clades that have undergone an increase in diversification are singlehandedly responsible for the effects of the two studied characters on diversification (Tables II.S5, II.S6). Finally, the fact that floral symmetry has no effect on net diversification demonstrates that the tree does not have a shape that would make BiSSE conclude that any tested character has an influence on net diversification.

Conclusions and perspectives

We used here a genus-level phylogeny of Proteaceae because a species-level phylogeny of the family is not yet available. Analyses at the species level would show more precise, and potentially different results. For example, diversification shifts found at the root of some genera might instead be identified within these genera; new diversification rate shifts may also be detected (e.g., [START_REF] Yu | A comparative study of mammalian diversification pattern[END_REF]. Thus, similar analyses carried on a detailed species-level phylogeny of Proteaceae, and with other candidate traits potentially influencing diversification, will eventually allow a refined understanding of the factors that have influenced the success of Proteaceae and of particular clades within the family. Still, our study strongly suggests that presence of species in Mediterranean hotspots is associated with higher diversification rates in Proteaceae. There is mounting evidence that diversification rates play a major role in explaining species richness in tropical regions, the predominant hotspots on Earth [START_REF] Pyron | Large-scale phylogenetic analyses reveal the causes of high tropical amphibian diversity[END_REF][START_REF] Rolland | Faster speciation and reduced extinction in the tropics contribute to the Mammalian latitudinal diversity gradient[END_REF]). If our results expand to other taxonomic groups, this would suggest that diversification rates also play a major role in explaining species richness in the second most predominant hotspots, Mediterranean regions.

CHAPTER 2: Perianth symmetry changed at least 199 times in angiosperm evolution

Written by Elisabeth Reyes, Hervé Sauquet and Sophie Nadot. Published in the October 2016 issue of Taxon.

This part of my thesis work was initially intended to test whether zygomorphy was indeed a key innovation in angiosperms. All of the methods available required knowing which portions of the tree included species (or more generally taxa) with a zygomorphic perianth. Existing optimizations of floral symmetry on phylogenetic trees did not provide the needed information, so I decided to produce my own optimization, which became more time consuming than initially planned and transformed into the second chapter of this thesis. The first step hence became to find where zygomorphy had appeared in the angiosperm tree, as well as where it had returned to the ancestral state of actinomorphy (i.e., radial symmetry; Figure I.5). Two of the requirements for this phylogeny were for it to reflect the actual taxonomic diversity of angiosperms and to include as many putative changes in perianth symmetry as possible.

Families in which symmetry was monomorphic could be represented by one species, while families in which perianth symmetry changed between actinomorphic and zygomorphic at least once were represented by the number of species necessary to display all the changes undergone by the family. To keep the amount of work reasonable, polymorphic genera were never represented by more than one species in each state. The starting point of my sampling was the species selection used by Magallón et al. (2015), the most recent dated phylogeny including most of the angiosperm families recognized today and for which most of the morphological data were already in the PROTEUS database due to being part of the eFLOWER project. In the process of building my own species sample, several species were added or deleted from the Magallón tree for various purposes. One of the purposes was to add species from families that were not in the tree, another was to add representatives of the other character state in families that were polymorphic for perianth symmetry and had species representing only one state in the Magallón tree. In other cases, we could not find symmetry data for the species from the Magallón tree, but could find such information for another member of the same family. In such cases, the member for which we had the information on symmetry was preferred, regardless of the presence or absence of molecular sequences in GenBank. Several species from my final sample did not have molecular sequences from closely related species that could be used as surrogates and were the only representatives I could find for some instances of perianth symmetry shifts. In addition, generating new sequences was not part of the objectives of the work for this chapter. Because of this combination of factors, I did not use molecular sequence data to make a chronogram and instead used other methods to build the phylogenetic tree.

To build the tree, we first used the PROTEUS database [START_REF] Sauquet | PROTEUS: A database for recording morphological data and creating NEXUS matrices[END_REF] to output a tree that reflected the relationships among orders, families and sometimes within families, based on the relationships that had been summarized in the Angiosperm Phylogeny Website [START_REF] Stevens | Angiosperm Phylogeny Website[END_REF]) in 2011. Resolution was manually added to some families using recently published studies. The family groupings were from APG III (APG 2009); they are similar enough to those of APG IV (APG 2016) to bring no change in the inferences for this study. The function used for dating the tree requires the user to enter ages for as many nodes as possible, and calculates an estimate of the age of the remaining nodes by evenly distributing them between the pre-dated ones. The user-entered dates used came from the Magallón et al. (2015) tree and were entered for 398 family-level and deeper nodes when nodes were shared between my tree and that of Magallón et al. (2015). Unfortunately, the transition rates reconstructed by maximum likelihood on the tree with branch lengths (dated tree) were extremely high, which resulted in all the nodes having identical state probabilities. We were only able to reconstruct ancestral states with parsimony, a non model-based method insensitive to branch-length. Due to parsimony having the same results regardless of branch lengths, we displayed the results on a non-dated tree. The parsimony results showed a number of changes far superior to those reported in the latest article to have counted them, [START_REF] Citerne | The evolution of floral symmetry[END_REF]. Where the latter had estimated about 70 origins of zygomorphy across angiosperms, I found close to 200 changes, among which at least 130 were origins. The true number of changes might be even higher, as the sampling method used limits the number of changes per genus to one, and some of the larger genera may have more. In addition, methods that take branch lengths into account allow more changes to happen on longer branches, which makes the number of changes found by parsimony likely to be a low estimate (see also the difference between parsimony and maximum likelihood reported in the derivative of the study presented in Chapter 1). I considered this to be an interesting enough result on its own to make an article out of it.

I decided to accompany the tree with a review of various aspects of perianth symmetry, which were to be occasionally linked to the changes I observed. My review of ontogeny showed that perianth zygomorphy could be expressed at various stages in flower development, ranging from sepal initiation to pre-anthesis stages. This stage can vary between closely related clades.

In addition, some species that are actinomorphic at anthesis can have early zygomorphy (during development) while not being closely related to zygomorphic species. These two facts show that the developmental stage at which perianth zygomorphy becomes detectable is a labile trait.

My review of the genetic control behind zygomorphy revealed that all zygomorphic clades in which it has been studied have recruited either CYCLOIDEA or a closely related gene for this control [START_REF] Hileman | Trends in flower symmetry evolution revealed through phylogenetic and developmental genetic advances[END_REF][START_REF] Horn | Analysis of the CYC/TB1 class of TCP transcription factors in basal angiosperms and magnoliids[END_REF]. Through the review of the selective advantages and disadvantages of zygomorphy, I saw that zygomorphy could be a promoter of species diversification or the cause of too extreme specialization that can lead to extinction depending on the group. I also considered the possibility that perianth zygomorphy could be a hitchhiking character state (e.g. a state that tends to appear alongside another trait that is the actual cause of higher diversification) in some clades where it is seemingly correlated with higher diversity.

Perianth symmetry changed at least 199 times in angiosperm evolution

INTRODUCTION

Flowers, the reproductive structures that set angiosperms apart from other land plants, have a relatively conserved groundplan consisting of a short axis bearing, from the center out, ovules protected by carpels, stamens and a perianth [START_REF] Bateman | Morphological and molecular phylogenetic context of the angiosperms: contrasting the "top-down" and "bottom-up" approaches used to infer the likely characteristics of the first flowers[END_REF]. Each of these elements can vary greatly in size, shape, color and number, leading to the diversity seen in extant flowers. Some derived floral traits may be found in many clades among the angiosperms.

One of such recurring traits is perianth zygomorphy, or bilateral symmetry, which may affect the androecium and gynoecium as well. Actinomorphy, or radial symmetry, on the other hand, is considered to be ancestral in angiosperms [START_REF] Endress | Evolutionary diversification of the flowers in angiosperms[END_REF]. Zygomorphic flowers restrict the angle by which a pollinator can approach and move within them, hence making pollen placement on the pollinator more precise and inducing reproductive isolation between flowers that place pollen on different parts of the pollinator's body [START_REF] Sargent | Floral symmetry affects speciation rates in angiosperms[END_REF]).

Some of the most species-rich families, such as Orchidaceae and Fabaceae, include a majority of zygomorphic species. The recurrence of speciose clades in which the majority of species have zygomorphic flowers has led to the widespread idea that zygomorphy in flowers is a key innovation, a trait that has a significant, positive impact on species diversification [START_REF] Hunter | Key innovations and the ecology of macroevolution[END_REF]). However, this conclusion has been reached mostly by comparing sister clades with contrasted floral symmetries [START_REF] Sargent | Floral symmetry affects speciation rates in angiosperms[END_REF], while ignoring other related clades. When considering all angiosperms, it appears that many entirely actinomorphic families are quite speciose while there are zygomorphic families with very few species. Families that include a majority of zygomorphic species, on the other hand, may in fact contain several origins of zygomorphy.

Patterns in the evolution of floral symmetry, in terms of exact number of transitions, still remain incompletely known. The most recent angiosperm-wide survey found a minimum of 70 origins of zygomorphy [START_REF] Citerne | The evolution of floral symmetry[END_REF]. However, understanding of phylogenetic relationships within angiosperms is constantly being improved [START_REF] Moore | Phylogenetic analysis of 83 plastid genes further resolves the early diversification of eudicots[END_REF][START_REF] Soltis | Angiosperm phylogeny: 17 genes, 640 taxa[END_REF][START_REF] Wickett | Phylotranscriptomic analysis of the origin and early diversification of land plants[END_REF][START_REF] Zeng | Resolution of deep angiosperm phylogeny using conserved nuclear genes and estimates of early divergence times[END_REF], enabling patterns of transitions in floral characters to become more and more open for detailed scrutiny.

The main objective of this study was to identify the majority of shifts in floral symmetry throughout angiosperm evolution. To do so, we took an exemplar approach, sampling 761 species chosen to represent all of these transitions as well as all currently recognized angiosperm families. We show with parsimony reconstructions on the latest phylogeny of angiosperms that the total number of transitions to and from zygomorphy is much higher than previously estimated. Using this new landmark reconstruction, we then review current evidence on the developmental control of floral symmetry at the molecular level, the diversity of zygomorphy expression at the morphological level, and the selective advantages and constraints of zygomorphy.

MATERIALS AND METHODS

We used an exemplar approach to record perianth symmetry in a large sample of angiosperm species. Since our purpose was to reconstruct all changes in perianth symmetry across angiosperms, our choice of exemplar species was guided by this particular trait, as explained below. Our focus on the perianth makes this character inapplicable to entirely perianthless families (i.e., those in which all known species lack any kind of perianth part, such as Piperaceae and Ceratophyllaceae), regardless of the symmetry of reproductive organs.

However, we decided to include representatives of such families (scored with missing data) so that all currently recognized families would be sampled. All data were scored in the PROTEUS database [START_REF] Sauquet | PROTEUS: A database for recording morphological data and creating NEXUS matrices[END_REF]. APG III (APG 2009) was followed for order and family delimitations, except where new families have been described and widely accepted since (e.g., the former paraphyletic Olacaceae s.l. that are now seven monophyletic families in Santalales [START_REF] Nickrent | A revised classification of Santalales[END_REF]). For names of all clades above the order level, we followed [START_REF] Cantino | Towards a Phylogenetic Nomenclature of Tracheophyta[END_REF] and [START_REF] Soltis | Angiosperm phylogeny: 17 genes, 640 taxa[END_REF].

Character coding and taxon sampling

It was first necessary to determine which families included zygomorphic species. Both visible differentiation in the shape or size of perianth parts and differential curvature of the perianth were considered forms of zygomorphy, which is defined here as the presence at anthesis of a single plane of perianth symmetry [START_REF] Endress | Symmetry in flowers: diversity and evolution[END_REF]. Following this definition, we included several genera subject to "non-structural" zygomorphy, such as Alstroemeria L. and Thismia Griff. [START_REF] Rudall | Evolution of zygomorphy in monocot flowers : iterative patterns and developmental constraints[END_REF]. It might seem more appropriate to score with different character states the many forms of zygomorphy observed across angiosperms.

However, at present, insufficient developmental and structural data are available to objectively attempt such characterization without assuming that all species of a systematic group follow the same process as those few species that have been investigated more thoroughly. In this study, our goal is instead to highlight the recurrent evolution of the attribute of perianth bilateral symmetry that most botanists easily recognize, without phylogenetically guided assumptions on the genetic and developmental processes that lead to this attribute. By mapping this attribute onto the phylogeny, we can then infer a number of independent origins, which might help guide more research in understanding the processes leading to this functionally important, recurring attribute. This is similar to studies investigating wood vs. herbaceous habit evolution in seed plants, where this trait has been scored as a binary character (e.g. [START_REF] Ricklefs | Species richness within families of flowering plants[END_REF][START_REF] Yang | The F-box gene family is expanded in herbaceous annual plants relative to woody perennial plants[END_REF]Soltis et al. 2013).

As a starting point, we used family-level descriptions from The Families of Flowering Plants (Watson and Dallwitz 2016), and the online Flora of North America, Flora of China and Flora of Pakistan. These sources were only used to score species explicitly cited in them.

Additional sources including morphological studies, taxonomic descriptions and revisions, and other online databases (in total 282) were investigated for families or species not covered by these sources (Appendix III.1). When descriptions did not explicitly mention perianth symmetry, drawings attached to taxonomic descriptions and trusted photos from Encyclopedia of Life (ww.eol.org) were used. For all families presenting no variation in perianth symmetry, we selected and scored a single representative species, chosen from the list of species explicitly listed in the flora. Polymorphic families were sampled so as to include at least one actinomorphic and one zygomorphic species. Available phylogenies for polymorphic families were taken into account so as to represent all transitions to and from zygomorphy in such families (e.g. [START_REF] Knapp | On "various contrivances": pollination, phylogeny and flower form in the Solanaceae[END_REF][START_REF] Reyes | Presence in Mediterranean hotspots affects speciation and extinction rates in Proteaceae[END_REF]. When no phylogeny was available for a polymorphic family, at least two species in each state were sampled as a reminder that multiple changes were possible. Species presenting both actinomorphy and zygomorphy due to sexual dimorphism (e.g. Cissampelos pareira L.) or intra-inflorescence variation (e.g. ray and disc florets of many species of Asteraceae) were scored as polymorphic in PROTEUS, but then rescored as zygomorphic for the present study, as our primary purpose here was to record origins of zygomorphy.

There are two other, rarer types of symmetry in angiosperms: disymmetry (two perpendicular symmetry planes) and asymmetry (no recognizable symmetry). We treated them as missing data in the analyses presented here. In families in which they coexist with other types of symmetry (e.g. Papaveraceae, Begoniaceae, Marcgraviaceae), they were usually ignored.

Marantaceae and Cannaceae (Zingiberales) are entirely asymmetric. Gunneraceae, Halophytaceae and Didiereaceae are disymmetric. Urticaceae and Begoniaceae are each represented by a species in which one sex has a disymmetric perianth, while the other is either actinomorphic (Urtica L., some Begonia L.) or zygomorphic (Begonia); these species are represented by the data of their non-disymmetric sex. Although some authors have described non-zygomorphic Brassicaceae as actinomorphic [START_REF] Hileman | An expanded evolutionary role for flower symmetry genes[END_REF]Busch et al. 2012), careful morphological studies show that they are instead disymmetric [START_REF] Endress | Evolution and floral diversity: the phylogenetic surroundings of Arabidopsis and Antirrhinum[END_REF][START_REF] Patchell | Comparative floral development in Cleomaceae reveals two distinct pathways leading to monosymmetry[END_REF]. We indicate the location of disymmetric Brassicaceae species on our angiosperm tree with missing data to illustrate variation within the family, which is quite frequent. In total, perianth symmetry was recorded for 761 species representing all 61 orders and 426 families of flowering plants.

Phylogenetic tree

The backbone tree used here is the consensus tree from the Angiosperm Phylogeny Website [START_REF] Stevens | Angiosperm Phylogeny Website[END_REF]. It was not possible to build a new molecular phylogenetic tree including all the species from our sample, given available sequence data in GenBank; due to excessive missing data, the resulting tree would have been incomplete and unreliable. An alternative approach would have been to design a study based on available angiosperm-wide dated molecular trees (Sauquet et al. 2015). However, without considerable additional DNA sequencing effort, this approach does not allow us to sample all transitions in a given trait, which was the primary focus of the study presented here. We thus chose to build on the Angiosperm Phylogenetic Website tree topology, and to use recently published phylogenetic studies to resolve within-family relationships where possible (Table . III.S1).

Ancestral state reconstruction

The character state matrix for perianth symmetry was exported from PROTEUS as a NEXUS matrix. Ancestral state reconstruction was performed using parsimony in Mesquite 3.04 (Maddison and Maddison 2015) (Appendix III.2). Polytomies were treated as hard polytomies, in which all branches are treated as having diverged from the same common ancestor. We counted the number of origins of zygomorphy in two ways. The minimum number of origins treats the branches of the tree with equivocal reconstruction as zygomorphic. The maximum number of origins for the tree was found by treating all branches with equivocal reconstruction as actinomorphic.

RESULTS

We found perianth zygomorphy in 30 orders (Fig.

DISCUSSION

Number of origins

The minimum number of origins found in this study ( 130) is much higher than the most recent published estimate [START_REF] Citerne | The evolution of floral symmetry[END_REF] , 2009) to include all recognized families in their analysis and took the possibility of multiple origins within families in account by basing their tree on published phylogenies, and using descriptions covering lower taxonomic levels than family. The present study used a more recent phylogenetic consensus tree for the angiosperms, used a higher number of family-level phylogenies, and counted reversals along with origins, allowing us to detect transitions that so far had been overlooked. We do note, however, that due to the treatment of hard polytomies by Mesquite, that considers each species in a non-ancestral state to be a different origin, the total number of changes may have been slightly overestimated here.

Here, we have used parsimony to reconstruct the number of transitions of floral symmetry in angiosperms. We note that parsimony is more suitable when the rate of change is low and may underestimate the number of transitions when the rate of change is higher [START_REF] Cunningham | Reconstructing ancestral character states: A critical reappraisal[END_REF]. To test how maximum likelihood would impact the results presented here, we built an ultrametric tree using the topology presented here and the bladj function of phylocom v.4.2 [START_REF] Webb | Phylocom: software for the analysis of phylogenetic community structure and trait evolution[END_REF] with node ages drawn from the recent study by Magallón et al. (2015).

However, we obtained unreasonably high transition rate estimates, resulting in complete uncertainty of ancestral states at all nodes of the tree (results not shown) [START_REF] Schluter | Likelihood of ancestor states in adaptive radiation[END_REF][START_REF] Pagel | The maximum likelihood approach to reconstructing ancestral character states of discrete characters on phylogenies[END_REF][START_REF] Hsiang | The origin of snakes: revealing the ecology, behavior, and evolutionary history of early snakes using genomics, phenomics, and the fossil record[END_REF]. We interpret this result as a direct consequence of the sampling bias inherent to the construction of our dataset, which aimed specifically to capture all transitions of the character without sampling clades proportionately to their extant number of species. As a result, our sample built comparatively more contrasts between terminal species than exist in the actual, 300,000-species tree of angiosperms, explaining why transition rates were considerably overestimated in this experiment. These results suggest that inferring the complete scenario of floral symmetry evolution across angiosperms using maximum likelihood will require a substantially larger tree and sample of species than presented here.

Developmental evidence on perianth symmetry evolution

Many studies have addressed the issue of floral symmetry during floral development.

They show that zygomorphy can range from being visible very early in floral development (before stamen initiation; early zygomorphy) to being visible only through the later stages of floral development, after all organs have been initiated (late zygomorphy; reviewed in [START_REF] Tucker | Evolutionary lability of symmetry in early floral development[END_REF].

Early zygomorphy appears to be widespread in angiosperms and can become manifest in various ways. The most commonly reported expression of early zygomorphy is unidirectional initiation of perianth parts: the organs start initiating on one end of the meristem, followed by lateral organs, which are themselves followed by the organs on the side opposite from that of the first organ that initiated. Such initiation has been reported for at least one of the perianth whorls in several superrosid families: papilionoid Fabaceae [START_REF] Tucker | Unidirectional organ initiation in leguminous flowers[END_REF][START_REF] Tucker | Overlapping Organ Initation and Common Primordia in Flowers of Pisum sativum (Leguminosae: Papilionoidae)[END_REF][START_REF] Tucker | Floral ontogeny in Sophoreae (Leguminosae: Papilionoideae): II. Sophora sensu lato (Sophora group)[END_REF][START_REF] Tucker | Development of the cymose inflorescence , cupulum and flower of Psoralea pinnata (Leguminosae: Papilionoideae: Psoraleeae)[END_REF][START_REF] Sampaio | Floral ontogeny of Aeschynomene falcata and A. sensitiva (Leguminosae: Papilionoideae) supports molecular phylogenetic data[END_REF][START_REF] Leite | Floral ontogeny in Dipterygeae (Fabaceae) reveals new insights into one of the earliest branching tribes in papilionoid legumes[END_REF], caesalpinioid Fabaceae [START_REF] Tucker | Unidirectional organ initiation in leguminous flowers[END_REF][START_REF] Tucker | Floral development in Caesalpinia (Leguminosae)[END_REF], Violaceae [START_REF] Mayers | Comparative flower development in the cleistogamous species Viola odorata[END_REF], and Resedaceae [START_REF] Tucker | Evolutionary lability of symmetry in early floral development[END_REF]. This pattern of initiation has also been found in superasterids: Lamiaceae [START_REF] Tucker | Evolutionary lability of symmetry in early floral development[END_REF]Naghiloo, Esmaillou, et al. 2014;[START_REF] Naghiloo | Comparative floral development in the tribe Mentheae (Nepetoideae: Lamiaceae) and its bearing on the evolution of floral patterns in asterids[END_REF][START_REF] Naghiloo | Floral development in Scutellaria pinnatifida (Lamiaceae): the ontogenetic basis for sepal reduction[END_REF],

Orobanchaceae [START_REF] Tucker | Evolutionary lability of symmetry in early floral development[END_REF], Plantaginaceae [START_REF] Bello | Floral morphology and development in Aragoa (Plantaginaceae) and related members of the order Lamiales[END_REF]), Paulowniaceae [START_REF] Erbar | Ontogeny of the flowers in Paulownia tomentosa: a contribution to the recognition of the resurrected monogeneric family Paulowniaceae[END_REF], Calceolariaceae [START_REF] Mayr | Calceolariaceae: floral development and systematic implications[END_REF], Gesneriaceae [START_REF] Haston | Inflorescence and floral development in Streptocarpus and Saintpaulia (Gesneriaceae) with particular reference to the impact of bracteole suppression[END_REF], Asteraceae [START_REF] Dadpour | The development of pistillate and perfect florets in Xeranthemum squarrosum (Asteraceae)[END_REF], Lecythidaceae (Tsou and Mori 2007) and

Caprifoliaceae [START_REF] Roels | A floral ontogenetic study in the Dipsacales[END_REF].

A second pattern of early zygomorphy expression is bidirectional initiation, in which the dorsal and ventral organ(s) are initiated before the lateral ones. Among superrosids, this has been reported for papilionoid Fabaceae [START_REF] Movafeghi | Inflorescence and floral development in Astragalus lagopoides Lam. (Leguminosae: Papilionoideae: Galegeae)[END_REF], Violaceae [START_REF] Mayers | Comparative flower development in the cleistogamous species Viola odorata[END_REF][START_REF] Mayers | Comparative flower development in the cleistogamous species Viola odorata[END_REF]Melianthaceae (Ronse De Craene et al. 2001). This pattern has also been observed in some superasterids: Lamiaceae [START_REF] Naghiloo | Comparative floral development in the tribe Mentheae (Nepetoideae: Lamiaceae) and its bearing on the evolution of floral patterns in asterids[END_REF] and Lecythidaceae (Tsou and Mori 2007). Another initiation order has also been reported, whereby the order of initiation is the exact opposite of that of bidirectional initiation: the lateral organs emerge first, to be followed by the dorsal and ventral organs. To our knowledge, reverse bidirectional initiation so far has only been reported in superasterids, specifically in the corolla of Asteraceae [START_REF] Oraei | Comparative ontogeny of perfect and pistillate florets in Senecio vernalis (Asteraceae)[END_REF]) and the calyx of Balsaminaceae [START_REF] Yu | Floral development in Impatiens chishuiensis (Balsaminaceae): formation of two well-developed anterolateral sepals and four carpels[END_REF].

These modes of initiation can coexist in the same family or even the same species; for example, Viola odorata L. has bidirectional sepal initiation and unidirectional petal initiation [START_REF] Mayers | Comparative flower development in the cleistogamous species Viola odorata[END_REF]. It should be noted that the presence of strictly lateral organs is necessary to make a distinction between unidirectional, bidirectional and reverse bidirectional;

these three modes are essentially the same for trimerous whorls (e.g. the Orchidaceae species described by or tetramerous whorls that initiate organs two by two (e.g. the sepals of Veronica speciosa R.Cunn. ex A.Cunn. as reported by [START_REF] Tucker | Evolutionary lability of symmetry in early floral development[END_REF].

For other species, the first manifestation of zygomorphy appears to be very early differentiation among organs. This has been observed in monocots (Commelinaceae: [START_REF] Hardy | Development of the gametophytes, flower and floral vasculature in Dichosandra thyrsifolia (Commelinaceae)[END_REF][START_REF] Hardy | Floral organogenesis in Plowmanianthus (Commelinaceae)[END_REF] Among families in which we know the stage at which zygomorphy appears, most cases of early zygomorphy are in large families with many known zygomorphic members or which are ancestrally zygomorphic. This applies to Fabaceae [START_REF] Tucker | Floral Evolution, development, and convergence: the hierarchicalsignificance hypothesis[END_REF]. Many occurrences of late zygomorphy tend to be in clades in which symmetry changes frequently, regardless of their apparent ancestral symmetry on our tree. It would be interesting to see if there is any overall tendency in angiosperms for families in which zygomorphy is fixed to have early zygomorphy and families with late zygomorphy to also have labile zygomorphy.

Both "early" and "late" zygomorphy appear to co-exist in some orders such as Lamiales (Lamiaceae: early and late; Bignoniaceae: late; Plantaginaceae: early; Tucker 1999; [START_REF] Bello | Floral morphology and development in Aragoa (Plantaginaceae) and related members of the order Lamiales[END_REF]Naghiloo, Esmaillou, et al. 2014;[START_REF] Naghiloo | Comparative floral development in the tribe Mentheae (Nepetoideae: Lamiaceae) and its bearing on the evolution of floral patterns in asterids[END_REF][START_REF] Naghiloo | Floral development in Scutellaria pinnatifida (Lamiaceae): the ontogenetic basis for sepal reduction[END_REF] and Brassicales (Cleomaceae: early; Brassicaceae: late; Capparaceae: late; Busch and Zachgo 2007; [START_REF] Patchell | Comparative floral development in Cleomaceae reveals two distinct pathways leading to monosymmetry[END_REF][START_REF] Naghiloo | Flower ontogeny in Capparis spinosa (Capparaceae) with special emphasis on symmetry expression[END_REF].

Last, flowers may also be zygomorphic in early development but actinomorphic at maturity. Such "late actinomorphy" has been reported in Nymphaeaceae [START_REF] Endress | Symmetry in flowers: diversity and evolution[END_REF] ). [START_REF] Endress | Symmetry in flowers: diversity and evolution[END_REF] suggested that such early zygomorphy may be due to space constraints and/or the growth of a subtending bract that causes a side of the early floral meristem to have fewer ressources for growth than the other.

Collectively, structural ontogenetic studies of zygomorphic flowers thus suggest that timing of the onset of zygomorphy during development is highly labile across angiosperms.

Although such studies bring critical evidence to better understand the variation of floral symmetry among closely related families, they also suggest that categorization of perianth zygomorphy into distinct, phylogenetically meaningful developmental character states at the angiosperm level is not a straightforward task.

Genetic bases of changes in perianth symmetry

Even Preston et al. 2009). The transitions to zygomorphy in Dipsacales [START_REF] Howarth | Diversification of CYCLOIDEA expression in the evolution of bilateral flower symmetry in Caprifoliaceae and Lonicera (Dipsacales)[END_REF]) and

Asterales [START_REF] Broholm | A TCP domain transcription factor controls flower type specification along the radial axis of the Gerbera (Asteraceae) inflorescence[END_REF][START_REF] Kim | Regulatory genes control a key morphological and ecological trait transferred between species[END_REF], both independent from those in Lamiales (Fig. III.2F and III.2G), also involve CYC-like genes. In rosids, at least three instances of zygomorphy evolution are associated with a CYC-dependent developmental programme (Fig.

III

.3) (Fabaceae: [START_REF] Feng | Control of petal shape and floral zygomorphy in Lotus japonicus[END_REF][START_REF] Zhou | Altered expression patterns of TCP and MYB genes relating to the floral developmental transition from initial zygomorphy to actinomorphy in Bournea (Gesneriaceae)[END_REF], Mapighiales: Zhang et al., 2010, Brassicaceae: Busch et al., 2012). Among the basal eudicots, CYC-like genes have been found

to play a role in the zygomorphy of Papaveraceae in Ranunculales [START_REF] Damerval | Diversity and evolution of CYCLOIDEA-like TCP genes in relation to flower development in Papaveraceae[END_REF][START_REF] Jabbour | Establishment of zygomorphy on an ontogenic spiral and evolution of perianth in the tribe Delphinieae (Ranunculaceae)[END_REF]). Two CYC-like genes were found to co-occur in many species of Proteaceae sampled across the family (Hélène Citerne, pers. comm.). In monocots, the expression of CYC- Aristolochia. However, their enhanced expression in the ventral side of the perianth occurs long after the initiation of the size differentiation between tepals, suggesting that they may not be involved in zygomorphy initiation but rather in the final growth processes in this genus. found [START_REF] Reardon | Different outcomes for the MYB floral symmetry genes DIVARICATA and RADIALIS during the evolution of derived actinomorphy in Plantago[END_REF]. There are also cases in which the flower has a zygomorphic perianth during most of its development and late actinomorphy is caused by a late regulation of the CYC-like paralogue responsible for the zygomorphy, such as in Bournea Oliv. in Gesneriaceae [START_REF] Zhou | Altered expression patterns of TCP and MYB genes relating to the floral developmental transition from initial zygomorphy to actinomorphy in Bournea (Gesneriaceae)[END_REF]. Two different reversals in Malpighiaceae (Fig. III.2C) have either outright lost the expression of both paralogues or maintained both at very low levels [START_REF] Zhang | Divergent genetic mechanisms underlie reversals to radial floral symmetry from diverse zygomorphic flowered ancestors[END_REF]. The interesting element of these systems is that in some of them, the programme inducing zygomorphy is still present (regulated relatively late in Bournea, maintained at very low levels in Malpighiaceae); such systems could account for the secondary origins of zygomorphy within secondarily actinomorphic clades and clades in which floral symmetry is labile.

Spatial distribution of perianth parts in zygomorphic flowers

There is a wide range of possible morphological differences between zygomorphic flowers and their closest actinomorphic relatives. On one extreme of the spectrum, the only or most visible difference is an uneven distribution of perianth parts around the flower. Perianth parts can be attracted either towards one side of the perianth or conspicuously sorted between two opposite sides (dorsal and ventral) of the perianth (Fig. III.4A). The phenomenon is called positional zygomorphy [START_REF] Endress | Symmetry in flowers: diversity and evolution[END_REF], in that the individual parts are identical within each whorl and the perianth would be actinomorphic if they were evenly distributed. In the species closest to this extreme, perianth parts concentrating toward one side of the flower can be found, for example, in some species of Lomatia R. Br. (Proteaceae). Tetramerous flowers can also have a similar arrangement, with three upper and one lower, such as in some species of Clarkia Pursh. (Onagraceae). Sorting between two sides tends to present two upper petals and three lower petals in pentamerous flowers, as in Saponaria L. (Caryophyllaceae). differentiation (e.g., the lower petals of Iberis L., Brassicaceae). In pentamerous flowers, there can be one petal that is different from all the others (Caesalpinia L., Fabaceae; Lonicera L., Caprifoliaceae). Cases in which three of the contiguous petals resemble each other, but are different from the two other petals can be found as well (Lobelia L., Campanulaceae; Saxifraga L., Saxifragaceae). There are also cases in which the dorsal, lateral and ventral sets of perianth parts look distinctly different from each other (Pisum L., Fabaceae; Lamium, Lamiaceae).

Thus, perianth zygomorphy at anthesis may be achieved in various ways, some of them appearing recurrently in distantly related families.

Selective advantages and constraints of zygomorphy

The quasi-absence of zygomorphy in basal angiosperms and its uneven distribution in the clades in which it is frequent may be due to the fact that it can be a selective advantage in some circumstances, but not in others. In this section, we review the advantages given by zygomorphy, but also the factors that can make it an evolutionary dead-end.

Advantages. Zygomorphy has some features that promote outcrossing. hypothesis" for pseudanthia (condensed inflorescences that look like flowers, many of which have peripheral flowers that look like petals). Provided that the inflorescence is rounded and flat-topped, an alternative solution is to have only the peripheral flowers expand into a platform while the others can remain actinomorphic and yet benefit from the pollinator landing on the inflorescence. More biomass tends to be allocated to zygomorphic flowers [START_REF] Herrera | Visibility vs. biomass in flowers: Exploring corolla allocation in Mediterranean entomophilous plants[END_REF], so dedicating the "landing platform" role to a specific part of the inflorescence rather than having each flower have its own could be a better investment of limited resources. We speculate that flower size in relation to the pollinator may also be a factor: inflorescences with flowers that are individually about the same size as their pollinator would probably benefit more from an individual "landing platform", while a platform made only of the inflorescence's marginal flowers could be a better strategy for cases where individual flowers are smaller than the pollinator. This system is found in many Asteraceae, such as Helianthus L. (Fig (2010), but rare cases involve bats [START_REF] Tripp | Is floral specialization an evolutionary dead-end? Pollination system transitions in Ruellia (Acanthaceae)[END_REF], could benefit from having its lower margin smaller than the upper one as it avoids visits from insects (some of which may be nectar thieves) and makes pollination easier for larger pollinators that cannot land on the flower. The oldest known zygomorphic flower fossil (Early Cenozoic) is younger than the earliest known bee fossil (Late Cretaceous) [START_REF] Citerne | The evolution of floral symmetry[END_REF]. This is compatible with the idea that floral zygomorphy only became widespread after the appearance of bees about 123 Ma years ago [START_REF] Cardinal | Bees diversified in the age of eudicots[END_REF]. Zygomorphic flowers are pollinated by bees, butterflies, birds [START_REF] Tripp | Is floral specialization an evolutionary dead-end? Pollination system transitions in Ruellia (Acanthaceae)[END_REF][START_REF] Leins | Flower and fruit: morphology, ontogeny, phylogeny, function and ecology[END_REF][START_REF] Mast | Timecalibrated phylogeny of the woody Australian genus Hakea (Proteaceae) supports multiple origins of insect-pollination among bird-pollinated ancestors[END_REF]), hawkmoths (van der Pijl 1961;[START_REF] Tripp | Is floral specialization an evolutionary dead-end? Pollination system transitions in Ruellia (Acanthaceae)[END_REF] and bats [START_REF] Tripp | Is floral specialization an evolutionary dead-end? Pollination system transitions in Ruellia (Acanthaceae)[END_REF]. The pollination syndromes associated with zygomorphy seem to be flexible in terms of pollinator preferences. For instance, shifts from bird to insect pollination have been documented in both Hakea Schrad. & J.C.Wendl. (Proteaceae; [START_REF] Mast | Timecalibrated phylogeny of the woody Australian genus Hakea (Proteaceae) supports multiple origins of insect-pollination among bird-pollinated ancestors[END_REF] and Ruellia L. (Acanthaceae; [START_REF] Tripp | Is floral specialization an evolutionary dead-end? Pollination system transitions in Ruellia (Acanthaceae)[END_REF]. The opposite transition has also been inferred, for instance in Penstemon (Plantaginaceae; [START_REF] Castellanos | Pollen transfer by hummingbirds and bumblebees, and the divergence of pollination modes in Penstemon[END_REF][START_REF] Castellanos | Anti-bee" and "pro-bird" changes during the evolution of hummingbird pollination in Penstemon flowers[END_REF][START_REF] Wilson | Constrained lability in floral evolution : counting convergent origins of hummingbird pollination in Penstemon and Keckiella[END_REF] and Aquilegia (Ranuculaceae: [START_REF] Whittall | Pollinator shifts drive increasingly long nectar spurs in columbine flowers[END_REF]. In some species, polymorphism in perianth symmetry may be maintained because both morphs present advantages. [START_REF] Gómez | Natural selection on Erysimum mediohispanicum flower shape: insights into the evolution of zygomorphy[END_REF], who focused on Erysimum mediohispanicum Polatschek (Brassicaceae), a species that can be actinomorphic, disymmetric or zygomorphic, found that the actinomorphic and zygomorphic forms were favored in different ways: actinomorphic flowers produced more seeds, but zygomorphic ones were those who produced most offspring. [START_REF] Gómez | Local adaptation and maladaptation to pollinators in a generalist geographic mosaic[END_REF] showed that the same species displayed different types of symmetry depending on the local pollinators.

Constraints. Evolutionary, ecological and developmental constraints can prevent symmetry transitions from happening or make zygomorphy a disadvantageous trait, even though perianth zygomorphy has been proven to promote outcrossing.

In monocots and asterids, zygomorphy and polyandry are almost mutually exclusive [START_REF] Jabbour | Evolutionary trends in the flowers of asteridae: Is polyandry an alternative to zygomorphy?[END_REF][START_REF] Citerne | The evolution of floral symmetry[END_REF], that is, possessing a number of stamens more than twice as large as the perianth merism. One of the reasons for this is that CYC and DICH, while inducing perianth zygomorphy, also inhibit stamen growth [START_REF] Howarth | Phylogenetic analysis of the "ECE" (CYC/TB1) clade reveals duplications predating the core eudicots[END_REF][START_REF] De Craene | Floral diagrams: an aid to understanding flower morphology and evolution[END_REF]. This reduces the chances for perianth zygomorphy to appear in clades that tend to be polyandrous, and zygomorphic flowers from developing many stamens, which prevents adaptation possibilities in both cases.

The fact that zygomorphy limits the pollinators that have access to the flowers can be a disadvantage in itself. The study of [START_REF] Tripp | Is floral specialization an evolutionary dead-end? Pollination system transitions in Ruellia (Acanthaceae)[END_REF] on Ruellia (Acanthaceae) found that some lineages pollinated by bats and hawkmoths were potentially an evolutionary deadend. Extremely specialized plant-pollinator relationships [START_REF] Leins | Flower and fruit: morphology, ontogeny, phylogeny, function and ecology[END_REF] may also be a constraint in that the plant species totally depends on a single species of pollinator for its survival. It is at risk to go extinct should the pollinator go extinct or change its distribution in such a way that it no longer overlaps with that of the plant. Perianth zygomorphy has some advantages in terms of pollination efficiency, but species in which it appears are on the specialist side of the generalist-specialist trade-off. The advantages can last for a given species only as long as compatible pollinators share its environment. If these pollinators move or decline in population density, the strategy-changing possibilities of the plant species are limited because of constraints in the floral shape. This also works the other way around, as some features present in actinomorphic flowers can prevent them from becoming zygomorphic in a context where the latter state could present an advantage.

Symmetry and species diversity

Zygomorphic species are subject to two opposing trends. On the one hand, they favor reproductive isolation via plant-pollinator specialization, and hence favor speciation. On the other hand, specialization may be so extreme that the high dependency on a limited number of pollinators may ultimately lead to extinction. A key question thus becomes the relative effect of these two factors on diversification, and how this effect depends on other clade-specific traits.

This study suggests that Proteaceae (ca. 1700 species) is the family with the highest number of origins of perianth zygomorphy across angiosperms (at least 13: Fig.

III.2B

). In a previous study, we found that perianth zygomorphy does not appear to have an impact on diversification rates in this family, in contrast to climate [START_REF] Reyes | Presence in Mediterranean hotspots affects speciation and extinction rates in Proteaceae[END_REF]. Similarly, [START_REF] Vamosi | Factors influencing diversification in angiosperms: at the crossroads of intrinsic and extrinsic traits[END_REF] showed that having a large distribution area can be more favorable to species richness than floral zygomorphy and other putative key innovations. These studies highlight that some presumed key innovations have no impact on species richness, and suggest that they are "hitchhiking" on other traits that have an impact on species diversification. Furthermore, [START_REF] Maddison | The unsolved challenge to phylogenetic correlation tests for categorical characters[END_REF] and [START_REF] Rabosky | Model inadequacy and mistaken inferences of traitdependent speciation[END_REF] point out that such a hitchhiking phenomenon causes potential problems in interpreting the results of methods that are intended to see if a character state is correlated with species diversification; an effect can be found when there is in reality none. Thus, more work needs to be done that takes into account these potentially confounding factors to further test whether or not zygomorphy may be viewed as a key innovation in angiosperms as a whole [START_REF] Sargent | Floral symmetry affects speciation rates in angiosperms[END_REF]. Our new framework of zygomorphy evolution across angiosperms, including the characterization of multiple origins and reversals within families, is a first step towards more detailed study and tests of zygomorphy-dependent diversification in angiosperms.

Future directions

Here, we have shown that perianth zygomorphy is derived in angiosperms and is a highly Last, it will also be important to test how frequently these origins of floral zygomorphy are associated with higher species diversity across angiosperms, and to look for evolutionary correlates between perianth zygomorphy and other floral traits. Merism is by nature a multistate character, which can be made binary in various ways. I decided to separate species in which pentamery is present (pentamerous) from those in which it is absent (non-pentamerous), as pentamery is the merism most commonly found in angiosperms. My initial species samples were those represented in my symmetry tree from

Chapter 2 and those present in a tree combining all the angiosperm species for which the state of these characters had been entered in PROTEUS, hereafter called the PROTEUS species tree.

To construct the so-called five-character tree, I used the following procedure. I optimized one of the four non-symmetry characters on the tree made with the symmetry species selection and compared it to an optimization on the PROTEUS species tree. For each change in character state that was present in the PROTEUS species tree, but not the symmetry tree, the species necessary to show the changes were added to the symmetry tree, thus making it a tree that showed all the changes for two characters. The third character was then mapped on the twocharacter tree and compared to its mapping on the tree made with the PROTEUS data, with species being added as needed. The procedure was repeated until I arrived to a five-character tree. Once this was done, I checked the character states present in each family against the family-level descriptions for changes that could have been absent from PROTEUS. Species were added to the sample as needed. Species that had data for all five characters were favored during every step. The end sample was made of 1232 species.

APG IV (APG 2016) had recently been published at the time, bringing changes to the circumscription of some of the families; the differences it brought to the optimizations compared to one with the APG III (APG 2009) definitions were fortunately very minor. The bladj function from the Phylocom program [START_REF] Webb | Phylocom: software for the analysis of phylogenetic community structure and trait evolution[END_REF]) enabled me to give branch lengths to my tree; it is the same function as the one used to date the symmetry tree, hence it involves the same process as the one described in the introduction to Chapter 2.

Trying to record all the changes of five characters instead of just one on a single tree proved to have several benefits. The addition of species needed to show the state change in nonsymmetry character breaks branches from the symmetry-only tree. As a consequence, a family with one change in perianth symmetry and many changes in and out of the fused state will be represented with more species in the tree than if sampled based on symmetry only. This changes state distribution and enhances the resolution of ancestral state reconstruction as well. This factor lowered the transition rates estimated by maximum likelihood compared to the symmetry-only tree and allowed me to use it for ancestral state reconstruction taking branch lengths into account.

To evaluate the extent of rate heterogeneity within angiosperms, I compared the rates estimated when the same model applied to the entire angiosperm tree to those that were estimated when different subsections of the tree had a different model applied to them. For this, the tree was divided into five partitions, on which the evolution of all five characters was optimized separately: a basal angiosperm grade (ANA grade and Magnoliidae), I also performed a series of Mk1 constrained rate tests on the full tree on a small logarithmic scale going from 0.0001 changes per Ma (the order of magnitude of the lowest estimated rates from the previous test) to 0.1. Ancestral states were overall insensitive to variations in transition rates, but a minority of nodes had a state that was variable as a function of the transition rate for at least one character. Others were quite visibly approaching the equivocal state probabilities characteristic of extremely high transition rates as the transition rate increased. All nodes had equivocal probabilities when the transition rate was 0.1.

INTRODUCTION

Studying the evolution of morphological characters requires establishing the evolutionary history of organisms. One way to do this is to use a phylogenetic tree of the set of species examined and reconstruct the ancestral states. Maximum likelihood using the continuous-time Markov model [START_REF] Pagel | Detecting correlated evolution on phylogenies: a general method for the comparative analysis of discrete characters[END_REF][START_REF] Pagel | The maximum likelihood approach to reconstructing ancestral character states of discrete characters on phylogenies[END_REF][START_REF] Schluter | Likelihood of ancestor states in adaptive radiation[END_REF][START_REF] Lewis | A likelihood approach to estimating phylogeny from discrete morphological character dat[END_REF]) is one of the most common methods available to reconstruct ancestral states for discrete morphological characters. The method can be used to calculate the probability (proportional marginal likelihood) of each node to be in each state. To do so, instantaneous transition rates among states must first be estimated by finding the set of parameter values that maximize the overall likelihood of the data, given a phylogenetic tree with branch lengths and a distribution of observed values at the tips [START_REF] Schluter | Likelihood of ancestor states in adaptive radiation[END_REF]. However, the transition rate in itself can affect the probabilities of states. One of the main advantages of maximum likelihood over parsimony, which simply infers the minimum number of changes necessary to explain the distribution of tip states, is that it takes into account the time that was available for the character to change. Under low transition rates, the common ancestor of two sister species with the same state will have a high probability of being in the same state as the two sister species and an extremely low probability of being in any other state.

Under higher rates (or longer divergence time between species), the probability of a state change happening between a node and its descendant or tip increases. This leads to increasing probability that node and tip have a different state.

Transition rates on trees using the maximum likelihood approach are conditioned by a given model. Moreover, the estimated rates may be different depending on the size of the tree on which they are assumed to remain homogenous; the larger the tree, the more likely it is that is contains several regions with different "true" transition rates (King and Lee 2015). While transition rates may certainly impact reconstructed ancestral states, it remains unknown to what extent transition rates need vary to have a noticeable impact. However, these issues have so far only been very little explored [START_REF] Beaulieu | Identifying hidden rate changes in the evolution of a binary morphological character: the evolution of plant habit in campanulid Angiosperms[END_REF][START_REF] King | Ancestral state reconstruction, rate heterogeneity, and the evolution of reptile viviparity[END_REF].

Angiosperms, commonly known as flowering plants, comprise an estimated 300,000 extant species. Flowers are the most distinctive attribute of the clade and, despite a wellconserved groundplan, they are remarkably variable. Due to the size of angiosperms, two main approaches have so far been used to study character evolution across the clade: an angiosperm-wide approach with a very limited number of representative taxa sampled from each clade [START_REF] Zanis | Phylogenetic analyses and perianth evolution in basal angiosperms[END_REF][START_REF] Hileman | More is better: the uses of deveopmental genetic data to reconstruct perianth evolution[END_REF] or an examination of smaller clades with more complete sampling [START_REF] Knapp | On "various contrivances": pollination, phylogeny and flower form in the Solanaceae[END_REF]Busch et al. 2012;[START_REF] Reyes | Presence in Mediterranean hotspots affects speciation and extinction rates in Proteaceae[END_REF]Sauquet et al. 2015) The first approach inevitably conceals the true extent to which some characters change across angiosperms. The second approach, while more likely to capture most if not all of the character evolution of the clade of focus, reveals only part of a much bigger picture. One of the factors making both these approaches possible is that the phylogeny of angiosperms is well-known [START_REF] Stevens | Angiosperm Phylogeny Website[END_REF]. This, combined with the existing record of flower morphology, makes angiosperms an ideal framework for reconstructing the evolution of floral characters across the clade and using this framework to evaluate the impact of various assumptions and modifications of the model on reconstructed ancestral states.

Perianth symmetry, fusion, phyllotaxy, pentamery and differentiation are important structural characters of the flower that can be identified and compared across all angiosperms.

Symmetry and fusion both contribute to plant-pollinator specialization by restricting flower access to specific animal pollinators. Phyllotaxy has an important impact on perianth organization, with some floral innovations being possible only on whorled flowers, but not spiral ones. Pentamery is the most frequent merism in angiosperms, for reasons that have yet to be discovered. Differentiation lets different sets of perianth parts specialize in different roles, including the most well-known division between protective but inconspicuous sepals and showy but fragile petals. Because of their functional significance, these characters have received much attention in previous works and they have been suggested as potential key innovations at the scale of angiosperms [START_REF] Sargent | Floral symmetry affects speciation rates in angiosperms[END_REF][START_REF] Endress | Evolutionary diversification of the flowers in angiosperms[END_REF]. Confirming the key innovation status of a given character state (e.g., perianth fusion) requires showing that its origins are correlated with a higher rate of species diversification, which in turn necessitates a clear understanding of where in the tree that state originates. This study focuses on providing the necessary background framework for the evolution of these five perianth characters in angiosperms. Although previous work has clarified some patterns in early-diverging angiosperms using parsimony, we here provide the largest dataset assembled to date to address this question, use maximum likelihood methods, and explore the sensitivity of our results to various assumptions of the models, in particular among-lineage rate constancy.

The first studies of models that took into account the possibility of among-lineage evolutionary rate variation were published in the 1990s [START_REF] Yang | On the use of nucleic acid sequences to infer early branchings in the tree of life[END_REF][START_REF] Galtier | Inferring pattern and process : maximum-likelihood implementation of a nonhomogeneous model of DNA sequence evolution for phylogenetic analysis[END_REF] We previously reconstructed ancestral states for perianth symmetry across all angiosperms, using a 761-species dataset sampling all putative transitions of this character and reconstructing these transitions using parsimony [START_REF] Reyes | Perianth symmetry changed at least 199 times in angiosperm evolution[END_REF]. In this study, we expand the floral symmetry dataset into a new one comprising five floral (perianth) traits recorded in 1232 species of angiosperms, representing all 424 families and 64 orders recognized by APG IV (APG IV, 2016). We use this new dataset to test the impact of various assumptions of models on estimated transition rates and ancestral states. First, we test the impact of symmetric (Mk1) vs. asymmetric (Mk2) rate models on discrete binary character evolution [START_REF] Dunn | Molecular phylogenetics of the Siphonophora (Cnidaria), with implications for the evolution of functional specialization[END_REF][START_REF] Vanderpoorten | Mapping uncertainty and phylogenetic uncertainty in ancestral character state reconstruction: an example in the moss genus Brachytheciastrum[END_REF][START_REF] Webster | Phylogenetic reconstruction and shell evolution of the Diplommatinidae (Gastropoda: Caenogastropoda)[END_REF][START_REF] King | Ancestral state reconstruction, rate heterogeneity, and the evolution of reptile viviparity[END_REF]. Further, we compare both best-fit models and estimated transition rates among five distinct characters in order to measure among-character rate heterogeneity [START_REF] Vanderpoorten | Mapping uncertainty and phylogenetic uncertainty in ancestral character state reconstruction: an example in the moss genus Brachytheciastrum[END_REF][START_REF] Couvreur | Evolution of syncarpy and other morphological characters in African Annonaceae: A posterior mapping approach[END_REF][START_REF] Bc | Evolutionary inferences from phylogenies: A review of methods[END_REF][START_REF] Berv | Molecular phylogenetics and evolution a comprehensive multilocus phylogeny of the Neotropical cotingas (Cotingidae, Aves) with a comparative evolutionary analysis of breeding system and plumage dimorphism and a revised phylogenetic classification[END_REF][START_REF] Zanne | Three keys to the radiation of angiosperms into freezing environments[END_REF]Wright et al. 2016). Last, we test the impact on ancestral state reconstruction of whole-tree rate constancy by relaxing this assumption and allowing five partitions of the angiosperm tree to evolve at their own rates [START_REF] Zanne | Three keys to the radiation of angiosperms into freezing environments[END_REF].

MATERIALS AND METHODS

We recorded five perianth characters (see below) in a large sample of angiosperm species using an exemplar approach. We included at least one species from each currently recognized family (see details below). Families lacking a perianth, such as Piperaceae and Ceratophyllaceae, were treated as missing data, but maintained in our sample in order to present a complete overview of floral trait evolution on mapped phylogenetic trees [START_REF] Reyes | Perianth symmetry changed at least 199 times in angiosperm evolution[END_REF].

All data were scored in the PROTEUS database [START_REF] Sauquet | PROTEUS: A database for recording morphological data and creating NEXUS matrices[END_REF]. APG IV (APG 2016) was followed for order and family delimitations. Higher-level clades above the rank of order follow the definitions given by [START_REF] Cantino | Towards a Phylogenetic Nomenclature of Tracheophyta[END_REF] and [START_REF] Soltis | Angiosperm phylogeny: 17 genes, 640 taxa[END_REF].

Choice of characters

To measure the impact of transition rate heterogeneity on ancestral state reconstruction, we selected five important perianth characters, chosen because of their broad applicability to all flowering plants, their biological significance, and their variability in most larger clades.

Symmetry. Perianth symmetry has two main states: actinomorphy, or radial symmetry, which is ancestral in angiosperms [START_REF] Endress | Evolutionary diversification of the flowers in angiosperms[END_REF][START_REF] Reyes | Perianth symmetry changed at least 199 times in angiosperm evolution[END_REF], and the derived state known as zygomorphy, or bilateral symmetry. Zygomorphy is easy to identify and is found across all major clades of angiosperms [START_REF] Citerne | The evolution of floral symmetry[END_REF][START_REF] Reyes | Perianth symmetry changed at least 199 times in angiosperm evolution[END_REF]. Rare cases of asymmetry and disymmetry are treated here as missing data, as in [START_REF] Reyes | Perianth symmetry changed at least 199 times in angiosperm evolution[END_REF].

Fusion. All floral organs are considered to have been free from each other in early flowers [START_REF] Endress | Evolutionary diversification of the flowers in angiosperms[END_REF]. Sympetaly, the fusion of petals, appears several times across angiosperms and is considered to be a key innovation in Asteridae [START_REF] Endress | Angiosperm floral evolution: morphological developmental framework[END_REF][START_REF] Endress | Evolutionary diversification of the flowers in angiosperms[END_REF]. Here we considered within-whorl fusion for the perianth as a whole, scored on a continuous scale of 0 to 1, and then transformed in PROTEUS as a binary character using a threshold of 5%. This means that flowers with free sepals and petals were scored as 0 and treated here as flowers with a free perianth, while those with entirely fused sepals and petals were scored as 1 and treated here as fused (even if the calyx remained free from the corolla), whereas flowers with, for instance, a fused calyx and a free corolla were scored as 0-1 and treated as polymorphic in PROTEUS.

Phyllotaxy. Phyllotaxy of perianth organs exhibits two main states: whorled and spiral.

Spiral perianth phyllotaxy is much more frequent in basal angiosperms (the ANA grade and Magnoliidae) than in the rest of the group and has been hypothesized to represent an obstacle to floral elaboration (synorganization) that evolved in many whorled flowers [START_REF] Endress | Patterns of floral construction in ontogeny and phylogeny[END_REF][START_REF] Endress | Floral phyllotaxis in basal angiosperms : development and evolution[END_REF]. Some characteristics of spiral flowers have led many authors to consider that it is the ancestral state in angiosperms [START_REF] Arber | The origin of angiosperms[END_REF][START_REF] Endress | Patterns of floral construction in ontogeny and phylogeny[END_REF]Soltis et al. 2000, 2005 and Following initial recording in PROTEUS, the matrix of five characters and 1232 species for this study was exported as a NEXUS file from the database and transformed in Mesquite 3.04 (Maddison and Maddison 2015) in such a way that all polymorphic cells were converted to the presumed derived state. In the case of phyllotaxy, the derived state was assumed to be spiral, as suggested by Bayesian analyses in a currently conducted study (Sauquet et al., unpubl. data). The transformation affected the symmetry state inferred for 22 species, the fusion state for 136 species, the phyllotaxy for seven species, the merism for 102 species and the differentiation state for 13 species. This was done because we were interested in the presence of the derived state rather than whether or not it appeared concurrently with the ancestral state.

All analyses were then conducted again with the original, untransformed matrix (see Appendix IV.7).

Character coding and taxon sampling

Family-level descriptions were used to identify families presenting variation in the studied characters. A total of 661 sources were then used to score the perianth traits of particular species, including a large number of scientific articles, The Families of Flowering Plants (Watson and Dallwitz 2016), and the online Flora of North America, Flora of China and Flora of Pakistan; the last four sources were also those used for family-level descriptions. Drawings linked to taxonomic descriptions and photos from Encyclopedia of Life (ww.eol.org) that had been marked as trusted were used to determine the state of perianth symmetry, merism, differentiation, and fusion when it was not mentioned in the descriptions themselves.

Families that presented no variation in any of the five characters were represented by a single species. For families that were polymorphic for any of the traits, we included as many species as necessary to represent the variation in character states, including multiple transitions and/or reversals, as in our previous study of perianth symmetry [START_REF] Reyes | Perianth symmetry changed at least 199 times in angiosperm evolution[END_REF]). We favored species in which the state of all five characters had been reported in PROTEUS. When no such species were available, we chose a species in which the state of four of the characters were known. If possible, the state of the missing character was informed by the addition of an extra species, with preference for those for which the state of several characters was known. This method resulted in a taxon sample of 1232 species.

Phylogenetic tree

The backbone tree used here is based on the consensus tree from the Angiosperm Phylogeny Website [START_REF] Stevens | Angiosperm Phylogeny Website[END_REF], with the internal phylogenetic structure of families resolved according to the same studies as in Reyes et al. (2016: Appendix II.1). Although it would be desirable to use molecular data to estimate branch lengths, our sampling strategy, designed specifically to capture the most of the variation in the focal perianth traits, did not allow us to do so because many of the species sampled do not have sufficient data in public DNA sequence databases (e.g., GenBank) and it was beyond the scope of this study to generate new sequence data for these species. Therefore, we used an alternative method to approximate branch times for this study. We employed the bladj function of phylocom [START_REF] Webb | Phylocom: software for the analysis of phylogenetic community structure and trait evolution[END_REF]) to transform the consensus tree topology into an ultrametric tree, via constraining 398 nodes defining families and deeper clades (Appendix IV.1) to be the same age as they are in the recent study by Magallón et al. (2015).

Ancestral state reconstruction and transition rate estimation

Ancestral state reconstruction was performed using parsimony and maximum likelihood in Mesquite 3.04 (Maddison and Maddison 2015). We used two models for maximum Ranunculales, Proteales, Trochodendrales, and Buxales), the fourth is Superrosidae (incl.

Dilleniales), and the fifth is Superasteridae. The rationale for including two paraphyletic grades in our tree partitioning scheme is that members of these grades may have inherited ancestral transition rates, while the large clades nested in them may have shifted to distinct evolutionary regimes characterized by different transition rates. Two orders were excluded from all analyses due to a lack of both overall morphological information and state diversity in the characters studied: Ceratophyllales, the perianthless sister order to all Eudicotyledoneae; and Gunnerales, which comprises two families, one (Gunneraceae) that is poorly described and monomorphic in regard to our study characters, another (Myrothamnaceae) that is perianthless.

In practice, we pruned the tree to isolate the taxa from a given partition and performed ancestral state reconstruction on the resulting subtree. The likelihood of a tree-wide model in which each partition has its own rate is proportional to the product of the likelihoods of the model fitting each of the isolated partitions for a given character [START_REF] Zanne | Three keys to the radiation of angiosperms into freezing environments[END_REF]. The Akaike Information Criterion (AIC) was then used to compare the relative fit of the data of the partitioned model to those of the default unpartitioned model.

Finally, we also tested the impact of four arbitrary transition rate values on the inferred character states and their probabilities under the Mk1 model on the full tree. Values for each node were recorded under transition rates (q) of 0.0001, 0.001, 0.01, and 0.1. From tests done for [START_REF] Reyes | Perianth symmetry changed at least 199 times in angiosperm evolution[END_REF], we know that a binary character under a Mk1 model always reaches a 0.5 probability for both states under extremely high rates; we refer to this phenomenon as the high transition rate equilibrium. This equilibrium is possible for all our test nodes under the higher test rates, whether or not the value of the transition rate affects which state is the mostprobable. Because of this, an observed change or absence of change in the most-probable state is the only criterion that we can use to distinguish nodes sensitive to arbitrary change in transition rate from those that are not. If a state was observed to become less probable as the transition rate increased, but never became less probable than the other state, it was considered simply to be converging towards the high transition rate equilibrium.

We also tested for transition rate asymmetry by fitting the Mk1 and the Mk2 models to each trait, both for angiosperms as a whole and for each partition of the tree. The relative fits of the two models were evaluated using the AIC. Further, to compare the relative magnitudes of transition rate asymmetry in Mk2 implementations, we here report on the transition rate symmetry ratio, calculated by dividing the lowest rate by the highest, creating a scale from 0 (unidirectional evolution) to 1 (both rates almost identical, virtually a Mk1 model). In the context of this ratio, "symmetry" is unrelated to perianth symmetry but rather the similarity between the forward and backward rates of Mk2. We also used the AIC to test which arbitrary rate best fitted the evolution of each character.

RESULTS

Rate differences between full tree and partition

We estimated the transition rates on an angiosperm-wide tree using Mk1 and Mk2 models. For each model, one set of estimates corresponds to the entire tree under the same model (which we will refer to as the full tree) while the other corresponds to different models for the five partitions of the tree (which we will refer to as the partitioned tree). The Mk1 transition rates of the five characters, which are plotted on Figure IV.2 for both the full and the partitioned tree, are used here for comparison.

Some partitions have much higher transition rates compared to the full tree version. We excluded unreasonably high rates from the histogram (see below). The [ANA+Magnoliidae] (Chloranthales not mentioned to keep name short in future references to it) and Monocotyledoneae partitions are the most noticeable cases of having a higher transition rate than the full tree: both have a differentiation transition rate close to 0.013, while the character is found to have a transition rate of 0.0042 when optimized on the full tree, suggesting that this trait evolved faster in these two parts of the tree. In contrast, some partition estimates are found to have much lower transition rates than full tree estimates. For instance, pentamery has a transition rate of 0.0001 in Monocotyledoneae, while having a transition rate of 0.0069 at the level of angiosperms.

Five combinations are absent from the graph from Figure IV.2: fusion in

[ANA+Magnoliidae] and Superrosidae (incl. Dilleniales), and symmetry in Monocotyledoneae and basal eudicots, all of which have transition rates so high (0.7-7) that the ancestral states of all nodes examined are equivocal. We interpret these unrealistically high rates as artefacts of ML ancestral state reconstruction due to our sampling approach (see Discussion). In any case, there is no change of perianth phyllotaxy in Monocotyledoneae in our dataset, rendering the inclusion of their estimated Mk1 rate (1.03×10 -10 ) in the histogram irrelevant to the test.

Best-fit tree models

Four out of five full-tree character tree mappings are better fitted by Mk2 than by Mk1 The results for the full tree and the five partitions, both under Mk1 and Mk2, for the 15 key nodes were assembled in Appendix IV.2. Table IV.2 shows the number of nodes that change for each pair of tests under Mk1 vs Mk2 and the full versus partitioned tree. The most frequent changes of most-likely state are between the Mk2 full tree and the Mk2 partitioned tree and between the Mk1 full tree and the Mk2 full tree.

Table IV.2: Number of changes in most-likely estimated ancestral state between models and tree types.

The method used to partition the tree reduced the reconstructable key node number to 13 rather than 15. The nodes that were lost have their names written in italics in 15 nodes (full) 13 nodes (part)

Mk1 (full) ≠ (part) Mk2 (full) ≠ (part) (full) Mk1 ≠ Mk2 (part) Mk1 ≠ Mk2 fusion 1 1 0 0 symmetry 0 0 1 0 phyllotaxy 0 4 5 0 pentamery 0 0 0 0 differentiation 1 4 6 0
The results for the full tree and the five partitions, both under Mk1 and Mk2, for the 54 tested order nodes, were assembled in Appendix IV.3. Table IV.3 shows the number of nodes that change for each pair of tests under Mk1 vs Mk2 and the full versus partitioned tree.

Mk2 (full) ≠ (part) (full) Mk1 ≠ Mk2 (part) Mk1 ≠ Mk2 fusion 1 1 0 0 symmetry 0 2 5 1 phyllotaxy 1 8 7 0 pentamery 0 0 0 0 differentiation 1 12 17 3
It should be noted that in many of the above cases, the order nodes in which fusion and differentiation states change between models are directly descended from key nodes that exhibit a similar behavior. For instance, the only nodes to change fusion state were Superasteridae and Caryophyllales. Concerning differentiation, all key nodes and the vast majority of order nodes that change states between models belong to the three basalmost partitions. This indicates that sensitivity of most-likely states to model changes tends to affect clusters of closely related nodes.

Most states reconstructed by maximum likelihood are identical to those inferred by parsimony. At the key node level (13-15 nodes), there are a few cases of conflict between the two methods: there are three such cases in fusion, one in symmetry, four for phyllotaxy, five for differentiation. For instance, the ancestral state for Superrosidae, Rosidae and Malvidae is fused according to parsimony, but free according to the Mk1 and Mk2 full tree models. At the order node level, there are four cases in fusion (three are orders of Malvidae), four in symmetry, seven in phyllotaxy, one in merism and 13 in differentiation.

Constrained Mk1 rates. All tested nodes for all characters have their high transition rate equilibrium at q = 0.1, suggesting that such a rate of evolution is too high to make any inference on ancestral states in angiosperms. Fusion and differentiation were found to be more sensitive to these arbitrary rate changes than symmetry, phyllotaxy and merism. Table IV.4 summarizes the results for Caryophyllales, as an example of a node subject to change depending on the transition rate. The results for the constrained rates for the 15 key nodes were assembled in Appendix IV.4 and those for the order nodes in Appendix IV.5. we tested intermediate transition rates was observed to become extremely close to 0. The probability of a differentiated perianth presents the pattern of a node that does not change state, with a gradual probability decrease that eventually reaches the high rate equilibrium (0.5) and

does not leave it. The most noticeable difference between the two curves is the slump formed by the fusion curve as the result of going under 0.5, then later converging towards it. In some nodes that kept the same most-probable state from 0.0001 to 0.01, the probabilities followed a pattern that resembled this slump or its mirror image rather than the pattern from the differentiation curve. They are indicated in italics in Appendices IV.4 and IV.5 and treated as nodes suspected to be subject to state change. Tables IV.5 and 6 show how many confirmed and suspected state change nodes are in each set.

DISCUSSION

Here, we have shown that reconstructed ancestral states were robust to the different models we tested. We showed that a change in the most-likely state for a given character was possible from altering transition rates while keeping all other parameters unchanged. We also showed that the probability of a given character state as a function of the Mk1 transition rate could form at least two different types of curves, which always converge towards an equilibrium of 0.5 at high transition rates.

Our choice of focal nodes to evaluate the impact of models and rates in this study consisted entirely of relatively deep nodes in the angiosperm phylogeny tree. While present in the tree, the derived states of the characters tested were sometimes virtually absent from these nodes, indicating that most of the origins of these states took place in clades nested within orders. For instance, our symmetry results show that zygomorphy appeared mostly within orders, consistent with our previous study of this character [START_REF] Reyes | Perianth symmetry changed at least 199 times in angiosperm evolution[END_REF]). Zygomorphy is a potential most-likely ancestral state for only seven orders (Asparagales, Commelinales, Poales, Zingiberales, Boraginales, Lamiales, Solanales) and one deeper key node (Commelinidae). However, some characters behaved differently. Pentamery, for example, appears to have evolved early in the evolution of angiosperms and is reconstructed here as a synapomorphy of Pentapetalae as a whole (with many reversals), which comprises 75% of species diversity.

The model made of five partitions corresponding to five major angiosperm groups was always better fitted to the tree than a single model made to fit a single tree of flowering plants.

A model based on even more tree partitions would probably fit the tree even better, but there would be a trade-off with the size of the partitions; the results could be biased if the partitions are too small. Here, we chose the strict minimum number of tree partitions we considered necessary. Our approach is similar to that used by [START_REF] Zanne | Three keys to the radiation of angiosperms into freezing environments[END_REF], with one version of their model uniform across the tree and the other allowed to have different rates in different subdivisions.

There are four character partitions in which neither Mk1 nor Mk2 is preferred despite a low symmetry ratio. They all correspond to characters for which, in that specific partition, one of the states has very few origins with no reversals, yet the estimated reversal rate is a level of magnitude higher than that of the very low origin rate. We suggest that these high reversal rates are an artifact of ML optimization. Similar artifacts have been observed by us in the present study (phyllotaxy in the Pentapetalae partitions, pentamery in [ANA+Magnoliidae] and Monocotyledoneae respectively), ongoing studies (Sauquet et al., unpubl. data) and previous authors [START_REF] Vanderpoorten | Mapping uncertainty and phylogenetic uncertainty in ancestral character state reconstruction: an example in the moss genus Brachytheciastrum[END_REF][START_REF] Goldberg | On phylogenetic tests of irreversible evolution[END_REF], and appear to emerge when one particular state is rare and asymmetric rates are allowed such as in the Mk2 model.

However, more work is clearly needed on characterizing and finding ways to prevent such reconstruction problems.

The effect of each test varied depending on the character. The differences between the full and partitioned tree under Mk1 and Mk2 only had an impact on fusion in Superasteridae and Caryophyllales, while the constrained rates test affected more nodes (5 key nodes and 8 order nodes). Differentiation was the character with the most nodes that were sensitive to all three means of changing the model. Pentamery was unaffected by Mk model and tree type changes, but an order node changed state under constrained rates. Symmetry and phyllotaxy showed similar sensitivity to all tests and always had many fewer sensitive nodes than differentiation.

In general, when mapping character evolution on the full tree, greater differences between the Mk1 and Mk2 trees were observed than when allowing among-lineage rate heterogeneity (i.e., partitioned tree analyses).

For phyllotaxy, one of the characters the most subject to this phenomenon, we suspect that the results from the ANA+Magnoliidae partition for phyllotaxy may be more accurate than the results of the Mk2 full tree. It may imply that the model that fits the phyllotaxy full tree best, Mk2, may actually be less accurate than the less well supported Mk1. Simulations may be required to confirm this observation. [START_REF] King | Ancestral state reconstruction, rate heterogeneity, and the evolution of reptile viviparity[END_REF] performed their tests on simulated trees, and were able to see if the model that was used to generate the tree would be favored in a model fit test. In doing so, they discovered that the highest likelihood could be found for inaccurate models. The evolution of phyllotaxy in the Mk2 full tree may be a case of an when giving different transition rates to each subdivision of the tree for growth form and habitat climate, had similar transitions rates between Superasteridae and Superrosidae. Such a proximity in transition rates between the two subdivisions was found here for phyllotaxy, pentamery and differentiation. However, Superrosidae have a much higher transition rate between fusion states than Superasteridae and the relation is inverted for symmetry. [START_REF] Wu | Ancestral state reconstruction reveals rampant homoplasy of diagnostic morphological characters in urticaceae, conflicting with current classification schemes[END_REF] mentioned that their maximum likelihood results were sometimes more equivocal than those for parsimony. This may be one of the two situations from Figure IV.4 in which the states probabilities are close to 0.5: the most-probable state change or of the high rate equilibrium. Soltis et al. (2013) found at least one node in which the parsimony inference and the maximum likelihood most-likely state were different. This is probably a case where the rate is high enough for the least parsimonious character to be the most-likely state.

We suspect spiral floral phyllotaxy to be a case of macroevolutionary self-destruction [START_REF] Bromham | Detecting Macroevolutionary Self-Destruction from Phylogenies[END_REF], more specifically the type that causes lower diversification in groups in which it has appeared. Self-destructing traits are characterized by a tendency to be present in several small clades at the tip of the phylogenetic tree. This is true of spiral phyllotaxy, especially in Pentapetalae, where it appears only in a handful of relatively small clades, such as Paeoniaceae family and a subclade of Theaceae. [START_REF] Doyle | Morphological phylogenetic analysis of basal angiosperms: comparison and combination with molecular data[END_REF] concluded that the perianth is free or basally fused in the common ancestor of all angiosperms, which is compatible with the free state found in our study.

Our results regarding phyllotaxy globally agree with the perianth phyllotaxy parsimony Most of our reconstructions find the common ancestor of angiosperms to be whorled. The common ancestor of Laurales is reconstructed as whorled, as in the reconstruction of Zanis et al. (2003). The only model among those we tested that reconstructs both Angiospermae and Laurales as ancestrally spiral, Mk2 fitted to the full tree, also reconstructs that state for the common ancestor of Monocotyledoneae, which do not contain any spiral species.

The larger regions of the tree in which the probability of pentamery is over 0.9 coincide with the origins of pentamery found by Ronse De Craene (2003), by [START_REF] Soltis | Gunnerales are sister to other core eudicots: Implications for the evolution of pentamery[END_REF], by Zanis (2003) full tree, which we will use as the main basis of comparison (see below). The results for fusion and symmetry are similar, with only one node that has a different most-probable state between the two studies for each character; Commelinidae for symmetry (moderate support for zygomorphy instead of strong support for actinomorphy) and Asteridae for fusion (weak support for the fused state rather than strong support for free). The same ancestral states for phyllotaxy and differentiation are found in the two studies. We should note, however, that in the case of phyllotaxy, the ML results of Sauquet et al. (unpubl. data) and ours for Mk2 fulltree both reconstruct the root of angiosperms as spiral, but our partitioned-tree analyses and their Bayesian analyses showed that the root was probably whorled instead. In the case of differentiation, all the reconstruction of Sauquet et al. (unpubl. data) agree on early nodes being undifferentiated, while only our Mk2 full tree for differentiation yielded similar results. The transition rates were much higher in our study (about twice as high) but the symmetry ratios were about the same between comparable characters. The symmetry ratio for fusion was, however, higher here than in Sauquet et al. (unpubl. data).

Conclusion and perspectives

In this study, we found that most ancestral states for deep and more shallow nodes of the angiosperm tree were unaffected by changes in models (number of transition rates in model, value of transition rates, taxonomic scale of the reconstruction). However, we found strong signal for among-lineage rate heterogeneity in perianth evolution, and we observed that accounting for this heterogeneity may influence some reconstructed ancestral states. We also observed that, for the equal-rate (Mk1) model, low rates lead to results most similar to the parsimony optimization, while very high rates lead to complete uncertainty, consistent with the predictions of the Markov model. These factors will need to be taken into account in future studies focusing on ancestral state reconstruction. Figure IV.4 shows the evolution of state probabilities as the Mk1 rate increases. It would be interesting to know how state probabilities evolve as Mk2 rates change. Such a test would have to factor in both the absolute value of the transition rates and their symmetry ratio, which will involve a protocol more complex than the one used to make these observations for Mk1.

GENERAL DISCUSSION

The aim of this thesis was to explore the evolutionary patterns of floral characters and their impact on species diversification. In Chapter 1, I investigated the impact of perianth zygomorphy and presence in Mediterranean hotspots on diversification in Proteaceae. I found one such state, perianth zygomorphy, to not be correlated with any changes in diversification, whereas the presence in Mediterranean hotspots was found to possibly be the source to a macroevolutionary sink [START_REF] Burin | Omnivory in birds is a macroevolutionary sink[END_REF]. In a derivative of that chapter, I optimized perianth symmetry on a species-level phylogeny of Proteaceae, using a maximum likelihood model and showed that there were 16 origins of zygomorphy and six reversals to actinomorphy (See Figure Many evolutionary studies require some degree of prior knowledge of where in the phylogenetic tree and how many times a given character state has appeared. In addition,

candidate key innovations now need to be proven to be recurrently correlated with higher diversity, as they may otherwise be "hitchhiking" on another character that is the actual cause of the higher diversity. The existence of self-destructive states and the possible late start in diversification of clades defined by derived states has made it important to know which state is the ancestral one and which is derived to be able to interpret test results accurately, including in comparisons between sister clades [START_REF] Käfer | Standard sister clade comparison fails when testing derived character states[END_REF][START_REF] Bromham | Detecting Macroevolutionary Self-Destruction from Phylogenies[END_REF]).

The species sampling method used in the second and third chapters, which focused on representing most changes in a character across the whole phylogeny of angiosperms, is somewhat of a novelty and by definition has a higher density of state changes than other sampling methods. The other sampling methods, such as random exemplars and using supraspecific taxa, inherently sample fewer changes in character state than the method I used, but result in character state distributions closer to reality. My trait-dependent exemplar approach will be hereafter referred to as "change-capture". An extensive discussion of the properties I have been able to observe for trees built with this approach is necessary to evaluate their utility for future studies. Below, I will also discuss what seems to be missing to better understand species diversification and other existing studies on angiosperm diversification.

PROPERTIES OF TREES CREATED BY "CHANGE-CAPTURING" TRANSITIONS IN BINARY CHARACTERS

What the reconstructed ancestral states of Proteaceae symmetry tell us

The "change-capture" method is focused on sampling changes in a given character, and hence tends to produce trees with estimated transition rates that, even when low enough not to make the reconstruction identical in all nodes, are overestimated. My first attempt at "changecapture" sampling was done on a single character, perianth symmetry, with the purpose of having at least one species from each family of flowering plants. Maximum likelihood analyses inferred transition rates so high that all nodes were reconstructed as having the same state probabilities between each other, so only a parsimony reconstruction was used (Figure II.2). In Chapter 3 of this thesis, the "change-capture" method was used with five characters, by adding the species that were needed to accommodate the variation of other characters to the symmetrybased tree. I was able to use both parsimony and a maximum likelihood reconstruction that was not subject to a high transition rate induced artifact on that tree. It should be noted, however, that this artifact occurred again in four out of the 25 character and tree partition combinations.

The parsimony reconstructions on these two "change-capture" trees for Proteaceae symmetry suggests that the family was ancestrally actinomorphic with several origins of zygomorphy and occasional reversals to actinomorphy. This pattern is the same as that seen in the genus-level maximum likelihood reconstruction presented in the supplementary material of Chapter 1 (Figure II.S7) and the species-level maximum likelihood reconstruction from Citerne et al.

(2016) (Figure V1). The maximum likelihood symmetry optimizations on the "change-capture" trees, on the other hand, reconstructed Proteaceae as ancestrally zygomorphic. This was the case on both the full angiosperm tree and the basal eudicots partition.

Transition rates estimated by "change capture" are much higher than those estimated in the first eFLOWER paper (H. Sauquet et al., in prep.), which uses random exemplar sampling.

This is probably the cause of the difference in ancestral state reconstruction found between maximum likelihood on the "change-capture" trees and the other Proteaceae reconstructions.

One additional reason why this difference is attributed to overestimated rates is the observation that in the Mk1 constrained rate test from Chapter 3, nodes that could change state depending on the transition rate had the same state as they did in parsimony under low transition rates and had the other state become more probable under higher rates. According to this pattern, the tree

The consequence of overestimated transition rates on other ancestral state reconstructions

The above comparison of the maximum likelihood reconstruction for Chapter 1, Citerne et al. ( 2016) and the Proteaceae selection from Chapter 3 sheds light on the main weakness of the "change-capture" sampling method when ancestral states are reconstructed with maximum likelihood methods. It first seems as if it may be a reliable method as long as one produces a tree in which the estimated transition rates are low enough to avoid creating a reconstruction made entirely of nodes with identical state probabilities. Once that condition is fulfilled, one would simply need to remember to consider the rates on a relative scale rather than an absolute one. However, the constrained transition rate tests done on data used in Chapter 3 show that, even when not high enough to reach the high transition rate equilibrium of state probabilities, the absolute value of the transition rates actually does matter. As shown in Chapter 3, some nodes can have their most-probable state under maximum likelihood change solely from the transition rates being high enough, with all else being equal. The transition rate value needed for this to happen varies greatly among the few nodes that display this pattern. Some of these values are lower than the rates estimated by the first eFLOWER paper (H. Sauquet et al., in prep.) while others are higher. If transition rates are greatly overestimated, the number of statevariable nodes that are past the point at which they change states is artificially increased as well.

This can cause the variable nodes of a "change-capture" phylogeny to have different mostlikely states than an eventual pre-existing tree with character state sampling proportions closer to reality for the clade. On the other hand, this change in most-likely character state only affects nodes in which it can happen, which have been shown to be a minority in the five characters tested in Chapter 3. They are consistently in places in the tree in which the character state is more labile than elsewhere, such as pre-Pentapetalae grades for differentiation in Chapter 3.

The majority of nodes simply keep the same most-probable character state, although even those start converging towards the 0.5 state probability characteristic of the high transition rate equilibrium when constrained rates are high enough. Nodes that don't change state at all or change most-probable states at extremely low transition rates will probably have a consistent most-probable state under most estimated transition rates. In future studies, however, it may be a good idea to conduct some constrained transition rate tests on the nodes of interest and see if one of them has a state affected by transition rates. Nodes in which the most-likely state changes a lot as the transition rate increases will be the ones whose inferred ancestral states will need to be taken with caution in a tree under a given set of estimated transition rates. Such nodes will probably be those most likely to have different states in different studies or simply be interpreted as equivocal. Another solution could be to have the constrained rates test presented as part of the study's results and highlight those that may change according to the inferred transition rate. This could be an alternative to a long MCMC search to measure one aspect of the uncertainty in reconstructed maximum likelihood states.

Impact of the differences in reconstruction model

A similar caution needs to be applied concerning the nodes that can change state between the Mk1 and Mk2 models. In this case, there is the extra complication that relative model fit to the data seems to be a poor indicator of both the accuracy of the reconstruction (King and Lee 2015) and of the extent to which the likelihood reconstruction resembles that from the parsimony analyses. The latter is shown by the fact that both the phyllotaxy and differentiation full-tree reconstructions from Chapter 3 are better fitted by Mk2 than by Mk1. However, the Mk1 reconstruction is the one that resembles parsimony the most for phyllotaxy, while the greatest resemblance is found for Mk2 in the character of differentiation.

In comparison to the maximum likelihood reconstructions, the parsimony reconstructions did not present too many complications and may represent a more suitable use of trees constructed with "change-capture" sampling. It was possible to reconstruct relevant ancestral states on a tree that was built to optimize a single character, as in Chapter 2. While equivocal branches are frequent in these reconstructions, the possibilities they suggested are still far fewer than what is possible via changing likelihood transition rates; the ancestral state probabilities presented in the appendices for Chapter 3 include several nodes that have only one state under parsimony but can have the other possible state be the most-probable one under high enough transition rates. However, the very principle of parsimony, which is to reach the tree's state distribution with as few changes possible, means that using it instead of maximum likelihood is nearly identical to arbitrarily imposing an extremely low transition rate on the tree rather than estimating the value of the transition rate [START_REF] Cunningham | Reconstructing ancestral character states: A critical reappraisal[END_REF]). However, if constrained transition rates are needed for a future study, they can be used on a "change-capture" sampled tree, as their main problem stems from high estimated rates.

Change capture versus sampling of sequenced species

Another element of "change-capture" sampling is that the variation of a given character for a given clade can sometimes only be illustrated by including species in the sampling that have been described but have yet to be sequenced and included in molecular phylogenetic trees.

For any ancestral state reconstruction method that requires a dated tree, including maximum likelihood, there will be a choice between dating via genes at the expense of ignoring some state changes or constructing a tree with all trait changes at the price of using "second-hand" tree dating (with Phylocom, for example). Avoiding this trade-off is possible by generating new sequences for species that are part of their sample but not represented in GenBank. If the dilemma is not avoidable, both solutions have their advantages and drawbacks. Using only species for which molecular data are available will give better support to the phylogenetic tree, but will underestimates the actual number of state changes in the clade. This may seem like a small loss, but doing so may contribute to maintaining in scientific obscurity the very species that would need to be sequenced to make character evolution optimizations more complete.

In summary, "change-capture" is recommended only for those who intend to use parsimony, trace the evolution of several characters, or use constrained transition rates. It is recommended to test the sensitivity of node state to transition rates if a method requiring branch lengths is used. Only using species from GenBank may result in a tree that lacks some of the changes in state, while strictly adhering to a protocol of sampling the character state variation of a clade may require adding species that have yet to be sequenced, which can make "secondhand dating" of the tree necessary to obtain branch lengths.

ELEMENTS MISSING TO UNDERSTAND BETTER THE DIVERSIFICATION OF ANGIOSPERMS

The need for both more floral data and better models

Efforts that need to be made to understand the causal factors that are responsible for driving angiosperm diversification better are on two fronts, both of which are unlikely to reach an ideal situation if kept separate from one another: one is better species sampling and phylogenetic resolution, and the other is the flexibility of models regarding the available species. Methods that link character states to diversification rates exist, but either assume complete sampling and full tree resolution [START_REF] Maddison | Estimating a binary character's effect on speciation and extinction[END_REF] or a limited number of missing species or unresolved clades [START_REF] Alfaro | Nine exceptional radiations plus high turnover explain species diversity in jawed vertebrates[END_REF][START_REF] Fitzjohn | Estimating trait-dependent speciation and extinction rates from incompletely resolved phylogenies[END_REF]). However, approaching complete sampling and resolution is a realistic possibility only for a limited number of clades. The variety of species that can be used for any given phylogenetic study is thus limited by the data accessible on GenBank, their reliability in respect to the published sequences and the accurate identification of the voucher specimen [START_REF] O'meara | Non-equilibrium dynamics and floral trait interactions shape extant angiosperm diversity[END_REF]) and the capacity to generate new data. In addition, availability on GenBank does not necessarily mean that all morphological and environmental characteristics of the species have been described. Obtaining the description of all characters of interest for all known angiosperm species would probably take a virtually infinite amount of time, and may actually be impossible, as species are regularly being discovered or, more rarely, going extinct. The PROTEUS database, which is designed to work towards this target by collecting floral data in a standardized format, is a step in the right direction concerning most of these issues. However, the morphological data that can be added to it must have been recorded in the form of a published flora treatment or scientific paper, which will leave gaps where nothing has been recorded. Filling those gaps will be hindered by determining which aspects of a flower are considered important (or trivial) by the person describing them (see the issue with underreporting below), vocabulary that varies over time or between people working in the same field, and the difficulty of accessing some species.

Because of this, it may take less time and be more efficient to come up with models that are more tolerant of sampling biases and lack of resolution in clades. Another problem with BiSSE is that it loses power if there is high tip ratio bias, which means that it should not be used if one of the states is found in less than 10% of the species in a clade [START_REF] Davis | Exploring power and parameter estimation of the BiSSE method for analyzing species diversification[END_REF]). This prevents it from being used on clades where one of the states is particularly rare. A method is needed that can handle large trees, polytomies, unresolved clades larger than 200 species (the current limit of BiSSE), multiple characters simultaneously (which is currently approximated using MuSSE, see below), missing data, high tip ratio bias, and ideally at least two of these elements at the same time. In addition, "change-capture" sampling might become a more viable method if there were a model that could take its inherent sampling bias into account, as the main problem with using basic maximum likelihood is high estimated transition rates. Such a model could also be of use on trees in which the state distribution is closer to reality but have an extremely labile character optimized on them. [START_REF] Sabath | Dioecy does not consistently accelerate or slow lineage diversification across multiple genera of angiosperms[END_REF], in a study focused on the evolution of dioecy, mentioned the possibility of hermaphroditism being underreported due to it being the most frequent state and hence not always mentioned in descriptions, while dioecy would always (or at least more often) be reported due to its relative rarity. While making an exhaustive list of all articles in which I have observed this phenomenon was not the purpose of my work, I have noticed a similar situation during the character coding phase of this thesis. There were frequent instances of species whose floral symmetry was not mentioned probably because it was actinomorphic, merism not mentioned for Monocotyledoneae (a large majority of which have trimerous flowers) and for Pentapetalae (named after the fact that most of its members are pentamerous), or pollination-oriented flower descriptions that mentioned petals but not sepals, which nevertheless had to be present given the family to which the species belonged. Such omissions, if they were part of the only individual description I could find for the species, ended up being recorded as missing data. This is why I recommend that future descriptions of species contain as many elements noticed by the observer as possible, even those that seem trivial and/or are shared by all related species, as a reader that has never personally observed the species can not otherwise be entirely sure that a given character state is expressed. Conversely, if most but not all species of a group (family, genus etc.) share a common attribute, it is best to specify the exception(s) in the group's description or in individual species descriptions if the latter exist.

New descriptions should be ideally accompanied by images and illustrations, as some elements that get nonetheless omitted by descriptions may be visible to those looking for them.

Developmental studies of flowers in general are also needed, including in families in which a few species have already been studied. Understanding developmental pathways may help understand why some character states with an apparent impact on diversification are transitioned into or out of more often than others.

Other existing approaches

There are several other approaches that aim to find out more about the causes of diversification in angiosperms. This thesis is a branch of the eFLOWER project, the aims of which include reconstructing the morphology of flowers in the deep nodes of the angiosperm tree and finding out which floral innovations are linked with major increases in diversification rates. Its first implementation (H. Sauquet et al., in prep.) uses the tree of Magallón et al. (2015) that was mentioned in Chapter 3 as well as in the present discussion. That tree is based on 792 angiosperms that were sampled from GenBank. Only 374 families (87% of the 424 recognized by APG IV) are represented, but they together account for 99% of angiosperm species. Due to the tree being initially built for the purpose of studying species relationships regardless of character state, the methods of Magallón et al. (2015) were quite close to a version of the species selection method used in this thesis, which gave priority to sequence availability rather than morphological character state availability. The species sampled by Magallón et al. (2015) were chosen in GenBank by giving priority to species that had all five markers used in their study. If there were no species with all five, the marker of a species from the same genus was used as a surrogate, if one was available; my analogue was to add the species with the missing character to the sample. This tree was greatly enhanced by the eFLOWER project via a focus on coding as many character states as possible for the species that were selected for the tree and to use these data to optimize 27 characters on the tree itself. The eFLOWER study on the Magallón tree has four characters that are equivalent to those used in Chapter 3 of this thesis.

For perianth symmetry, phyllotaxy and differentiation, the maximum likelihood transition rates are generally lower in value in the eFLOWER study than those presented in Chapter 3, but the Mk2 symmetry ratios remain extremely close to each other. In the case of perianth fusion, however, the results in Chapter 3 show a higher Mk2 symmetry ratio than in the eFLOWER study. This indicates that the number of character state changes in the eFLOWER study is somewhat proportional to those found in Chapter 3, but the origin to reversal ratio for perianth fusion is lower in the eFLOWER study. In order to include both a member of each family and all the changes in perianth symmetry, I was able to find that, for Chapter 2 of this thesis, a set of 761 species was required, which is less than what was used for the Magallón tree. Adding four other perianth characters brought the sample to 1232 species. The only elements of this thesis that can be directly compared to those of the eFLOWER study are the parsimony and maximum likelihood full-tree optimizations for perianth fusion, symmetry, phyllotaxy and differentiation. The two studies otherwise use different approaches to taking rate heterogeneity and most-probable state uncertainty into account. In the case of perianth phyllotaxy, the eFLOWER study took rate heterogeneity into account via the use of a tree from which core monocots and core eudicots had been removed. This differs from the way partitions were done in Chapter 3, but gives the same ancestral state results as the ANA+Magnoliidae and basal eudicots partitions. In addition, the eFLOWER study takes phylogenetic uncertainty into account, whereas we do not, and it tests many more models while Chapter 3 included many more state transitions.

O'Meara et al. ( 2016) used another approach to studying character evolution. They selected 500 species first by calculating the proportion of the angiosperm species represented by each family, then had members of that family represent the same proportion in their sample.

After this, they selected the required number of species among the members of that family that had at least the ITS marker sequenced. These species were scored for six floral characters:

presence of petals, fusion of perianth parts, flower symmetry, number of stamens compared to perianth parts, carpel fusion, and ovary position. The 500 species set was reduced to 464 that covered 134 angiosperm families (31% of the total) because they could not score the character state for some species. The lack of missing data in the species retained enabled them to use MuSSE (FitzJohn 2012), a counterpart to BiSSE intended for multistate characters or combinations of binary characters. This latter variant was used to test the influence of combinations of the states of several characters by treating each combination as a different state of a single character; for example, a combination of two binary characters can be divided in four states that represent 00, 01, 10 and 11, respectively. They found that all combinations that included the presence of a corolla, a zygomorphic flower, and a small number of stamens diversified faster than the rest, but had a low origination rate. One of the problems of this method is an extremely low sampling fraction, which excludes most families that have less than 500 species.

In [START_REF] Soltis | Phylogeny and evolution of angiosperms[END_REF] In summary, there is need for a continued effort of DNA sampling and assembling as exhaustive as possible species descriptions of flowers to know the characteristics of as many species as possible. However, it is impossible to do this for every single angiosperm species, so new macroevolutionary analytical models that can account for and accommodate gaps in data need to be developed in the meantime. There are other studies seeking more information about the causes of character diversification, each with their strengths and weaknesses compared to this thesis.

I first went through the process of testing whether two character states were key innovations in the Proteaceae family. I found floral zygomorphy not to have any impact on diversification and presence in Mediterranean hotspots to be the source to a macroevolutionary sink. I also came to the conclusion that perianth zygomorphy is not a key innovation in the family, contrary to what seems to be the case in other families, such as Orchidaceae and Fabaceae; these families are two of the most species-rich among the angiosperms.

I found that my "change-capture" sampling method generates maximum likelihood transition rates too high to give conclusive ancestral state reconstruction results when used with a single character. This makes the use of parsimony a necessity for ancestral state reconstruction with this sampling strategy. The parsimony results showed that perianth symmetry was an extremely labile character. I found that perianth zygomorphy could contribute both to higher species diversification and species specialization, which can lead to extinction if the niche into which species were specialized disappears.

Chapter 3 showed that there was high transition rate heterogeneity among the five partitions into which I divided the angiosperms. It showed that using the "change-capturing" method on several characters instead of one could lead to transition rates that are lower than with only a single character, but possibly still high enough to produce biased results. The chapter also showed that diversification rates could have an impact on inferred diversification state and that this influence was strong enough to change the most-probable state of a node between a model adapted to the entire angiosperm tree and a model adapted to a partition of the tree.

Taken together, these chapters and my contribution to the article published by [START_REF] Citerne | Characterization of CYCLOIDEA-like genes in Proteaceae, a basal eudicot family with multiple shifts in floral symmetry[END_REF] show that there are several ways to sample species and several ways to reconstruct ancestral states. Combination of these factors can lead to a large variety of possible ancestral state reconstruction results in nodes that can have different states depending on the sampling method and ancestral state reconstruction method. Choices made in sampling methods will depend on what aspect of morphological evolution a study aims to put forward. One of the reasons these choices have to be made is that the ideal situation for studying floral morphology evolution, in which all angiosperm species are described and sequenced, is unlikely to happen, at least in the near future. However, we need to continue getting as close to it as we can, as some little-known species or clades can potentially hold important information for floral evolution. After all, the basalmost known order and family of angiosperms consists of a single species, Amborella trichopoda. Its existence is the main reason why the root state is ambiguous in parsimony reconstructions of perianth phyllotaxy of angiosperms; without this species, the basalmost angiosperm order would be interpreted to be the whorled Nymphaeales, sister to the spiral Austrobaileyales and all other angiosperms. Building models that can account for various forms of biased sampling is necessary as well, as the content of GenBank and scientific literature as a whole is likely to remain biased for a very long time compared to what actually exists in nature. This thesis will hopefully help with future angiosperm diversification studies by providing a record of the clades in which each state is present and describing the properties of trees made with change-capture sampling.

Some of the ancestral state reconstruction for this thesis may be the first step of a study using the method of [START_REF] Käfer | Standard sister clade comparison fails when testing derived character states[END_REF] of sister clade comparisons, as the method does not require clade resolution and attaches great importance to which of two character states displayed by sister clades is ancestral or derived. Interestingly, this method sums up two partially conflicting ideas of the level of phylogenetic resolution that is necessary to study character evolution. The need of two distinct sister clades points towards the need to resolve the phylogenetic tree as much as we can, because making such analyses on shallow clades will require resolving them to some extent. The lack of need for internal clade resolution, on the other hand, shows that the ideal situation in which the relationships of every single species to each other is known may not be strictly necessary to clarify the evolutionary history of some characters. These two aspects cohabitate via the fact that many large clades are still unresolved and even well-supported deeper nodes are not considered completely certain, thus making any model that can handle unresolved clades or take phylogenetic uncertainty into account extremely useful. Meanwhile, a level of phylogenetic certainty, in the form of largely accepted relationships represented by these very same deeper nodes, keeps the character evolution optimizations from becoming completely irrelevant. However, what constitutes a sufficient level of phylogenetic resolution to reconstruct most of the evolutionary history of an infrequently evolving character may not be sufficient for a more labile one. In addition, the need to detect both key innovations and self-destructive character states may involve demonstrating the existence of extremely small clades defined by the latter. Because of this, character evolution will certainly continue, for a long time, to be one of the drivers of further phylogenetic resolution.

However, there are other factors besides floral character evolution that potentially contribute to angiosperm diversification. Non-floral characters, environmental factors, genomics, evo-devo and paleobotany could hold some of these answers as well.

Extinction rate

Probability density mu0 mu1

(a) colored according to the highest probability state of the corresponding node. Terminal pie charts represent the actual proportion of species in each state in each terminal taxon. However, these proportions could not be taken into account explicitly in the model used for this reconstruction (see Methods S1), which is instead based on the most common state scored for each polymorphic terminal taxon. The analysis with polymorphic terminal taxa scored as missing data yielded essentially the same character reconstruction (results not shown). Beauprea 13 13 0 13 0 Table II.S4. Parameter estimates obtained in the BiSSE analysis of the impact of floral symmetry on diversification rates in Proteaceae when a third of the diversification time passes between each split of Grevillea (mean estimates followed with 95% confidence intervals). r = net diversification rate (λ -µ); ε = relative extinction rate (µ / λ); q = transition rate. [START_REF] Su | Phylogenetic placement of two enigmatic genera, Borthwickia and Stixis, based on molecular and pollen data, and the description of a new family of Brassicales, Borthwickiaceae[END_REF] Brassicaceae+Cleomaceae+Capparaceae [START_REF] Hall | Phylogeny of Capparaceae and Brassicaceae based on chloroplast sequence data[END_REF][START_REF] Warwick | Closing the gaps: Phylogenetic relationships in the Brassicaceae based on DNA sequence data of nuclear ribosomal ITS region[END_REF]Busch et al. 2012;[START_REF] Patchell | Resolved phylogeny of Cleomaceae based on all three genomes[END_REF][START_REF] Hohmann | A time-calibrated road map of Brassicaceae species radiation and evolutionary history[END_REF]

(d) (c) (b) 0.8 1.
Beaupreopsis 1 1 0 0 Bellendena 1 1 0 0 Bleasdalea 2 2 0 2 Brabejum 1 0 1 0 Buckinghamia 2 2 0 2 Cardwellia 1 1 0 1 Carnarvonia 1 1 0 0 Catalepidia 1 1 0 0 Cenarrhenes 1 1 0 0 Conospermum 53 10 43 53 Darlingia 2 2 0 0 Diastella 7 0 7 0 Dilobeia 2 2 0 0 Eidothea 2 2 0 0 Embothrium 1 1 0 1 Eucarpha 2 2 0 0 Euplassa 20 20 0 20 Faurea 15 14 1 15 Finschia 3 3 0 3 Floydia 1 1 0 0 Franklandia 2 0 2 0 Garnieria 1 1 0 0 Gevuina 1 1 0 1 Grevillea1 1 0 1 1 Grevillea2

Reversals (min-max) Species

Families not assigned to order Appendix IV.7 : Results and discussion for original data.

Boraginaceae

Full tree and partitions under Mk1 and Mk2. When compared with the rescored data, fusion and pentamery are both more prone to give different results between reconstructions. These characters are the ones with the largest number of species that have states affected by rescoring. The nodes in which there are difference between the two type of data tend to be ancestors of clades in which there are several rescored species. As in the rescored results, the most frequently fond difference in inferred state are between the Mk2 full and partitioned trees and the MK1 and Mk2 full trees. One of the differences compared to the rescored data is a more frequent occurrence of differences between the Mk1 and Mk2 partitioned trees. Most inferred states are identical to those inferred by parsimony or can be both states according to parsimony. At key node level (13-15 nodes), nodes in which at least one of the maximum likelihood estimates does not match the parsimony state are four in fusion, one in symmetry, five in phyllotaxy, four in pentamery, four in differentiation. This is a few more than with rescored data, but still in the same order of magnitude. At order node level (54 nodes) mismatch between parsimony and at least one of the tested maximum likelihood inferred states are five in fusion, four in symmetry, six in phyllotaxy, three in pentamery and 13 in differentiation. This is a higher but close total number than in the rescored data as well.

Constrained Mk1 rates. At key node level, only differentiation has nodes that change most probable states depending on transition rates (Table IV All the fusion nodes suspected to be state-changing with the rescored data show a what seems to be a simple probability decrease pattern with the original data. The state-changing node numbers for symmetry, phyllotaxy and differentiation remain the same and are the same nodes as in the rescored data.

Original and rescored data. When comparing the original and rescored versions of the Mk1 and Mk2 full and partitioned trees, the differences between the two are rare. They are the most frequently found in fusion and pentamery. The nodes that display differences tend to be ancestors of clades in which there are several rescored species. The Mk2 partitioned tree has the most frequent difference between the original data and the rescored data. Abstract: Angiosperms are a clade known for its great species diversity and the uneven distribution of this diversity among its lineages. This work focuses on the ancestral state reconstruction of floral characters on phylogenies in the purpose of studying their impact on diversification. We first focused on two potential key innovations in Proteaceae, bilateral perianth symmetry and presence in Mediterranean-climate hotspots. Using character state dependent diversification models, we found that the first character state did not have any significant impact on species diversification in this group, contrary to the second one. We then reconstructed ancestral states for perianth symmetry in angiosperms as a whole, using a sampling strategy aimed at capturing all of the transitions in this character. We found a minimum of 130 origins of bilateral symmetry, followed by 69 subsequent reversals to radial symmetry. Lastly, the same approach was extended to the study of four other perianth characters. Different ancestral state reconstruction models were used on a phylogenetic tree of 1232 species to test the influence of model changes on reconstructed ancestral states. Our results show that changes in reconstruction models have an impact on the inferred ancestral state of some nodes, but not all of them. The various results obtained for symmetry, a character shared among the three chapters, indicate that our sampling method has the drawback of estimating transition rates too high to give conclusive results with maximum likelihood. On the other hand, results are much less biased when several characters are examined simultaneously.

Figure I. 1 :

 1 Figure I.1: Examples of the variation in flower and inflorescence form. From upper left to lower right: Row 1, Anagallis arvensis (Primulaceae), Eucryphia cordifolia (Cunoniaceae), Alisma plantago-aquatica (Alismataceae), Stellaria holostea (Caryophyllaceae), Mimulus luteus (Phrymaceae), Dactylorhiza maculata (Orchidaceae) Lotus corniculatus (Fabaceae), Row 2, Beta vulgaris (Amaranthaceae), Akebia quinata (Lardizabalaceae), Butomus umbellatus (Butomaceae), Brugmansia sanguinea (Solanaceae), Hyacinthoides non-scripta (Asparagaceae) Arbutus unedo (Ericaceae), Cypripedium calceolus (Orchidaceae), Row 3, Leucanthemum vulgare (Asteraceae), Plantago lanceolata (Plantaginaceae), Anthoxanthum odoratum (Poaceae), Piper excelsum (Piperaceae), Isopogon anemonifolius (Proteaceae), Ficaria verna (Ranunculaceae), Nymphaea sp. (Nymphaeaceae). Photos by Hervé Sauquet.

Figure I. 2 :

 2 Figure I.2: Histogram of species diversity per family across angiosperms.

Figure I. 3 :

 3 Figure I.3: Phylogenetic tree of angiosperms showing relationships among orders (Figure 1 from: Endress PK. 2011. Evolutionary diversification of the flowers in angiosperms. American Journal of Botany 98(3): 370-396). Numbers are red when the corresponding trait is a potential key innovation in the clade, black when it appears without having the consequences expected of a key innovation. Reproduced with permission.

Figure I. 4 :

 4 Figure I.4: Three scenarios of ancestral state reconstruction and how they tend to be interpreted. The ancestral state is blue in the left-hand scenario, brown in the middle scenario, blue or brown in the right-hand scenario.

Figure I. 5 :

 5 Figure I.5: Characters optimized in Chapter 3 and the states in which they were divided. The state colored in blue is the hypothesized ancestral state while the derived one is colored in red.

Figure I. 6 :

 6 Figure I.6: Species of Proteaceae with zygomorphic flowers: Adenanthos sericeus, Triunia montana and Lomatia ferruginea. Photos by Hervé Sauquet.

  .1; Fig. II.2c). These results were robust to various subclade arrangements within Grevillea (results not shown) as well as when the splits within Grevillea were more evenly distributed (Table II. S3; Fig. II.S2). The mapping of ancestral states shows that the 'hotspot' and 'nonhotspot' states are not located in one single or a few clades, suggesting that our results are likely not a spurious outcome of pseudoreplication (Fig. II.S3

Figure II. 1 .

 1 Figure II. 1. (a) Genus level time-calibrated phylogenetic tree of Proteaceae from Sauquet et al. (2009), with significant shifts in diversification rates obtained from the multiMEDUSA analysis of 4000 trees randomly sampled from the BEAST posterior. The numbers of extant species in each genus are indicated in parentheses. Node pie charts indicate the proportion of trees in which a significant shift was detected at the node, for the 17 nodes where a shift was detected in at least 5% of the trees. Terminal pie charts represent the proportion of species (magenta) in each state for the two traits of interest considered in the character-dependent analyses (Hot = proportion of species in Mediterranean-climate regions; Zyg = proportion of zygomorphic species). (b) Distribution of the number of rate shifts detected across the sample of trees. (c) Distributions of the magnitude (difference in net diversification rate) of the rate shifts for each of the five most recurrent shifts (identified with the same node numbers as on the tree). Colors indicate whether the shift corresponds to an increase (red) or a decrease (blue) in net diversification rate. Percentages specify the proportion of trees concerned.

Figure II. 2 .

 2 Figure II.2. Parameter estimates obtained for the best BiSSE models selected for each trait of interest. (a,c) Presence in Mediterranean climate regions (red) vs. other regions (blue). (b,d) Floral zygomorphy (red) vs. actinomorphy (blue), assuming Banksia is unknown for this trait. (a,b) Net diversification rates. (c,d) Transition rates. Additional parameter estimates for these analyses are illustrated in Supporting Information (Figs. II.S1, S4).

Fig. II. 1 .

 1 Fig. II.1. Order-level phylogeny of angiosperms based on the Angiosperm Phylogeny Website (Stevens, 2001-) highlighting all orders in which perianth zygomorphy evolved. For each order with zygomorphy, we indicate the number of origins followed by the number of reversals in the minimum origins scenario. Ordinal and supra-ordinal names follow APG III (2009) and Cantino et al. (2007), respectively.

Fig. II. 2 .

 2 Fig. II.2. A, Basal angiosperms (including magnoliids), monocots excluding Commelinidae; B, Commelinidae, basal eudicots; C, basal superrosids; D, Malvidae; E, Basal superasterids; F, Campanulidae; G, Lamiidae. The order names are transcribed without the "ales" suffix.

  , basal eudicots (Proteaceae: Douglas 1997), superrosids (Moringaceae: Olson 2003; Cleomaceae: Patchell et al. 2011), and superasterids (Asteraceae: Harris 1995; Ren and Guo 2015). In other cases, zygomorphy is due to a missing perianth part, which either was suppressed very early or did not emerge at all (Asteraceae: Harris 1995; Sapindaceae: Ronse De Craene et al. 2000; Menispermaceae: Meng et al. 2012). Late zygomorphy also appears to be widely distributed in angiosperms. It has been observed in basal eudicots (Ranunculaceae: Tucker 1999; Jabbour et al. 2009; Papaveraceae: Damerval et al. 2013), superrosids (Fabaceae, Polygalaceae: Tucker 1999; Tropaeolaceae: Ronse De Craene and Smets 2001; Brassicaceae: Busch and Zachgo 2007; Capparaceae: Naghiloo, Fathollahi, et al. 2015) and superasterids (Asteraceae: Harris 1995; Bignoniaceae, Lamiaceae: Tucker 1999). The symmetry of the flower may also vary throughout development, as observed in Couroupita Aubl. and Cariniana Casar., two of the basalmost zygomorphic genera of Lecythidaceae (superasterids): both are zygomorphic at calyx initiation, go through an actinomorphic (Endress 1999)/disymmetric (Tsou and Mori 2007) phase, then become zygomorphic again.

  , monocots (Potamogetonaceae:[START_REF] Poslusny | Floral development of Potamogeton richardsonii[END_REF] Xanthorrhoeaceae, Melanthiaceae, Araceae: Endress 1999), basal eudicots (Trochodendraceae: Endress 1999), superrosids (Cistaceae[START_REF] Nandi | Floral development and systematics of Cistaceae[END_REF] Saxifragaceae: Ronse De Craene et al., 1998), and superasterids (Adoxaceae: Endress 1999; Plantaginaceae:[START_REF] Bello | Floral morphology and development in Aragoa (Plantaginaceae) and related members of the order Lamiales[END_REF] Lecythidaceae: Tsou and Mori, 2007; Gesneriaceae: Zhou et al., 2008). The relatedness of these species to species that are zygomorphic at anthesis varies greatly. Those of Plantaginaceae, Gesneriaceae and Lecythidaceae are more or less nested in zygomorphic clades, making them potential (Lecythidaceae: Fig. III.2E) or certain (Plantaginaceae and Gesneriaceae: Fig. III.2G) reversals. Those of Adoxaceae, Saxifragaceae and Xanthorrhoeaceae are in a clade that is ancestrally actinomorphic on our tree but have zygomorphic species as relatives within the same family (Saxifragaceae and Xanthorrhoeaceae: Figs. III.2A and III.2C), the same order (Potamogetonaceae: Fig. III.2A) or a sister order (Adoxaceae: Fig. III.2F). Nymphaeaceae, Trochodendraceae and Cistaceae are part of entirely actinomorphic families with no obvious zygomorphic relatives (Figs. III.2B. and III.2D

  though different clades might express zygomorphy in various ways, each clade seems to have recruited the same genes for controlling the mechanisms involved in the establishment of zygomorphy (Fig. III.3). This suggests that relatively few genes are involved in the genetic control of zygomorphy. Considerable knowledge has accumulated on the genetic bases of changes in floral symmetry in monocots and eudicots in the past few years (Hileman 2014). Floral zygomorphy has been found to be linked to two transcription factors from the TCP family, CYCLOIDEA (CYC) and DICHOTOMA (DICH), which are paralogues with partially redundant functions that specify dorsal floral identity. Other influencing genes have been found in the MYB family of transcription factors: DIVARICATA (DIV) and RADIALIS (RAD). DIVARICATA (DIV) specifies ventral identity during late floral development, but is also expressed in the dorsal domain in the flower during early development (Almeida et al. 1997). CYC and DICH, which are expressed in the dorsal domain, positively regulate RAD. The role of RAD is to posttranslationally restrict the DIV function to the ventral domain. In asterids, the CYC/DIV/RAD developmental programme, first identified in Antirrhinum majus L., seems to have been conserved among the other Lamiales (Fig. III.3)[START_REF] Zhou | Altered expression patterns of TCP and MYB genes relating to the floral developmental transition from initial zygomorphy to actinomorphy in Bournea (Gesneriaceae)[END_REF] Preston and Hileman 2009;

  like genes, which has been investigated in Commelinales (Preston and Hileman 2012) and Zingiberales (Bartlett and Specht 2011) (Fig. III.3), has been found to concentrate in the ventral side of the flower, contrary to what occurs in eudicots. Horn et al. (2014) recently showed that CYC-like genes were found to be expressed in developing flowers of the magnoliid genus

Fig. III. 3 .

 3 Fig. III. 3. Simplified phylogeny of angiosperms showing the families in which the genetic bases of zygomorphy have been explored.

Fig. III. 4 .

 4 Fig. III.4. Illustration of the various forms of floral symmetry. A, Zygomorphy mostly due to perianth part displacement. B, Zygomorphy mostly due to perianth part differentiation; darker blue can mean both size and morphological differentiation.

  [START_REF] Fenster | Specialization of flowers: is floral orientation an overlooked first step?[END_REF] found horizontal orientation (Fig.III.5) to have an influence on pollinator approach even in the case of an actinomorphic flower, leading to speculation that horizontal orientation was a first step toward zygomorphy. Three hypotheses discussed in[START_REF] Neal | Floral symmetry and its role in plant-pollinator sytems: terminology, distribution, and hypotheses[END_REF] give weight to the idea of zygomorphic flowers first appearing as favorably selected variants of actinomorphic horizontally oriented flowers (Fig. III.6A). The "Inflorescence type-flower orientation hypothesis" stipulates that pollinators do not land as well in horizontally-oriented actinomorphic flowers as in flowers whose lower perianth margin is expanded in such a way that it is usable as a landing platform. Selection would hence favor expansion of the lower margin of the perianth, which may also be used as advertising, such as in Viola (Violaceae) and Lamium L. (Lamiaceae) (Figs. III.2C and III.2G). The "marginal flower-landing platform hypothesis" (Fig III.6B) could be the equivalent of the "Inflorescence type-flower orientation

  . III.2F). The "dangerous lower margin hypothesis" (Fig. III.6C) is the complete opposite of the two previous ones: a species pollinated by flying vertebrates (most likely birds according to Leins and Erbar

Flowers

  with such a configuration include Chasmanthe N. E. Br. (Iridaceae) and Musa L. (Zingiberaceae) (Fig. III.2A and III.2B). Neal et al. (1998) also hypothesized that horizontallyoriented flowers whose higher margins are longer could have been selected because of better protection of pollen and nectar from rain.

Fig. III. 5 .

 5 Fig. III.5. Clarification of the floral orientation terminology used in this paper.

Fig. III. 6 .

 6 Fig. III.6. Illustration of three hypotheses by[START_REF] Neal | Floral symmetry and its role in plant-pollinator sytems: terminology, distribution, and hypotheses[END_REF] to explain the relationship between floral symmetry, floral orientation, inflorescence type, and type of pollinator. A, Flower lacking a landing platform (actinomorphic) versus a flower whose lower margin is extended into a platform (zygomorphic). B, Inflorescence whose flowers are actinomorphic and smaller than the pollinator vs. inflorescence whose marginal flowers develop into a platform. C, Accessibility of an actinomorphic flower to a pollinating bird vs. that of a flower lacking a lower margin (zygomorphic).

  homoplastic trait distributed throughout angiosperms (Fig. III.2). Zygomorphy can occur in many forms (Fig. III.4), but the developmental programmes behind these diverse forms are only starting to be deciphered (Fig. III.3). We reviewed the reasons why flowers with a zygomorphic perianth could have been selected and why reversals to actinomorphy are comparatively less frequent. Our results highlight the families in which detailed studies of the development of floral symmetry or pollination could be interesting. Many studies have been made in the ontogeny of zygomorphic species across angiosperms, but many clades containing zygomorphic species of great interest have yet to be explored or have only been explored via their actinomorphic species: Iridaceae (Figure III.2A), Saxifragaceae, Malpighiaceae, Geraniaceae, Sapindaceae (Figure III.2C and III.2C) and several non-Lamiales families of Lamiidae (Boraginaceae, Rubiaceae and Gentianacaeae) (Figure III.2G).Efforts have been made to study the genetic pathways linked with perianth zygomorphy in several clades (Fig.III.3), but much work remains to be done in this domain also. So far, most efforts have concentrated on a few families of the superrosids and superasterids. A study on magnoliids was published very recently[START_REF] Horn | Analysis of the CYC/TB1 class of TCP transcription factors in basal angiosperms and magnoliids[END_REF], and some clades to our knowledge still remain unexplored, such as Orchidaceae and Geraniaceae. Orchidaceae as a whole and Pelargonium L'Hér. ex Aiton (Geraniaceae) each display their zygomorphy in various forms (e.g.,[START_REF] Struck | Pelargonium (Geraniaceae) in southern Africa: ecological and evolutionary considerations[END_REF]), which makes them excellent candidate clades for studying the mechanics behind various perianth part modifications. More work needs to be done in the orders in which the exploration of zygomorphy-inducing pathways has already begun. In some cases (Asterales, Fabales, Commelinales), the exploration so far has focused on a single family, sometimes a single species (Fig.III.3). However, the variability of zygomorphy within families such as the Lamiaceae, Caprifoliaceae or Proteaceae, suggests that investigation of intrafamilial variation in genetic pathways could be just as informative as inter-familial variation.

  Written byElisabeth Reyes, Jürg Schönenberger, Maria von Balthazar, Sophie Nadot, Hervé Sauquet. In preparation, planned for a submission to Nature: Scientific Reports In this chapter, I address the issue of whether reconstruction methods and models (e.g. parsimony, Mk1 or Mk2 in maximum likelihood) and transition rate differences between various portions of a phylogenetic tree affect the ancestral states that are reconstructed and if so, to what extent? To find this out, I used the same methods as the previous chapter, except with five perianth characters instead of just one: perianth symmetry, fusion, phyllotaxy, pentamery and differentiation(Figure I.5). Four of the five perianth characters had a natural dichotomy in their forms, which could be easily used to produce binary states: actinomorphy or zygomorphy for symmetry, free or united organs for fusion, whorled or spiral organization of organs for phyllotaxy, and undifferentiated or differentiated perianth for differentiation(Figure I.5).

  Monocotyledoneae, basal eudicots (Ranunculales to Buxales), superrosids (incl. Dilleniales), and superasterids(Figure IV.1). Parsimony, Mk1 and Mk2 were used to reconstruct ancestral states on both the full angiosperm tree and the partitions (collectively the partitioned tree). Here, most of the inferred transition rates were slow enough for each node to have distinct state probabilities, unlike the high transition rate induced artefact that appeared in the study presented in Chapter 2.To test the impact of changing optimization models between Mk1 and Mk2 and optimizing on the full or partitioned trees, I compared the inferred ancestral states of the various optimizations on two sets of nodes. One set consisted of 15 nodes that defined the larger commonly accepted subdivisions of the tree[START_REF] Cantino | Towards a Phylogenetic Nomenclature of Tracheophyta[END_REF]): Angiospermae, Mesangiospermae (all angiosperms except the ANA grade), Magnoliidae, Monocotyledoneae, Commelinidae, Eudicotyledoneae, Pentapetalae, Superrosidae, Rosidae, Malvidae, Fabidae, Superasteridae, Asteridae, Campanulidae and Lamiidae. These are the same 15 key nodes used in the first eFLOWER paper (H.Sauquet et al., in prep.), allowing for immediate comparison of results between the two studies. The other set was intended to comprise the ancestral crowngroup nodes of all 64 orders. In reality, only 54 nodes were examined due to ten orders being monospecific on the tree. The transition rate heterogeneity between the angiosperm partitions was shown to be strong; for a given character, partitions always had transition rates different from that of the full tree and very frequently from each other. Despite this, in both sets of nodes, a majority of them kept the same state despite the change of maximum likelihood model, but a minority of them were extremely sensitive to the model used. The most-probable ancestral states inferred using the MK2 model were prone to be different from those inferred in comparable circumstances: an Mk1 model used on a full tree and an Mk2 model used on a partitioned tree. By comparison, Mk1 used on a full tree, Mk1 used on a partitioned tree and Mk2 used on a partitioned tree had more similarities between each other in terms of inferred most-probable ancestral states.

  likelihood character optimization: an equal-rate model (Mk1; i.e., single rate of transition for both forward and backward change) and a two-rate model (Mk2; i.e., a model allowing asymmetric rates of forward and backward change). To test and account for among-lineage rate heterogeneity, we used a similar approach as Zanne et al. (2014) and subdivided the tree into five partitions consisting of two grades and three large clades, each with its own model and transition rates (Figure IV.1). The first partition comprises the ANA grade, Chloranthales, and Magnoliidae, the second is Monocotyledoneae, the third includes the basal eudicots (incl.

(

  Figure IV.3; Appendix IV.6), suggesting strong rate asymmetry for most traits. Assuming that all partitions follow the same model (i.e., five Mk1 or five Mk2 models), a combination of five partition models is always much better fit to the data than a single model for the entire angiosperm tree (Appendix IV.6), suggesting a strong signal for among-lineage rate heterogeneity in the evolution of these characters. The smallest AIC difference between the full tree and the combination of partition models is 10 (Mk2 in symmetry and phyllotaxy), which is high enough for the models to be considered very different. When partitions are taken separately, each of them is best fitted by Mk1 or Mk2, or no better fitted by one model than the other(Figure IV.3; Appendix IV.6). If these best-fitted models are combined for a given character, they will fit the entire angiosperm tree better than five Mk1 models or five Mk2 models. For instance, according to Figure IV.3, the best composite model for differentiation would consist of the Mk1 models for [ANA+Magnoliidae], Monocotyledoneae and basal eudicots, and the MK2 models for Superrosidae and Superasteridae.

  Figure IV.1. Each column compares the results of two of the model and tree type combinations and reports the number of nodes that change their most-likely state in each case. Mk1 = one rate ML model; Mk2 = two-rate ML model; full = full tree; part = partitioned tree.

  inaccurate model being favored by AIC. More precisely, we suspect that the advantage of the Mk2 model over the Mk1 model for the full phyllotaxy tree may be an artifact due to the artificially high reversal rate of this character. Our constrained rate results are consistent with the observation by Cunningham et al. (1998) that use of parsimony is only suitable when rates of character state change are low. While a convergence towards a probability of 0.5 without most-likely character state change and a change in most-likely character state were the most frequently found patterns in the constrained rate tests, other patterns were found as well (Figure IV.4).[START_REF] Vanderpoorten | Mapping uncertainty and phylogenetic uncertainty in ancestral character state reconstruction: an example in the moss genus Brachytheciastrum[END_REF] reported that the inferred root state can change between Mk1 and Mk2 when one of the character states is rare or unique. This finding is similar to what we observed with phyllotaxy, and may be linked to the rarity of the spiral state and the artefact affecting states with few origins an no reversals discussed above.[START_REF] Zanne | Three keys to the radiation of angiosperms into freezing environments[END_REF]

  reconstructions by Ronse DeCraene et al. (2003),[START_REF] Zanis | Phylogenetic analyses and perianth evolution in basal angiosperms[END_REF],[START_REF] Endress | Floral phyllotaxis in basal angiosperms : development and evolution[END_REF],[START_REF] Doyle | Morphological phylogenetic analysis of basal angiosperms: comparison and combination with molecular data[END_REF],[START_REF] Endress | Reconstructing the ancestral angiosperm flower and its initial specializations[END_REF],[START_REF] Doyle | Tracing the early evolutionary diversification of the angiosperm flower[END_REF] and[START_REF] Soltis | Phylogeny and evolution of angiosperms[END_REF]. These reconstructions, however, leave the state of the common ancestors of angiosperms equivocal (all) and also that of Laurales either equivocal[START_REF] De Craene | Evolution of floral structures in basal angiosperms[END_REF][START_REF] Soltis | Phylogeny and evolution of angiosperms[END_REF] Endress and Doyle 2007, 2009) or spiral[START_REF] Doyle | Tracing the early evolutionary diversification of the angiosperm flower[END_REF].

  and by[START_REF] Soltis | Phylogeny and evolution of angiosperms[END_REF] (Hernandiaceae from Magnoliidae, Ranunculaceae and Sabiaceae form basal eudicots, Pentapetalae themselves). All the extra pentamery occurrences we found were either isolated species or small families outside Pentapetalae (four in Magnoliidae, one in Monocotyledonae, one in the basal eudicots). We also note that there are several potential or confirmed re-originations of pentamery within parts of Pentapetalae in which the state was lost, (such as the presence of pentamerous species nested within the nonpentamerous Fagales).Most previous reconstructions of perianth differentiation[START_REF] Doyle | Morphological phylogenetic analysis of basal angiosperms: comparison and combination with molecular data[END_REF][START_REF] De Craene | Evolution of floral structures in basal angiosperms[END_REF][START_REF] Zanis | Phylogenetic analyses and perianth evolution in basal angiosperms[END_REF][START_REF] Hileman | More is better: the uses of deveopmental genetic data to reconstruct perianth evolution[END_REF] agree that angiosperms are ancestrally undifferentiated and that the ancestral state of this character in Eudicotyledoneae is equivocal (undifferentiated in[START_REF] Soltis | Phylogeny and evolution of angiosperms[END_REF]. Results for nodes basal to Pentapetalae are very sensitive to model changes in the full tree and tend to have weak support (0.6 probability or under) in the five partitioned trees. Pentapetalae are mostly differentiated, with occasional undifferentiated shallow clades. The reconstructions of Ronse De Craene (2003) and[START_REF] Soltis | Phylogeny and evolution of angiosperms[END_REF] agree with the Mk2 version of the full tree in our study, while that of[START_REF] Endress | Reconstructing the ancestral angiosperm flower and its initial specializations[END_REF] reconstruction is closer to our Mk1 full tree.The as yet unpublished first eFLOWER paper bySauquet et al. (H. Sauquet et al., in prep.) included a similar, complementary study focusing on 21 floral traits sampled from 792 species and using three reconstruction methods (parsimony, ML and Bayesian). The results for the four perianth traits shared with our study are, in general, very consistent with those presented here, despite important differences in the sampling approach and the source used for branch lengths. The set of key nodes we chose overlaps with those whose states are shown in the eFLOWER paper (H.Sauquet et al., in prep.). Among the reconstruction methods used in the latter, the results for maximum likelihood are very close to what we obtained in the Mk2

Figure IV. 1 .

 1 Figure IV.1. Order-level tree of angiosperms. The members of each partition/subdivision are contained in rectangles. The key nodes in italics are those not reconstructed in the partitioned tree.

Figure IV. 2 .

 2 Figure IV.2. Histogram of the Mk1 transition rates for the full tree (dark colors) and partitions (light colors) for each of the five characters.

Figure IV. 3 .

 3 Figure IV.3. Histogram of Mk2 symmetry ratios for the full tree (dark colors) and partitions (light colors). Blue bars are best fitted by Mk1 or have no difference in fit between Mk1 and Mk2. Red bars are best fitted by Mk2. The white bar is from a partition in which the transition rate was exceptionally high under Mk1 but not Mk2, making the latter the only one available for comparison.

Figure IV. 4 .

 4 Figure IV.4. Caryophyllales state probabilities in function of fixed Mk1 transition rate. Black dots correspond to the points closest to the rate and probability obtained by estimation. Each of these states are also the one inferred by parsimony reconstruction. In both cases, the probability of the others state has the exact opposite evolution

  V.1). In Chapter 2, I investigated the number of times zygomorphy has appeared across the angiosperm tree, which resulted in finding at least 130 origins accompanied by 69 reversals to actinomorphy. I also conducted a review on what was currently known about floral zygomorphy in terms of ecology, evolution and development. In Chapter 3, I tested the influence of transition rate heterogeneity and the use of different reconstruction models on ancestral states, and found that rate heterogeneity within angiosperms was strong, but this heterogeneity and the change in reconstruction models only affected ancestral state reconstruction in a minority of nodes. All three chapters involved ancestral state reconstruction and were based on the assumption that the ancestral states reconstructed were robust as long as the same tree remained in use. Chapter 3 demonstrated that some ancestral state results were not robust to model changes and that one of the causes is rate heterogeneity among angiosperm clades, meaning that a change of the scale on which ancestral states are reconstructed can lead to changes in the inference of mostprobable ancestral states.

  presented in Chapter 1 and that in from[START_REF] Citerne | Characterization of CYCLOIDEA-like genes in Proteaceae, a basal eudicot family with multiple shifts in floral symmetry[END_REF] would be the ones under lower transition rates and the tree presented in Chapter 3 the one under high rates. This idea was confirmed by an extra test done on a partition consisting only of the Proteaceae selection included in the study presented in Chapter 3: lower transition rate values for Mk1 (identical transition rate for origins and reversals) and Mk2 (two different rates for origin and reversal), with preserved symmetry ratio of rates for Mk2, make Proteaceae ancestrally actinomorphic with several origins of zygomorphy. An important element to note is that in the case of the analyses presented in Chapter 3, there is an extra factor besides the "change-capture" sampling method that has almost certainly led to overestimated transition rates in Proteaceae. Due to different dating sources(Sauquet et al. 2009 for Chapter 1, and[START_REF] Citerne | Characterization of CYCLOIDEA-like genes in Proteaceae, a basal eudicot family with multiple shifts in floral symmetry[END_REF] andMagallón et al. 2015 for Chapter 3), the estimated age of Proteaceae in Chapter 1 and in Citerne et al. (2016) is around 85 million years old, while they are estimated to be only 42.5 million years old in Chapter 3. I did not use the ages from the first chapter in Chapter 3on the basis of considering the ages inMagallón et al. (2015) as relative to each other and equal treatment of all families that could have inaccurate ages in the tree. A possible additional factor is that there is a higher proportion of zygomorphic terminal taxa in the Proteaceae used in Chapter 3 compared to those from Chapter 1 and[START_REF] Citerne | Characterization of CYCLOIDEA-like genes in Proteaceae, a basal eudicot family with multiple shifts in floral symmetry[END_REF].

Figure V. 1 :

 1 Figure V.1: Figure 1 from Citerne et al. (2016). Maximum likelihood reconstruction (equal rates model) of perianth symmetry evolution in Proteaceae on a new species-level tree (bestscoring RAxML tree dated with penalized likelihood). Branches are colored according to the state with highest marginal likelihood of their terminal node (or the tip state for terminal branches). Grey branches correspond to missing or inapplicable data (i.e. perianth absent). For full details, see Figs. S1 and S2. The photographs on the right-hand side illustrate some of the variation in perianth symmetry found across Proteaceae. (A) Persoonia amaliae (Persoonioideae), actinomorphic flower. (B) Synaphea sp. (Proteoideae: Conospermeae), zygomorphic flower. (C) Buckinghamia celsissima (Grevilleoideae: Embothrieae), pair of zygomorphic flowers. (D) Virotia leptophylla (Grevilleoideae: Macadamieae), pair of actinomorphic flowers. (E) Banksia ericifolia (Grevilleoideae: Banksieae), pair of zygomorphic flowers. Photograph credits: A-D, Peter Weston; E, Hervé Sauquet.

  Figure II.S1. Additional parameter estimates obtained for the best BiSSE models selected for each trait of interest. (a,c,e) Presence in Mediterranean climate regions (red) vs. other regions (blue). (b,d,f ) Floral zygomorphy (red) vs. actinomorphy (blue), assuming Banksia is unknown for this trait. (a,b) Speciation rates. (c,d) Extinction rates. (e,f ) Relative extinction rates.

Figure

  Figure II.S2. Parameter estimates obtained for the best BiSSE models selected for each trait of interest when nodes are spread evenly within Grevillea. (a,c) Presence in Mediterranean climate regions (red) vs. other regions (blue). (b,d) Floral zygomorphy (red) vs. actinomorphy (blue), assu-

  Figure II.S4. tion rate estimates). (a) Proportion unknown (same as Fig. II.2b). (b) 0% (Banksia actinomorphic). (c) 25%. (d) 50%. (e) 75%. (f ) 100% (Banksia zygomorphic).

Figure

  Figure II.S5. Banksia (speciation rate estimates). (a) Proportion unknown (same as Fig. II.S1b). (b) 0% (Banksia actinomorphic). (c) 25%. (d) 50%. (e) 75%. (f ) 100% (Banksia zygomorphic).

  Figure II.S7.colored according to the highest probability state of the corresponding node. Terminal pie charts represent the actual proportion of species in each state in each terminal taxon. However, these proportions could not be taken into account explicitly in the model used for this reconstruction (see Methods S1), which is instead based on the most common state scored for each polymorphic terminal taxon. The analysis with polymorphic terminal taxa scored as missing data yielded essentially the same character reconstruction (results not shown).

  S6: Number of changes in inferred most likely ancestral state between models and tree types in the order node series. Each column compares the results of two of the model and tree type combinations and reports the number of nodes that change most likely state between rescored and original data in each case. Mk1= one rate maximum likelihood model; Mk2= two-rate maximum likelihood model; full= full tree; part= partitioned tree; rescor= rescored used in article; orig= data as it was entered in PROTEUS. qui sont les structures reproductrices caractérisant le grand clade des Angiospermes, présentent des formes morphologiques très diverses. Parmi les nombreux attributs morphologiques des fleurs, certains sont souvent trouvés dans des clades fortement diversifiés en termes de nombre d'espèces. Ces attributs sont par conséquent suspectés d'être la cause de la diversité de ces clades. De tels attributs, dont l'apparition semble corrélée à une plus forte diversification des espèces, sont appelés innovations clés. Toutefois, prouver la nature d'innovation clé d'un attribut donné peut s'avérer compliqué, car d'autres facteurs peuvent expliquer une apparente corrélation entre un attribut morphologique et la diversité des espèces. Prouver qu'un attribut morphologique est une innovation clé inclut la reconstruction d'états ancestraux, qui permet d'identifier à quels endroits de l'arbre phylogénétique l'attribut est apparu. Cette thèse fait partie du projet eFLOWER, dont les objectifs incluent la reconstruction de la morphologie des fleurs dans les noeuds profonds de l'arbre des angiospermes et quelles innovations florales sont liées à des augmentations majeures des taux de diversification. L'un des outils utilisés pour cet objectif est la base de données collaborative pour traits morphologiques floraux PROTEUS, qui a également été beaucoup utilisée pour cette thèse. Cette thèse se focalise sur l'évolution des caractères floraux chez les angiospermes et leur impact sur la diversification des espèces. Le premier chapitre vise à tester la nature d'innovation clé de deux états de caractère, la symétrie florale bilatérale et la présence dans les hotspots à climat Méditerranéen, au sein de la famille des Proteaceae. Le second chapitre présente une reconstruction de l'évolution de la symétrie du périanthe sur un arbre des Angiospermes dont l'échantillonnage des espèces est orienté vers les changements d'états présumés. Il passe également en revue certaines propriétés de la symétrie bilatérale du périanthe. Le troisième chapitre relève d'une approche similaire, mais avec un échantillonnage basé sur cinq caractères du périanthe : la symétrie, la fusion, la phyllotaxie, la pentamérie et la différenciation. Il pose aussi la question de l'impact de l'hétérogénéité des taux de transition au sein des Angiospermes sur les états ancestraux reconstruits à différentes échelles taxonomiques. ii Chapitre 1 -La présence dans les hotspots à climat Méditerranéen et la symétrie florale affectent les taux de spéciation et d'extinction chez les Proteaceae Le premier chapitre de ma thèse se focalise sur la famille des Proteaceae (1750 espèces), un clade de plantes à fleurs, dont la majorité des espèces se trouvent dans des hotspots à climat Méditerranéen, qui sont connus pour avoir une diversité spécifique très élevée. Un précédent article avait montré l'existence d'une corrélation entre la présence dans les hotspots et des taux de diversification élevés dans la famille. La famille des Proteaceae inclut par ailleurs de nombreuses espèces avec un périanthe présentant une symétrie bilatérale, un trait de caractère qui est corrélé avec de forts taux de diversification chez les Angiospermes. Deux méthodes d'analyse de la diversification des espèces ont été testées sur ces deux caractères pour vérifier si la présence dans les hotspots et la symétrie bilatérale avaient un impact sur la diversification des espèces au sein de la famille. La famille a été choisie pour ce test parce que la diversité de chaque genre et les relations de parenté entre eux sont bien connues. La morphologie florale des espèces est bien connue également ; les fleurs ont un plan d'organisation conservé (quatre tépales, quatre étamines opposées aux tépales et un ovaire unicarpellé).La symétrie bilatérale est aussi connue sous le nom de zygomorphie et est un état de caractère caractéristique de plusieurs grandes familles d'Angiospermes, telles que les Fabaceae et les Orchidaceae. Il a été suggéré précédemment que la zygomorphie est une innovation-clé au sein des Angiospermes. La première méthode que j'ai utilisée pour analyser la diversification des espèces est MEDUSA, qui permet de détecter des changements dans le taux de diversification au sein d'un arbre phylogénétique. La seconde méthode que j'ai employée est le modèle BiSSE, qui permet de tester si un état de caractère donné est associé à des taux de diversification des espèces plus élevés qu'un autre état de caractère.Les résultats de MEDUSA ont permis de mettre en évidence au moins cinq changements probables des taux de diversification au sein des Proteaceae : quatre augmentations et une diminution du taux de diversification. Ces résultats, bien que suggérant quels clades pouvaient avoir bénéficié d'une innovation-clé, sont indépendants de l'état de caractère des espèces et montrent seulement que des changements de taux de diversification ont eu lieu. Les résultats de BiSSE ont montré que les espèces trouvées dans les hotspots à climat Méditerranéen ont un taux de diversification significativement plus élevé que celui des espèces trouvées uniquement hors des hotspots. Ils ont également montré que le taux de transition de hotspot à région non-hotspot est beaucoup plus élevé que le taux de transition iii allant de non-hotspot à hotspot. De plus, j'ai observé que le taux de diversification des clades non-hotspot était négatif et que le taux de transition net entre les hotspots et les régions nonhotspot était assez élevé pour compenser la perte d'espèces des régions non-hotspot. En d'autres termes, mes résultats suggèrent que les régions à non-hotspot sont globalement un puits macroévolutif pour les Proteaceae, c'est-à-dire un état de caractère qui cause une extinction globale chez les espèces qui le présentent, mais est acquis par de nouvelles espèces assez fréquemment (ici par migration) pour compenser la perte des espèces qui s'éteignent.Les résultats pour la symétrie du périanthe ont montré que la zygomorphie du périanthe n'a pas d'impact discernable sur la diversification, mais qu'il y a un changement plus fréquent d'actinomorphe (symétrie radiaire) à zygomorphe que de zygomorphe à actinomorphe. Nous en avons conclu que les Proteaceae étaient une exception à la règle (de l'impact de la symétrie sur la diversification chez les Angiospermes) et que d'autres caractéristiques de la famille pourraient avoir une plus grande importance pour expliquer la diversification des espèces que la zygomorphie des fleurs individuelles. Cet article a été publié à peu près en même temps que deux articles discréditant l'approche BiSSE et d'autres méthodes qui en étaient dérivées. Le premier d'entre eux était accepté, mais pas encore publié au moment où le premier chapitre était en revue. Du point de vue de mon étude, ce premier article prévenait simplement d'un piège potentiel de BiSSE. Ce piège était de conclure qu'un état de caractère avait un impact sur le taux de diversification même quand il n'apparaissait que dans un seul clade qui se trouvait avoir un taux de diversification élevé. Pour donner du soutien à mes résultats, j'ai démontré via une reconstruction d'états ancestraux par maximum de vraisemblance que les espèces vivant dans des hotspots Méditerranéens et les espèces à périanthe zygomorphe avaient plusieurs origines indépendantes pour chacun des deux caractères. Cela montrait qu'aucun des aspects du piège potentiel ne s'appliquaient aux données de la présente étude. Un second article publié plus tard a démontré que l'approche BiSSE et ses variantes avaient tendance à conclure que des états de caractère neutres avaient un impact sur la diversification. Dans le cas de la présente étude, toutefois, la symétrie du périanthe (qui n'a aucun effet sur la diversification) a été démontrée comme étant neutre chez les Proteaceae et le climat non-hotspot s'est trouvé être un puits macroévolutif plutôt que d'être simplement un état dans lequel les espèces se diversifiaient moins vite que les espèces se trouvant dans un hotspot. Par conséquent, ces deux résultats reflètent probablement une réalité biologique. iv Suite à la présente étude, j'ai reconstruit un nouvel arbre daté (chronogramme) des Proteaceae à l'échelle de l'espèce avec un échantillonnage proportionnel à la diversité de chaque genre, ce qui nous a permis d'établir un scénario plus fin pour l'évolution de la symétrie du périanthe au sein de la famille. Cette étude est plus tard devenue une partie d'un article co-signé notamment par mes directeurs de thèse Sophie Nadot et Hervé Sauquet et moi-même. J'ai construit le jeu de données au niveau des espèces avec l'aide de Peter Weston et j'étais en charge de la reconstruction phylogénétique et de la datation. La reconstruction par parcimonie a résulté en un minimum de 10 origines et 12 reversions. Le maximum de vraisemblance a résulté en 16 origines de la zygomorphie et six reversions vers l'actinomorphie. Chapitre 2 -La symétrie du périanthe a changé au moins 199 fois au cours de l'évolution des angiospermes Le second chapitre de ma thèse avait initialement pour objectif de tester si la zygomorphie était bel et bien une innovation-clé chez les Angiospermes. Toute méthode que j'aurais pu utiliser pour cela nécessitait de connaître la distribution de la zygomorphie au sein de l'arbre phylogénétique des Angiospermes. Les optimisations existantes de la symétrie florale sur des arbres phylogénétiques demeuraient incomplètes, donc j'ai décidé de produire ma propre reconstruction. La première étape a donc consisté à identifier où la zygomorphie était apparue dans l'arbre, ainsi qu'où elle était retournée à l'état ancestral d'actinomorphie. Deux de mes impératifs pour ma stratégie d'échantillonnage de cette phylogénie étaient de refléter la diversité taxonomique des Angiospermes et d'inclure autant de changements présumés de la symétrie du périanthe que possible. J'ai choisi de représenter les familles monomorphes pour la symétrie du périanthe par une seule espèce, tandis que les familles dans lesquelles la symétrie du périanthe changeait au moins une fois entre actinomorphe et zygomorphe ont été représentées par le nombre d'espèces nécessaire pour montrer tous les changements subis par la famille. Pour garder la charge de travail raisonnable, les genres polymorphes n'ont jamais été représentés par plus d'une espèce dans chaque état. Le point de départ de mon échantillonnage était un précédent article, qui était la phylogénie datée incluant le plus grand nombre de familles d'angiospermes actuellement reconnues et dont les espèces avaient déjà été codées dans la base de données PROTEUS, dans le cadre du projet eFLOWER. Dans le processus de la construction de mon propre échantillon d'espèces, plusieurs espèces ont été ajoutées ou enlevées de cette phylogénie de départ pour diverses v raisons. Tout d'abord, j'ai ajouté des espèces venant de familles qui n'étaient pas échantillonnées dans l'arbre de départ. Ensuite, j'ai ajouté des représentants de l'autre état dans des familles qui étaient polymorphes pour la symétrie du périanthe, mais avaient des espèces dans un seul état dans l'arbre de départ. Dans d'autres cas, des données fiables sur la symétrie n'existaient pas pour les espèces de l'arbre de départ, ce qui m'a conduit à choisir un autre représentant de la même famille pour lequel ces données étaient disponibles. Plusieurs espèces de mon échantillon final n'avaient pas de séquences moléculaires et générer de nouvelles séquences moléculaires ne faisait pas partie des objectifs de ma thèse. En raison de cette combinaison de facteurs, je n'ai pas utilisé de séquences moléculaires pour faire un chronogramme et j'ai utilisé d'autres méthodes pour obtenir la topologie d'arbre phylogénétique.Pour construire la topologie de l'arbre, j'ai d'abord utilisé la fonction d'export de la base de données PROTEUS pour produire un super-arbre correspondant aux relations entre ordres, entre familles et parfois à l'intérieur des familles basé sur les relations qui avaient été résumées sur l'Angiosperm Phylogeny Website (site de la phylogénie des angiospermes) en 2011. J'ai ensuite résolu manuellement la phylogénie interne de certaines familles en utilisant des études publiées récemment. Les groupements de familles étaient ceux d'APG III ; ils sont suffisamment similaires à ceux d'APG IV pour ne pas apporter de changement dans les inférences de cette étude. J'ai ensuite transformé cet arbre dépourvu de longueurs de branches en un arbre ultramétrique grâce à une fonction d'étirement des noeuds utilisée en écologie évolutive. Cette fonction requiert d'indiquer l'âge du plus grand nombre de noeuds possibles à partir d'une source externe et calcule l'âge des autres noeuds en les répartissant équitablement entre les noeuds pré-datés. Les dates entrées par l'utilisateur viennent du même article que celui qui a été utilisé comme point de départ de mon échantillonnage et ont été entrées pour 399 noeuds, à des niveaux allant du noeud menant à une famille à des noeuds plus profonds partagés entre mon arbre et celui de l'article de référence. Malheureusement, les taux de transition reconstruits sur l'arbre avec longueurs de branches (arbre daté) se sont révélés extrêmement élevés, ce qui a donné une reconstruction des états ancestraux pour la symétrie complètement équivoque pour tous les noeuds de la phylogénie (ayant tous des probabilités d'état identiques). Je n'ai donc pu reconstruire les états ancestraux qu'avec la méthode de parcimonie, ne nécessitant pas de longueurs de branches. Les résultats obtenus montrent un nombre de changements nettement supérieur à celui du dernier article présentant une estimation de ces transitions. Là où l'article en question avait proposé 70 origines de la vi zygomorphie parmi les Angiospermes, j'ai trouvé 199 changements, dont 130 origines et 69 réversions. Le véritable nombre de changements pourrait être encore plus élevé, car ma méthode d'échantillonnage limite le nombre de changements par genre à un seul et les genres les plus grands pourraient en avoir plus. De plus, les méthodes qui prennent les longueurs de branches en compte permettent plus de changements sur les branches plus longues, ce qui fait du nombre de changements trouvé par parcimonie une sous-estimation probable (voir aussi les différences entre parcimonie et maximum de vraisemblance rapportés pour le dérivé du premier chapitre).J'ai décidé d'accompagner cette étude d'une revue des aspects développementaux, génétiques et fonctionnels de la symétrie du périanthe. Ma revue de l'ontogénie met en évidence que la zygomorphie du périanthe pouvait se manifester à diverses étapes du développement, de l'initiation des sépales au stade pré-anthèse. Cette étape peut varier entre des clades fortement apparentés. De plus, certaines espèces qui sont actinomorphes à l'anthèse peuvent avoir une zygomorphie précoce (durant le développement) tout en n'étant pas fortement apparentées à des espèces zygomorphes. Ces deux faits montrent que le stade du développement auquel la zygomorphie apparaît est un trait labile. Ma revue du contrôle génétique de la zygomorphie a révélé que dans chaque clade au sein duquel cela a été étudié, le gène CYCLOIDEA ou l'un de ses proches parents a été recruté pour le contrôle de la zygomorphie. Enfin, à travers ma revue des avantages et des inconvénients de la zygomorphie, il apparaît que la zygomorphie pourrait aussi bien être un promoteur de la diversification des espèces que la cause d'une spécialisation trop extrême qui peut mener à l'extinction. La zygomorphie pourrait également être un état faisant de l'« auto-stop » dans certains clades où elle semble corrélée avec une diversité plus importante.Chapitre 3 -Est-ce que l'hétérogénéité des taux de transition affecte les reconstructions d'états ancestraux ? Un test empirique avec cinq caractères floraux Dans le troisième chapitre, j'examine la manière dont les méthodes de reconstruction des états ancestraux (c'est-à-dire la méthode de parcimonie et la méthode du maximum de vraisemblance avec les modèles Mk1 et Mk2) et les différences de taux de transition entre différentes parties de l'arbre phylogénétique affectent les états ancestraux qui sont reconstruits. Et si cela s'avère être le cas, à quel point sont-ils affectés ? Pour apporter une réponse à cela, j'ai utilisé les mêmes méthodes que dans le précédent chapitre, mais avec cinq vii caractères du périanthe au lieu d'un seul. Les caractères étaient la symétrie, la fusion, la phyllotaxie, la pentamérie et la différentiation. Trois des cinq caractères avaient une dichotomie naturelle dans leur forme, qui pouvait être facilement utilisée pour produire des états binaires : l'actinomorphie et la zygomorphie pour la symétrie, des organes libres et fusionnés pour la fusion, un périanthe différencié ou non différencié pour la différentiation.En revanche, le mérisme est un caractère multi-état par nature, qui peut être rendu binaire de diverses façons. J'ai décidé de faire une division entre les espèces chez lesquelles la pentamérie est présente (pentamères) et celles dont la pentamérie est absente (nonpentamères), la pentamérie étant le mérisme le plus commun parmi les Angiospermes. Mon échantillonnage de départ était celui du précédent chapitre. J'y ai ajouté des espèces se trouvant dans la base de données PROTEUS permettant de montrer les changements présumés des autres caractères en dehors de la symétrie. L'échantillon final était constitué de 1232 espèces représentant toutes les familles (416 dans le système APG IV) d'Angiospermes. APG IV avait été récemment publié au moment où ce travail a été effectué, apportant des changements aux définitions de certains clades ; les différences apportées à mes optimisations comparées à celles réalisée avec les définitions d'APG III étaient heureusement mineures. La fonction bladj du programme Phylocom m'a permis de donner des longueurs de branches à mon arbre ; il s'agit de la fonction utilisée pour dater l'arbre dans le second chapitre et implique donc le même processus que celui décrit dans l'introduction du précédent chapitre. Relever tous les changements de cinq caractères au lieu d'un seul sur un même arbre s'est révélé avoir plusieurs avantages. L'ajout d'espèces nécessaires pour montrer les changements de caractères hors symétrie divise les branches de l'arbre montrant uniquement la symétrie. L'une des conséquences est qu'une famille avec un seul changement de symétrie et de nombreux changements entre l'état fusionné et l'état libre sera représentée par davantage d'espèces que si elle avait été échantillonnée en se basant uniquement sur la symétrie. Cela ix de transition Mk1 ont montré que cela pouvait poser des problèmes car, dans les régions dans lesquelles un caractère binaire change souvent d'état, les taux bas aboutissent à des états similaires à ceux reconstitués par la parcimonie, alors que l'autre l'état devient plus probable sous des taux de transition plus élevés. Cela peut mener à la reconstruction d'un état différent que celui qui aurait été reconstruit dans un échantillonnage reflétant la véritable répartition des états de caractère au sein du clade. De plus, les problèmes rencontrés par les arbres utilisés dans ce chapitre existent aussi pour les caractères qui sont naturellement très labiles. Cet élément devra être pris en compte dans de futures reconstructions d'états ancestraux. Le premier chapitre a montré que les zones en dehors des hotspots à climat Méditerranéen sont des puits macroévolutifs pour les Proteaceae et que la zygomorphie florale n'avait aucun effet sur la diversification de cette famille. Le second chapitre a montré que ma méthode d'échantillonnage basée sur les changements d'états présumés permet de reconstituer les états ancestraux uniquement avec la parcimonie et que la zygomorphie peut aussi bien être un avantage qu'un inconvénient vis-à-vis de la diversification des espèces. Le troisième chapitre a montré qu'il y avait une forte hétérogénéité des taux de transition au sein des différents clades des Angiospermes et qu'elle causait parfois une différence dans les états ancestraux reconstruits comparé à un modèle homogène appliqué à toutes les Angiospermes. Dans son ensemble, cette thèse montre qu'il existe diverses méthodes d'échantillonnage des espèces et de reconstruction des états ancestraux, qui peuvent être adaptées selon l'aspect de l'évolution des caractères que l'on veut montrer. La méthode d' échantillonnage orientée vers les transitions entre états de caractère en particulier est une approche inhabituelle dans l'étude de leur évolution. Cette thèse montre aussi deux choses qui sont nécessaires pour mieux comprendre l'évolution des fleurs. L'une est la nécessité de collecter le plus de données possibles sur les caractères floraux, car les modèles ont tendance à être construits en supposant que les états de caractère sont connus pour le clade entier. L'autre est la nécessité de construire des modèles plus flexibles vis-à-vis des informations disponibles, car ces dernières sont souvent très incomplètes vis-à-vis de la réalité de la famille, malgré les efforts d'échantillonnage. Ces deux points amènent aussi la question du niveau jusqu'auquel l'arbre phylogénétique des Angiospermes a besoin d'être résolu pour pouvoir montrer toute l'évolution d'un caractère donné. D'un côté, une résolution complète au niveau de l'espèce pourrait ne pas être strictement nécessaire, car beaucoup d'états de caractère restent inchangés dans des clades entiers de tailles diverses. De l'autre, certains caractères sont très labiles ou x ont un état présenté par un très petit nombre d'espèces au sein de certains clades, ce qui peut rendre une résolution très fine du clade nécessaire pour reconstruire son histoire évolutive. Titre : Histoire évolutive des innovations-clés florales chez les Angiospermes Mots clés : reconstruction d'état ancestraux, Angiospermes, évolution florale, taux de diversification, symétrie florale, Proteaceae.Résumé : Les Angiospermes forment un clade connu pour sa grande diversité d'espèces et une répartition inégale de cette diversité en son sein. Ce travail se concentre sur la reconstruction d'états ancestraux de caractères floraux sur les phylogénies dans le but d'étudier leur impact sur la diversification. En premier lieu, nous nous sommes focalisés sur deux innovations-clés potentielles chez les Proteaceae, la symétrie bilatérale du périanthe et la présence dans les hotspots à climat méditerranéen. L'utilisation sur une phylogénie de modèles de diversification dépendants des états de caractère a permis de montrer que le premier état caractère n'a pas d'impact significatif sur la diversification des espèces dans ce groupe, contrairement au second. Ensuite, nous avons reconstruit les états ancestraux de la symétrie du périanthe à l'échelle de toutes les Angiospermes, avec une stratégie d'échantillonnage permettant de refléter toutes les transitions de ce caractère. Nous avons mis en évidence un minimum de 130 origines de la symétrie bilatérale, suivies de 69 réversions vers la symétrie radiaire. Enfin, la même méthode a été étendue à l'étude de quatre autres caractères du périanthe. Différents modèles de reconstruction d'états ancestraux ont été utilisés sur une phylogénie de 1232 espèces pour examiner l'influence des changements de modèle sur les états ancestraux reconstruits. Nos résultats montrent que les changements de modèles de reconstruction ont une influence sur l'état de certains noeuds seulement, jamais sur l'ensemble. Les différents résultats trouvés pour la symétrie, caractère commun aux trois chapitres, révèlent que notre méthode d'échantillonnage présente l'inconvénient d'estimer des taux de transition trop élevés pour donner des résultats concluants avec la méthode du maximum de vraisemblance. Les résultats sont en revanche beaucoup moins biaisés lorsque l'on examine plusieurs caractères simultanément.Title: Evolutionary history of floral key innovations in angiospermsKeywords: ancestral state reconstruction, angiosperms, floral evolution, diversification rates, floral symmetry, Proteaceae.

Table II .

 II These seven shifts included the five most recurring shifts from the birth-death model. MEDUSA analyses with the Yule model found a number of rate shifts per tree ranging from seven to 17, with a peak frequency of 11 rate shifts, and eight shifts supported in more than 50% of trees. Out of these eight shifts, only three are shared with the birth-death model top five shifts and four with the mixed model top S2), suggesting that speciation and extinction differ between hotspots and non-hotspot regions, and that transition rates from/to hotspots and non-hotspot regions are significantly different(Table II.1; Fig. II.2a,c; Fig. II.S1). Specifically, we found both speciation and extinction rates to be higher in Mediterranean hotspots than outside them (TableII.1; Fig. II.S1).

	seven shifts.
	Applied to occurrence in Mediterranean-type hotspots, character-dependent analyses
	identified the model with all parameters different as the best supported model (i.e., lowest AIC;

  Table II.2; Table II.S2; Fig. II.2d;

Table II .

 II 1. Parameter estimates obtained from the BiSSE analysis testing the impact of occurring in Mediterranean hotspots on diversification rates in Proteaceae (mean estimates followed with 95% confidence intervals). λ = speciation rate; µ = extinction rate; r = net diversification rate (λµ); ε = relative extinction rate (µ / λ); q = transition rate.

		λ	µ	r	ε	q01	q10
	non-hotspot	1.06	1.08	-0.02	1.02
	(0)	(0.84 -1.25)	(0.89 -1.27)	(-0.04 -0.01)	(1.00 -1.04)	0.002	0.029
	hotspot (1)	1.62	1.58	0.04	0.97	(0.000 -0.006)	(0.019 -0.041)
		(1.39 -	(1.34 -	(0.02 -	(0.96 -
		1.81)	1.78)	0.06)	0.99)

  . Early applications of such models on non-molecular data include those of[START_REF] Collar | Comparative analysis of morphological diversity: does disparity accumulate at the same rate in two lineages of centrarchid fishes?[END_REF][START_REF] O'meara | Testing for different rates of continuous trait evolution using likelihood[END_REF] for continuous traits, and[START_REF] Thomas | Comparative analyses of the influence of developmental mode on phenotypic diversification rates in shorebirds[END_REF] for discrete traits.[START_REF] Beaulieu | Identifying hidden rate changes in the evolution of a binary morphological character: the evolution of plant habit in campanulid Angiosperms[END_REF] proposed a model to take hidden transition rate changes into account and applied it to plant habit in Campanulidae. As part of exploring the evolution of traits that enable plants to survive freezing temperatures,[START_REF] Zanne | Three keys to the radiation of angiosperms into freezing environments[END_REF] compared a set of transition rate estimates at the level of the angiosperms to those estimated for Magnoliidae, Monocotyledoneae, Superrosidae and Superasteridae. These four subdivisions had noticeably different transition rates from each other and from angiosperms as a whole, as well as different frequencies of the occurrence of combinations of character states.

  references within[START_REF] Soltis | Phylogeny and evolution of angiosperms[END_REF]. However, most recent parsimony ancestral state reconstructions find the two states to be equivocal at the root of angiosperms[START_REF] De Craene | Evolution of floral structures in basal angiosperms[END_REF][START_REF] Zanis | Phylogenetic analyses and perianth evolution in basal angiosperms[END_REF][START_REF] Soltis | Phylogeny and evolution of angiosperms[END_REF] Endress and Doyle 2007, 2009;[START_REF] Doyle | Tracing the early evolutionary diversification of the angiosperm flower[END_REF].

	Pentamery. Flowers with a pentamerous perianth are characteristic of one of the largest
	clades in angiosperms, Pentapetalae (Cantino et al. 2007). This group has more species than all
	remaining angiosperms taken together, representing 75% of all angiosperms, making
	pentamery the most frequent form of perianth merism found across angiosperms (Ronse De
	Craene 2010). However, pentamery is present in other parts of the tree, such as Ranunculaceae

in basal eudicots and Siparunaceae in Magnoliidae

[START_REF] De Craene | Merosity in flowers: definition, origin, and taxonomic significance[END_REF][START_REF] Endress | Evolutionary diversification of the flowers in angiosperms[END_REF]

; Ronse De Craene 2016), and the reason why it is so predominant in Pentapetalae remains unknown.

Differentiation. A perianth made entirely of parts identical to each other, i.e., an undifferentiated perianth, is the most common type in basal angiosperms. By contrast, most flowers of angiosperms are characterized by a differentiated perianth, comprising at least two whorls of parts different from each other in color, size and/or shape, or of spiral series displaying different type of perianth parts such as members of the genus Camellia (Theaceae). Some studies have suggested that the undifferentiated perianth is ancestral in angiosperms

[START_REF] Doyle | Morphological phylogenetic analysis of basal angiosperms: comparison and combination with molecular data[END_REF][START_REF] De Craene | Evolution of floral structures in basal angiosperms[END_REF][START_REF] Zanis | Phylogenetic analyses and perianth evolution in basal angiosperms[END_REF][START_REF] Soltis | Phylogeny and evolution of angiosperms[END_REF][START_REF] Hileman | More is better: the uses of deveopmental genetic data to reconstruct perianth evolution[END_REF]

, while others have interpreted the ancestral state as equivocal

[START_REF] Endress | Reconstructing the ancestral angiosperm flower and its initial specializations[END_REF][START_REF] Doyle | Tracing the early evolutionary diversification of the angiosperm flower[END_REF]

.

Table IV .1: Ancestral state reconstruction for Caryophyllales; most parsimonious character state; most-likely character state of full tree and partitions under Mk1 and Mk2

 IV (full = full-tree model; part = partitioned-tree model). Asterisks in the maximum likelihood columns: none = weak support (0.51-0.60), one = moderate support (0.61-0.89), two = strong support (0.90-1).

	Caryophyllales	Parsimony	Mk1 (full)	Mk1 (part)	Mk2 (full)	Mk2 (part)
	fusion	fused	free*	fused*	free*	fused
	symmetry	actinomorphic	actinomorphic **	actinomorphic **	actinomorphic **	actinomorphic **
	phyllotaxy	whorled	whorled**	whorled**	whorled**	whorled**
	pentamery	pentamerous	pentamerous* *	pentamerous* *	pentamerous* *	pentamerous*
	differentiation	undifferentiat ed	differentiated **	differentiated **	differentiated *	undifferentiat ed

Table IV .3: Number of changes in most-likely estimated ancestral state between models and tree types.

 IV Each column compares the results of two of the model and tree type combinations and reports the number of nodes that change most-likely state in each case. Mk1 = one rate ML model; Mk2 = two-rate ML model; full = full tree; part = partitioned tree.

	54 nodes	Mk1 (full) ≠ (part)

Table IV .4: Most-likely state and state probability under constrained rates

 IV . q = imposed Mk1 transition rate. The indicated state is the most-likely, followed by its marginal probability. (hr) = high rate equilibrium.Two main types of results were observed. Figure IV.4 shows, for the Caryophyllales node, the evolution of the state probability of a fused and a differentiated perianth as a function of the transition rate with denser sampling than with all other nodes. The probability of a fused perianth shows the general pattern of a node that can change most-probable states. Its lowest point is a 0.35 chance of being differentiated, but the lowest point from other nodes on which

	Caryophyllales	Parsimony	q=0.0001	q=0.0010	q=0.0100	q=0.1000
	fusion	fused	fused (0.99)	fused (0.92)	free (0.65)	equivocal (hr)
	symmetry	actinomorphic actinomorphic	actinomorphic	actinomorphic	equivocal (hr)
			(1)	(1)	(1)
	phyllotaxy	whorled	whorled (1)	whorled (1)	whorled (1)	equivocal (hr)
	pentamery	pentamerous pentamerous	pentamerous	pentamerous	equivocal (hr)
			(1)	(1)	(1)
	differentiation	differentiated differentiated	differentiated	differentiated	equivocal (hr)
			(1)	(1)	(0.90)

Table IV .5: Number of nodes confirmed or suspected to state changes under different Mk1 rates (Key nodes).

 IV Confirmed: observed change in most-probable state. Suspected: state change not observed, but pattern includes a slump or a bump.

	15 nodes	Total	Confirmed	Suspected
	fusion	5	1	4
	symmetry	0	0	0
	phyllotaxy	0	0	0
	pentamery	0	0	0
	differentiation	5	4	1
		90

Table IV .6: Number of nodes confirmed or suspected to state changes under different Mk1 rates (Order nodes).

 IV Confirmed: observed change in most-probable state. Suspected: state change not observed, but pattern includes a slump or a bump.

	54 nodes	Total	Confirmed	Suspected
	fusion	8	2	6
	symmetry	0	0	0
	phyllotaxy	1	1	0
	pentamery	1	1	0
	differentiation	12	10	2

  The chapter presents a thorough review of what is known of various floral characters and how they can influence species diversification. It is, however, greatly lacking in terms of phylogenetic trees on which character evolution is optimized compared to the rest of the book, in which the trees presented, while relevant to the evolution of specific characters in specific clades, vary too

	much in terms of taxon sampling to give a clear visual picture of character evolution across the
	angiosperms.
	Several studies of angiosperm evolution have included many more characters than used
	in this thesis, but focused almost exclusively on basal eudicots and only explored the results
	using parsimony (Doyle and Endress 2000; Ronse De Craene et al. 2003; Zanis et al. 2003;
	Endress and Doyle 2009).

, an entire chapter is dedicated to floral diversification, in which whorled phyllotaxy, stabilizing merism, floral zygomorphy, perianth fusion and various adaptations to pollinators are singled out as possible causes of diversification.

Table III .

 III S1: List of sources used to resolve relationships within families in the supertree used for this study.

	Clade						Sources
	Asteraceae						(Funk et al. 2009)
	Boraginaceae					(Cohen 2014)
	Shift 1 Before After After Borthwickiaceae+Stixaceae+Resedacea λ non-hotspot (0) 0.607 0.622 µ hotspot (1) 1.593 1.558 non-hotspot (0) 0.706 0 zygomorphic (1) 0 0 actinomorphic(0) 0.706 0 zygomorphic (1) 1.599 1.577 Shift 1 λ µ e+ Before actinomorphic(0) 0.541 0.513 Gyrostemonaceae	r -0.015 0.035 0.706 0 0.706 0.033 r 0.028	ε 1.02 0 0 0.98 0 0.98 ε 0.95	q01 0.002 0 0.001 q01 0.010	0.032 0.032 0.020 q10 q10 0.001
	Shift 2	hotspot (1)	0		0		0	0
	Shift 2 Before Before After After	λ λ actinomorphic(0) 0.808 non-hotspot (0) 0.497 zygomorphic (1) 1.521 hotspot (1) 1.219 actinomorphic(0) 0.019 non-hotspot (0) 0.629 zygomorphic (1) 2.274	µ µ 0.789 0.495 1.496 1.193 0 0.072 0	r r 0.019 0.002 0.025 0.026 0.019 0.557 2.274	ε ε 0.98 0.99 0.98 0 0.98 0.11 0	q01 q01 0.006 0.002 0.264 0.307	q10 0.001 q10 0.012 4.368 0.012
	Shift 3	hotspot (1)	1.715	1.707	0.008	0.99
	Shift 3 Before Before After After	λ λ actinomorphic(0) 0.931 non-hotspot (0) 0.959 zygomorphic (1) 1.562 hotspot (1) 1.569 actinomorphic(0) 0.019 non-hotspot (0) 0.020 zygomorphic (1) 0	µ µ 0.912 0.979 1.538 1.529 0 0 0	r r 0.019 -0.020 0.024 0.040 0.019 0.020 0	ε ε 0.98 1.02 0.98 0 0.97 0 0	q01 q01 0.006 0.000 0.000 0.000	q10 0.001 q10 0.025 0.119 0.117
	Shift 4	hotspot (1)	0		0		0	0
	Shift 4 Before Before After After	λ λ actinomorphic(0) 3.029 non-hotspot (0) 0 zygomorphic (1) 0 hotspot (1) 4.582 actinomorphic(0) 0.785 non-hotspot (0) 0.866 zygomorphic (1) 1.526	µ µ 3.086 0.263 0 4.319 0.762 0.879 1.498	r r -0.057 -0.263 0 0.263 0.023 -0.013 0.028	ε ε 1.02 NA 0 0.97 0.94 1.02 0.98	q01 q01 0.043 0.041 0.006 0.000	q10 0.296 q10 0.415 0.001 0.022
	Shift 5	hotspot (1)	1.454	1.412	0.042	0.97
	Shift 5 Before Before After After	λ λ actinomorphic(0) 0.808 non-hotspot (0) 0.837 zygomorphic (1) 1.514 hotspot (1) 1.525 actinomorphic(0) 0.292 non-hotspot (0) 0 zygomorphic (1) 0	µ µ 0.789 0.852 1.489 1.488 0 0 0	r r 0.019 -0.015 0.025 0.037 0.292 0 0	ε ε 0.98 1.02 0.98 0 0.98 0 0	q01 q01 0.006 0.000 0.076 0.216	q10 0.001 q10 0.022 0.412 0.625
		hotspot (1)	0.568	0		0.568	0
			λ		µ		r	ε	q01	q10
	actinomorphic (0) zygomorphic (1)	1.17 (0.98 -1.36) 1.62 (1.14 -2.11)	1.15 (0.96 -1.35) 1.60 (1.10 -2.10)	0.02 (0.00 -0.03) 0.02 (0.00 -0.04)	0.99 (0.97 -1.00) 0.99 (0.96 -1.00)	0.006 (0.003 -0.011)	0.001 (0.000 -0.003)

Table III .

 III S2: Summary of famil y-level states for floral symmetry and transitions recon structed from this study (Fig. III.2).

	Clade	States present	Ancestral state	Origins (min-max)
				al.
			2015)
	Bromeliaceae		GRIN Taxonomy for plants
			(http://www.ars-grin.gov/cgi-
			bin/npgs/html/index.pl?language=en)("Germplas
			m Resources Information Network -(GRIN)
			[Online Database]" 2015)
	Commelinaceae		(Evans et al. 2003; Burns et al. 2011)
	Ericaceae		(Kron et al. 2002)
	Fabaceae		(Cardoso et al. 2012)
			GRIN Taxonomy for plants
			(http://www.ars-grin.gov/cgi-
			bin/npgs/html/index.pl?language=en)("Germplas
			m Resources Information Network -(GRIN)
			[Online Database]" 2015),
	Gentianaceae		(Mansion and Struwe 2004)
			GRIN Taxonomy for plants
			(http://www.ars-grin.gov/cgi-
			bin/npgs/html/index.pl?language=en)("Germplas
			m Resources Information Network -(GRIN)
			[Online Database]" 2015)
	Iridaceae		(Goldblatt et al. 2008)
	Lecythidaceae		(Tsou and Mori 2007)
	Loranthaceae		(Wilson and Calvin 2006; Vidal-Russell and
			Nickrent 2008)
	Proteaceae		(Mast et al. 2008; Sauquet et al. 2009)
	Malpighiaceae		(Davis and Anderson 2010)
	Plantaginaceae		(Albach et al. 2005)
	Sapindaceae		(Buerki et al. 2011)
	Saxifragales		(Soltis et al. 2013)
	Scrophulariaceae		(Oxelman et al. 2005)
	Solanaceae		(Olmstead et al. 2008)
	Tecophileaceae		(Buerki et al. 2013)
	Violaceae		(Tokuoka 2008)
	Literature cited

Albach DC, Meudt HM, Oxelman B. 2005. Piecing together the "'new'" Plantaginaceae.

  Parismony steps, Mk1 and Mk2 transition rates, Mk2 rate symmetry ratios, logLilkelihoods and AICs for the full tree an partitions Parismony steps, Mk1 and Mk2 transition rates, Mk2 rate symmetry ratios, logLilkelihoods and AICs for the full tree an partitions Parismony steps, Mk1 and Mk2 transition rates, Mk2 rate symmetry ratios, logLilkelihoods and AICs for the full tree an partitions Parismony steps, Mk1 and Mk2 transition rates, Mk2 rate symmetry ratios, logLilkelihoods and AICs for the full tree an partitions Parismony steps, Mk1 and Mk2 transition rates, Mk2 rate symmetry ratios, logLilkelihoods and AICs for the full tree an partitions

	Appendix IV.2: Parsimony, Mk1 and Mk2 for 15 key nodes Symmetry no star= 0.51-0.6 probability Appendix IV.2: Parsimony, Mk1 and Mk2 for 15 key nodes Fusion no star= 0.51-0.6 probability Appendix IV.2: Parsimony, Mk1 and Mk2 for 15 key nodes Phyllotaxy no star= 0.51-0.6 probability Appendix IV.2: Parsimony, Mk1 and Mk2 for 15 key nodes Pentamery no star= 0.51-0.6 probability Appendix IV.2: Parsimony, Mk1 and Mk2 for 15 key nodes Differentiation no star= 0.51-0.6 probability Appendix IV.3: Parsimony, Mk1 and Mk2 for the 54 order nodes *= 61-89% probability **= 90-100% probability *= 61-89% probability **= 90-100% probability *= 61-89% probability **= 90-100% probability *= 61-89% probability **= 90-100% probability *= 61-89% probability **= 90-100% probability Symmetry no star= 0.51-0.6 probability *= 61-89% probability **= 90-100% probability Appendix IV.3: Parsimony, Mk1 and Mk2 for the 54 order nodes Fusion no star= 0.51-0.6 probability *= 61-89% probability **= 90-100% probability Celastrales free free** free** free** Commelinales free free** free* free** Appendix IV.3: Parsimony, Mk1 and Mk2 for the 54 order nodes Phyllotaxy no star= 0.51-0.6 probability *= 61-89% probability **= 90-100% probability Celastrales whorled whorled** whorled** whorled** Commelinales whorled whorled** whorled** whorled** Appendix IV.3: Parsimony, Mk1 and Mk2 for the 54 order nodes Pentamery no star= 0.51-0.6 probability *= 61-89% probability **= 90-100% probability Celastrales pentamerous pentamerous** pentamerous* pentamerous** Commelinales non-penta non-penta** non-penta** non-penta** Appendix IV.3: Parsimony, Mk1 and Mk2 for the 54 order nodes. Differentiation no star= 0.51-0.6 probability *= 61-89% probability **= 90-100% probability Santalales pentamerous pentamerous 1 pentamerous Sapindales pentamerous pentamerous 1 pentamerous Poales non-penta non-penta 1 non-penta Proteales non-penta non-penta 1 non-penta Sapindales differentiated differentiated 1 differentiated Saxifragales differentiated differentiated 1 differentiated Ranunculales differentiated differentiated 1 differentiated Rosales differentiated differentiated 0.99 differentiated Appendix IV.6: Symmetry q= transition rate; 0= actinomorphic; 1= zygomorphic Appendix IV.6: Fusion q= transition rate; 0= free; 1= fused Appendix IV.6: Phyllotaxy q= transition rate; 0= whorled; 1= spiral Appendix IV.6: Pentamery q= transition rate; 0= non-pentamerous; 1= pentamerous Appendix IV.6: Differentiation q= transition rate; 0= undifferentiated; 1= differentiated	0.98 0.94	free* free* whorled** whorled** pentamerous non-penta**	pentamerous 1 pentamerous 1 non-penta 1 non-penta 1 differentiated 1 differentiated 1 differentiated differentiated	0.83 0.97 0.85 0.99 0.99 0.97 0.75	equivocal (high rate) equivocal (high rate) 1 equivocal (high rate) equivocal (high rate) equivocal (high rate) equivocal (high rate) equivocal (high rate) equivocal (high rate)	0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
	Clade Zingiberaceae Cornales Cornales Cornales Saxifragales Ranunculales Solanales Santalales Zygophyllales Krameriaceae Zygophyllaceae RESCORED DATA Angiospermae Mesangiospermae Magnoliidae Monocotyledoneae Commelinidae Eudicotyledoneae Pentapetalae Superrosidae Rosidae Malvidae Fabidae Superasteridae Asteridae Campanulidae Lamiidae ORIGINAL DATA Angiospermae Mesangiospermae Magnoliidae Monocotyledoneae Commelinidae Eudicotyledoneae Pentapetalae Superrosidae Rosidae Malvidae Fabidae Superasteridae Asteridae Campanulidae Lamiidae RESCORED DATA Angiospermae Mesangiospermae Magnoliidae Monocotyledoneae Commelinidae Eudicotyledoneae Pentapetalae Superrosidae Rosidae Malvidae Fabidae Superasteridae Asteridae Campanulidae Lamiidae ORIGINAL DATA Angiospermae Mesangiospermae Magnoliidae Monocotyledoneae Commelinidae Eudicotyledoneae Pentapetalae Superrosidae Rosidae Malvidae Fabidae Superasteridae Asteridae Campanulidae Lamiidae RESCORED DATA Angiospermae Mesangiospermae Magnoliidae Monocotyledoneae Commelinidae Eudicotyledoneae Pentapetalae Superrosidae Rosidae Malvidae Fabidae Superasteridae Asteridae Campanulidae Lamiidae ORIGINAL DATA Angiospermae Mesangiospermae Magnoliidae Monocotyledoneae Commelinidae Eudicotyledoneae Pentapetalae Superrosidae Rosidae Malvidae Fabidae Superasteridae Asteridae Campanulidae Lamiidae RESCORED DATA Angiospermae Mesangiospermae Magnoliidae Monocotyledoneae Commelinidae Eudicotyledoneae Pentapetalae Superrosidae Rosidae Malvidae Fabidae Superasteridae Asteridae Campanulidae Lamiidae ORIGINAL DATA Angiospermae Mesangiospermae Magnoliidae Monocotyledoneae Commelinidae Eudicotyledoneae Pentapetalae Superrosidae Rosidae Malvidae Fabidae Superasteridae Asteridae Campanulidae Lamiidae RESCORED DATA Angiospermae Mesangiospermae Magnoliidae Monocotyledoneae Commelinidae Eudicotyledoneae Pentapetalae Superrosidae Rosidae Malvidae Fabidae Superasteridae Asteridae Campanulidae Lamiidae ORIGINAL DATA Angiospermae Mesangiospermae Magnoliidae Monocotyledoneae Commelinidae Eudicotyledoneae Pentapetalae Superrosidae Rosidae Malvidae Fabidae Superasteridae Asteridae Campanulidae Lamiidae RESCORED DATA Alismatales Apiales Aquifoliales Arecales Asparagales Asterales Austrobaileyales Berberidopsidales Boraginales Brassicales Bruniales Buxales Canellales Caryophyllales Celastrales Commelinales Cornales Crossosomatales Cucurbitales Dioscoreales Dipsacales Ericales Escalloniales Fabales Fagales Garryales Gentianales Geraniales Huerteales Icacinales Lamiales Laurales Liliales Magnoliales Malpighiales Malvales Myrtales Nymphaeales Oxalidales Pandanales Paracryphiales Petrosaviales Piperales Poales Proteales Ranunculales Rosales Santalales Sapindales Saxifragales Solanales Vitales Zingiberales Zygophyllales RESCORED DATA Alismatales Apiales Aquifoliales Arecales Asparagales Asterales Austrobaileyales Berberidopsidales Boraginales Brassicales Bruniales Buxales Canellales Caryophyllales Celastrales Commelinales Cornales Crossosomatales Cucurbitales Dioscoreales Dipsacales Ericales Escalloniales Fabales Fagales Garryales Gentianales Geraniales Huerteales Icacinales Lamiales Laurales Liliales Magnoliales Malpighiales Malvales Myrtales Nymphaeales Oxalidales Pandanales Paracryphiales Petrosaviales Piperales Poales Proteales Ranunculales Rosales Santalales Sapindales Saxifragales Solanales Vitales Zingiberales Zygophyllales Crossosomatales Cucurbitales Dioscoreales Dipsacales Ericales Escalloniales Fabales Fagales Garryales Gentianales Geraniales Huerteales Icacinales Lamiales Laurales Liliales Magnoliales Malpighiales Malvales Myrtales Nymphaeales Oxalidales Pandanales Paracryphiales Petrosaviales Piperales Poales Proteales Ranunculales Rosales Santalales Sapindales Saxifragales Solanales Vitales Zingiberales Zygophyllales RESCORED DATA Alismatales Apiales Aquifoliales Arecales Asparagales Asterales Austrobaileyales Berberidopsidales Boraginales Brassicales Bruniales Buxales Canellales Caryophyllales Celastrales Commelinales Cornales Crossosomatales Cucurbitales Dioscoreales Dipsacales Ericales Escalloniales Fabales Fagales Garryales Gentianales Geraniales Huerteales Icacinales Lamiales Laurales Liliales Magnoliales Malpighiales Malvales Myrtales Nymphaeales Oxalidales Pandanales Paracryphiales Petrosaviales Piperales Poales Proteales Ranunculales Rosales Santalales Sapindales Saxifragales Solanales Vitales Zingiberales Zygophyllales Crossosomatales Cucurbitales Dioscoreales Dipsacales Ericales Escalloniales Fabales Fagales Garryales Gentianales Geraniales Huerteales Icacinales Lamiales Laurales Liliales Magnoliales Malpighiales Malvales Myrtales Nymphaeales Oxalidales Pandanales Paracryphiales Petrosaviales Piperales Poales Proteales Ranunculales Rosales Santalales Sapindales Saxifragales Solanales Vitales Zingiberales Zygophyllales RESCORED DATA Alismatales Apiales Aquifoliales Arecales Asparagales Asterales Austrobaileyales Berberidopsidales Boraginales Brassicales Bruniales Buxales Canellales Caryophyllales Celastrales Commelinales Cornales Crossosomatales Cucurbitales Dioscoreales Dipsacales Ericales Escalloniales Fabales Fagales Garryales Gentianales Geraniales Huerteales Icacinales Lamiales Laurales Liliales Magnoliales Malpighiales Malvales Myrtales Nymphaeales Oxalidales Pandanales Paracryphiales Petrosaviales Piperales Poales Proteales Ranunculales Rosales Santalales Sapindales Saxifragales Solanales Vitales Zingiberales Zygophyllales Zygophyllales Zingiberales Vitales Solanales Saxifragales Sapindales Santalales Rosales Crossosomatales Cucurbitales Dioscoreales Dipsacales Ericales Escalloniales Fabales Fagales Garryales Gentianales Geraniales Huerteales Icacinales Lamiales Laurales Liliales Magnoliales Malpighiales Malvales Myrtales Nymphaeales Oxalidales Pandanales Paracryphiales Petrosaviales Piperales Poales Proteales Ranunculales Rosales Santalales Sapindales Saxifragales Solanales Vitales Zingiberales Zygophyllales RESCORED DATA Alismatales Apiales Aquifoliales Arecales Asparagales RESCORED DATA Alismatales Apiales Aquifoliales Arecales Asparagales Asterales Solanales Vitales Zingiberales Zygophyllales ORIGINAL DATA Alismatales Rosales Santalales Sapindales Saxifragales Solanales Vitales Zingiberales RESCORED DATA Alismatales Apiales Aquifoliales Arecales Asparagales Vitales Zingiberales Zygophyllales ORIGINAL DATA Alismatales Sapindales Saxifragales RESCORED DATA RESCORED DATA RESCORED DATA RESCORED DATA RESCORED DATA Solanales Parsi steps Parsi steps Parsi steps Parsi steps Parsi steps Vitales Mk1 q Mk1 q Mk1 q Mk1 q Mk1 q Zingiberales Mk1 logLik Mk1 logLik Mk1 logLik Mk1 logLik Mk1 logLik Zygophyllales Mk1 AIC Mk1 AIC Mk1 AIC Mk1 AIC Mk1 AIC Apiales Mk2 q01 Mk2 q01 Mk2 q01 Mk2 q01 Mk2 q01 Apiales Zygophyllales Asterales Aquifoliales Mk2 q10 Mk2 q10 Mk2 q10 Mk2 q10 Mk2 q10 Asterales Austrobaileyales Aquifoliales Austrobaileyales Arecales symmetry ratio symmetry ratio symmetry ratio symmetry ratio symmetry ratio Austrobaileyales Berberidopsidales Boraginales Brassicales Bruniales Buxales Canellales Caryophyllales Celastrales Commelinales Cornales Crossosomatales Cucurbitales Dioscoreales Dipsacales Ericales Escalloniales Fabales Fagales Garryales Gentianales Geraniales Huerteales Icacinales Lamiales Laurales Liliales Magnoliales Malpighiales Malvales Myrtales Nymphaeales Oxalidales Pandanales Paracryphiales Petrosaviales Piperales Poales Proteales Ranunculales Berberidopsidales Boraginales Brassicales Bruniales Buxales Canellales Caryophyllales Celastrales Commelinales Cornales Crossosomatales Cucurbitales Dioscoreales Dipsacales Ericales Escalloniales Fabales Fagales Garryales Gentianales Geraniales Huerteales Icacinales Lamiales Laurales Liliales Magnoliales Malpighiales Malvales Myrtales Nymphaeales Oxalidales Pandanales Paracryphiales Petrosaviales Piperales Poales Proteales Ranunculales Rosales Arecales Asparagales Asterales Austrobaileyales Berberidopsidales Boraginales Brassicales Berberidopsidales Boraginales Brassicales Bruniales Buxales Canellales Caryophyllales Asparagales Asterales Mk2 logLik Mk2 logLik Mk2 logLik Mk2 logLik Mk2 logLik Austrobaileyales Mk2 AIC Mk2 AIC Mk2 AIC Mk2 AIC Mk2 AIC Berberidopsidales delta AIC delta AIC delta AIC delta AIC delta AIC Boraginales Delta AIC angio-mixed (Mk1)= 41,4 full = full tree; part = partitioned tree; high rate= high rate equilibrium States present Ancestral state full = full tree; part = partitioned tree; high rate= high rate equilibrium full = full tree; part = partitioned tree; high rate= high rate equilibrium full = full tree; part = partitioned tree; high rate= high rate equilibrium full = full tree; part = partitioned tree; high rate= high rate equilibrium full = full tree; part = partitioned tree; high rate= high rate equilibrium full = full tree; part = partitioned tree; high rate= high rate equilibrium free free* free full = full tree; part = partitioned tree; high rate= high rate equilibrium whorled whorled** whorled** full = full tree; part = partitioned tree; high rate= high rate equilibrium pentamerous pentamerous* pentamerous* full = full tree; part = partitioned tree; high rate= high rate equilibrium pentamerous pentamerous non-penta non-penta differentiated differentiated differentiated differentiated zygomorphic zygomorphic actinomorphic, zygomorphic actinomorphic zygomorphic zygomorphic actinomorphic, zygomorphic actinomorphic Parsimony Both "full" and "part" Mk1 Likelihood (full) Mk1 Likelihood (part) Mk2 Likelihood (full) Mk2 Likelihood (part) Origins (min-max) Reversals (min-max) Difference between models Difference between models Difference between models Difference between models Difference between models Difference between models Difference between models free* free** Difference between models whorled** whorled** Difference between models pentamerous** pentamerous Difference between models 1 pentamerous 1 pentamerous 1 non-penta 1 non-penta 1 differentiated 1 differentiated 1 differentiated 1 differentiated Species 0 0 2 0 0 0 1 0 actinomorphic actinomorphic** actinomorphic** actinomorphic* actinomorphic** actinomorphic actinomorphic** ? actinomorphic* ? actinomorphic actinomorphic** actinomorphic** actinomorphic* actinomorphic** actinomorphic, zygomorphic actinomorphic** equivocal (high rate) actinomorphic* actinomorphic (high rate) actinomorphic actinomorphic** equivocal (high rate) zygomorphic* actinomorphic (high rate) actinomorphic actinomorphic** equivocal (high rate) actinomorphic* actinomorphic* actinomorphic actinomorphic** ? actinomorphic* ? actinomorphic actinomorphic** actinomorphic** actinomorphic* actinomorphic** actinomorphic actinomorphic** actinomorphic** actinomorphic* actinomorphic** actinomorphic actinomorphic** actinomorphic** actinomorphic* actinomorphic** actinomorphic actinomorphic** actinomorphic** actinomorphic** actinomorphic** actinomorphic actinomorphic** actinomorphic** actinomorphic* actinomorphic* actinomorphic actinomorphic** actinomorphic** actinomorphic* actinomorphic* actinomorphic actinomorphic** actinomorphic** actinomorphic* actinomorphic* actinomorphic actinomorphic** actinomorphic** actinomorphic* actinomorphic* Parsimony Both "full" and "part" Mk1 Likelihood (full) Mk1 Likelihood (part) Mk2 Likelihood (full) Mk2 Likelihood (part) actinomorphic actinomorphic** actinomorphic** actinomorphic* actinomorphic** actinomorphic actinomorphic** ? actinomorphic* ? actinomorphic actinomorphic** actinomorphic** actinomorphic* actinomorphic** actinomorphic, zygomorphic actinomorphic** equivocal (high rate) actinomorphic* actinomorphic (high rate) actinomorphic actinomorphic** equivocal (high rate) zygomorphic* actinomorphic (high rate) actinomorphic actinomorphic** actinomorphic* actinomorphic* actinomorphic* actinomorphic actinomorphic** ? actinomorphic** ? actinomorphic actinomorphic** actinomorphic** actinomorphic** actinomorphic** actinomorphic actinomorphic** actinomorphic** actinomorphic** actinomorphic** actinomorphic actinomorphic** actinomorphic** actinomorphic* actinomorphic** actinomorphic actinomorphic** actinomorphic** actinomorphic** actinomorphic** actinomorphic actinomorphic** actinomorphic** actinomorphic** actinomorphic** actinomorphic actinomorphic** actinomorphic** actinomorphic** actinomorphic** actinomorphic actinomorphic** actinomorphic** actinomorphic* actinomorphic* actinomorphic actinomorphic** actinomorphic** actinomorphic* actinomorphic* Maximum Likelihood (Mk1 model) Maximum Likelihood (Mk2 model) Maximum Likelihood (Mk1 model) Maximum Likelihood (Mk2 model) Parsimony Both "full" and "part" Mk1 Likelihood (full) Mk1 Likelihood (part) Mk2 Likelihood (full) Mk2 Likelihood (part) free free** equivocal (high rate) free** free (high rate) free free** ? free** ? free free** equivocal (high rate) free** equivocal (high rate) free free** free free** free* free free** free free** free* free free** free** free** free* free, fused free** ? free** ? fused free** equivocal (high rate) free** equivocal (high rate) fused free** equivocal (high rate) free** equivocal (high rate) fused free* equivocal (high rate) free* equivocal (high rate) free free** equivocal (high rate) free** equivocal (high rate) free, fused free* fused** free* fused* fused fused* fused** fused fused* fused fused** fused** fused** fused** fused fused** fused** fused** fused** Parsimony Both "full" and "part" Mk1 Likelihood (full) Mk1 Likelihood (part) Mk2 Likelihood (full) Mk2 Likelihood (part) free free** free** free** free (high rate) free free** ? free** ? free free** free** free** free (high rate) free free** free* free** free* free free** free** free** free* free free** free** free** free** free free** ? free** ? free free** free** free** free* free free** free** free** free* free free** free** free** free* free free** free** free** free* free, fused free** fused* free* free** free,fused free* fused* free* free** fused fused* fused** fused** free** fused fused* fused** fused** free** Maximum Likelihood (Mk1 model) Maximum Likelihood (Mk2 model) Maximum Likelihood (Mk1 model) Maximum Likelihood (Mk2 model) Parsimony Both "full" and "part" Mk1 Likelihood (full) Mk1 Likelihood (part) Mk2 Likelihood (full) Mk2 Likelihood (part) whorled, spiral whorled** whorled** spiral** whorled** whorled whorled** ? spiral** ? whorled whorled** whorled** spiral** whorled** whorled whorled** whorled** spiral* whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** spiral** whorled* whorled whorled** ? whorled** ? whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** Parsimony Both "full" and "part" Mk1 Likelihood (full) Mk1 Likelihood (part) Mk2 Likelihood (full) Mk2 Likelihood (part) whorled, spiral whorled** whorled** spiral** whorled** whorled whorled** ? spiral** ? whorled whorled** whorled** spiral** whorled** whorled whorled** whorled** spiral* whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** spiral** whorled* whorled whorled** ? whorled** ? whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** Maximum Likelihood (Mk1 model) Maximum Likelihood (Mk2 model) Maximum Likelihood (Mk1 model) Maximum Likelihood (Mk2 model) Parsimony Both "full" and "part" Mk1 Likelihood (full) Mk1 Likelihood (part) Mk2 Likelihood (full) Mk2 Likelihood (part) non-penta non-penta** non-penta** non-penta** non-penta* non-penta non-penta** ? non-penta** ? non-penta non-penta** non-penta** non-penta** non-penta* non-penta non-penta** non-penta** non-penta** non-penta** non-penta non-penta** non-penta** non-penta** non-penta** non-penta non-penta** non-penta** non-penta** non-penta** pentamerous pentamerous** ? pentamerous** ? pentamerous pentamerous** pentamerous** pentamerous** pentamerous pentamerous pentamerous** pentamerous** pentamerous** pentamerous pentamerous pentamerous** pentamerous** pentamerous** pentamerous pentamerous pentamerous** pentamerous** pentamerous** pentamerous pentamerous pentamerous** pentamerous** pentamerous** pentamerous* pentamerous pentamerous** pentamerous** pentamerous** pentamerous* pentamerous pentamerous** pentamerous** pentamerous** pentamerous* pentamerous pentamerous** pentamerous** pentamerous** pentamerous* Parsimony Both "full" and "part" Mk1 Likelihood (full) Mk1 Likelihood (part) Mk2 Likelihood (full) Mk2 Likelihood (part) non-penta non-penta** non-penta** non-penta** non-penta** non-penta non-penta** ? non-penta** ? non-penta non-penta** non-penta** non-penta** non-penta** non-penta non-penta** non-penta** non-penta** non-penta** non-penta non-penta** non-penta** non-penta** non-penta** non-penta non-penta** non-penta** non-penta** non-penta* non-penta, pentamerous pentamerous* ? pentamerous** ? pentamerous pentamerous** pentamerous** pentamerous** non-penta pentamerous pentamerous** pentamerous** pentamerous** non-penta pentamerous pentamerous** pentamerous** pentamerous** non-penta pentamerous pentamerous** pentamerous** pentamerous** non-penta non-penta, pentamerous pentamerous* pentamerous* pentamerous* pentamerous pentamerous pentamerous** pentamerous** pentamerous** pentamerous pentamerous pentamerous** pentamerous** pentamerous** pentamerous* pentamerous pentamerous** pentamerous** pentamerous** pentamerous Maximum Likelihood (Mk1 model) Maximum Likelihood (Mk2 model) Maximum Likelihood (Mk1 model) Maximum Likelihood (Mk2 model) Parsimony Both "full" and "part" Mk1 Likelihood (full) Mk1 Likelihood (part) Mk2 Likelihood (full) Mk2 Likelihood (part) undifferentiated differentiated* differentiated undifferentiated** differentiated undifferentiated differentiated** ? undifferentiated** ? undifferentiated differentiated* differentiated undifferentiated** differentiated undifferentiated differentiated** undifferentiated undifferentiated** undifferentiated undifferentiated, differentiated differentiated** differentiated* undifferentiated** differentiated differentiated differentiated** differentiated** undifferentiated* differentiated** differentiated differentiated** ? differentiated** ? differentiated differentiated** differentiated** differentiated** differentiated** differentiated differentiated** differentiated** differentiated** differentiated** differentiated differentiated** differentiated** differentiated** differentiated** differentiated differentiated** differentiated** differentiated** differentiated** differentiated differentiated** differentiated** differentiated** differentiated* differentiated differentiated** differentiated** differentiated** differentiated** differentiated differentiated** differentiated** differentiated** differentiated** differentiated differentiated** differentiated** differentiated** differentiated** Parsimony Both "full" and "part" Mk1 Likelihood (full) Mk1 Likelihood (part) Mk2 Likelihood (full) Mk2 Likelihood (part) undifferentiated differentiated* undifferentiated undifferentiated** undifferentiated undifferentiated differentiated* ? undifferentiated** ? undifferentiated differentiated* equivocal undifferentiated** undifferentiated undifferentiated differentiated* undifferentiated undifferentiated** undifferentiated undifferentiated, differentiated differentiated* differentiated undifferentiated** differentiated differentiated differentiated** differentiated** undifferentiated* differentiated** differentiated differentiated** ? differentiated** ? differentiated differentiated** differentiated** differentiated** differentiated** differentiated differentiated** differentiated** differentiated** differentiated** differentiated differentiated** differentiated** differentiated** differentiated** differentiated differentiated** differentiated** differentiated** differentiated** differentiated differentiated** differentiated** differentiated** differentiated* differentiated differentiated** differentiated** differentiated** differentiated** differentiated differentiated** differentiated** differentiated** differentiated** differentiated differentiated** differentiated** differentiated** differentiated** Maximum Likelihood (Mk1 model) Maximum Likelihood (Mk2 model) Maximum Likelihood (Mk1 model) Maximum Likelihood (Mk2 model) Parsimony Both "full" and "part" Mk1 Likelihood (full) Mk1 Likelihood (part) Mk2 Likelihood (full) Mk2 Likelihood (part) actinomorphic actinomorphic** equivocal (high rate) actinomorphic* actinomorphic (high rate) actinomorphic actinomorphic** actinomorphic** actinomorphic* actinomorphic* actinomorphic actinomorphic** actinomorphic** actinomorphic* actinomorphic* actinomorphic actinomorphic** equivocal (high rate) actinomorphic* actinomorphic (high rate) actinomorphic actinomorphic** equivocal (high rate) zygomorphic actinomorphic (high rate) actinomorphic actinomorphic** actinomorphic** actinomorphic actinomorphic actinomorphic actinomorphic** actinomorphic** actinomorphic* actinomorphic** actinomorphic actinomorphic** actinomorphic** actinomorphic** actinomorphic** actinomorphic actinomorphic** actinomorphic** zygomorphic actinomorphic* actinomorphic actinomorphic** actinomorphic** actinomorphic* actinomorphic actinomorphic actinomorphic** actinomorphic** actinomorphic* actinomorphic* actinomorphic actinomorphic** equivocal (high rate) actinomorphic* actinomorphic* actinomorphic actinomorphic** actinomorphic** actinomorphic* actinomorphic** actinomorphic actinomorphic** actinomorphic** actinomorphic** actinomorphic** actinomorphic actinomorphic** actinomorphic** actinomorphic* actinomorphic** actinomorphic, zygomorphic zygomorphic* equivocal (high rate) zygomorphic** actinomorphic (high rate) actinomorphic actinomorphic** actinomorphic** actinomorphic* actinomorphic* actinomorphic actinomorphic** actinomorphic** actinomorphic** actinomorphic** actinomorphic actinomorphic** actinomorphic** actinomorphic** actinomorphic** actinomorphic actinomorphic** equivocal (high rate) actinomorphic* actinomorphic (high rate) actinomorphic actinomorphic* actinomorphic* equivocal actinomorphic actinomorphic actinomorphic** actinomorphic** actinomorphic** actinomorphic* actinomorphic actinomorphic** actinomorphic** actinomorphic* actinomorphic* actinomorphic actinomorphic* actinomorphic* actinomorphic* actinomorphic actinomorphic actinomorphic** actinomorphic** actinomorphic** actinomorphic** actinomorphic actinomorphic** actinomorphic** actinomorphic** actinomorphic** actinomorphic actinomorphic** actinomorphic** actinomorphic* actinomorphic* actinomorphic actinomorphic** actinomorphic** actinomorphic* actinomorphic* actinomorphic actinomorphic** actinomorphic** actinomorphic** actinomorphic** actinomorphic actinomorphic** actinomorphic** actinomorphic* actinomorphic* actinomorphic, zygomorphic actinomorphic* actinomorphic* zygomorphic* zygomorphic* actinomorphic actinomorphic** actinomorphic** actinomorphic* actinomorphic** actinomorphic actinomorphic** equivocal (high rate) actinomorphic actinomorphic (high rate) actinomorphic actinomorphic** actinomorphic** actinomorphic* actinomorphic** actinomorphic actinomorphic** actinomorphic** actinomorphic** actinomorphic** actinomorphic actinomorphic** actinomorphic** actinomorphic* actinomorphic** actinomorphic actinomorphic** actinomorphic** actinomorphic* actinomorphic* actinomorphic actinomorphic** actinomorphic** actinomorphic* actinomorphic** actinomorphic actinomorphic** actinomorphic** actinomorphic** actinomorphic** actinomorphic actinomorphic** equivocal (high rate) actinomorphic* actinomorphic (high rate) actinomorphic actinomorphic** actinomorphic** actinomorphic** actinomorphic** actinomorphic actinomorphic** equivocal (high rate) actinomorphic* actinomorphic (high rate) actinomorphic actinomorphic** actinomorphic** actinomorphic* actinomorphic** actinomorphic actinomorphic** equivocal (high rate) zygomorphic* actinomorphic (high rate) actinomorphic actinomorphic** equivocal (high rate) actinomorphic* actinomorphic* actinomorphic actinomorphic** equivocal (high rate) actinomorphic* actinomorphic* actinomorphic actinomorphic** actinomorphic** actinomorphic** actinomorphic** actinomorphic actinomorphic** actinomorphic** actinomorphic* actinomorphic* actinomorphic actinomorphic** actinomorphic** actinomorphic** actinomorphic** actinomorphic actinomorphic** actinomorphic** actinomorphic** actinomorphic** actinomorphic actinomorphic** actinomorphic** zygomorphic* actinomorphic actinomorphic actinomorphic** actinomorphic** actinomorphic* actinomorphic** zygomorphic zygomorphic** equivocal (high rate) zygomorphic** actinomorphic (high rate) actinomorphic actinomorphic** actinomorphic** actinomorphic** actinomorphic** Maximum Likelihood (Mk1 model) Maximum Likelihood (Mk2 model) Parsimony Both "full" and "part" Mk1 Likelihood (full) Mk1 Likelihood (part) Mk2 Likelihood (full) Mk2 Likelihood (part) free free** free* free** free* free, fused fused** fused** fused** fused* fused free** fused** fused* fused* free free* free* free* free* free free** free* free** free* fused fused** fused** fused** fused** free free** equivocal (high rate) free** equivocal (high rate) free free** free** free** free** fused fused** fused** fused** fused** free, fused free* equivocal (high rate) free* equivocal (high rate) free, fused fused* fused fused fused* free free* free* free* free* free, fused free** free** equivocal (high rate) fused free* fused* free* fused free free** equivocal (high rate) free** equivocal (high rate) free, fused free* free* free* free* fused fused fused** fused fused* fused free* equivocal (high rate) free* equivocal (high rate) free free* equivocal (high rate) free* equivocal (high rate) free free* free free* free fused fused** fused** fused** fused** fused fused** fused** fused** fused** fused fused** fused** fused** fused** free free* equivocal (high rate) free* equivocal (high rate) free, fused free** equivocal (high rate) free** equivocal (high rate) free, fused free* free* free* free* fused fused** fused** fused** fused** fused free** equivocal (high rate) free** equivocal (high rate) free, fused free* equivocal (high rate) free* equivocal (high rate) fused fused** fused** fused** fused** fused fused** fused** fused** fused** free free** equivocal (high rate) free** equivocal (high rate) free free** free* free** free* free free** equivocal (high rate) free** equivocal (high rate) free free** equivocal (high rate) free** equivocal (high rate) free, fused fused* equivocal (high rate) fused* equivocal (high rate) fused free* equivocal (high rate) free equivocal (high rate) free free* equivocal (high rate) free equivocal (high rate) free free* equivocal (high rate) free** equivocal (high rate) free free* free* free* free* free free* free* free* free* free free* free* free* free* free, fused free* equivocal (high rate) free* equivocal (high rate) free, fused free** free* free** free free free** free** free** free* free free** free** free** free* free free* equivocal (high rate) free** equivocal (high rate) fused fused* fused** fused* fused** free, fused free* equivocal (high rate) free* equivocal (high rate) fused free* equivocal (high rate) free* equivocal (high rate) fused fused** fused** fused** fused** fused fused* equivocal (high rate) fused* equivocal (high rate) fused fused** fused* fused** fused* free free** equivocal (high rate) free** equivocal (high rate) Maximum Likelihood (Mk1 model) Maximum Likelihood (Mk2 model) free, fused free* free* free* free* free free* free* free* free free free* free* free* free fused fused** fused** fused* fused free, fused fused* fused** fused* free** fused fused** fused** fused** fused** free free** free* free* free* free free** free** free** free* free, fused free* free* free* free** fused fused** fused** fused** fused** free free** free** free** free* free free** free* free** free fused fused* fused** fused** fused fused fused** fused** fused** fused** free free** free** free** free (high rate) free free** free** free** free* free free** free** free** free (high rate) free free** free** free** free* free, fused fused* fused fused* free free, fused free** free* free* free* free free** free** free** free (high rate) free free** free** free** free* free free* free* free* free* free free* free* free* free** free free* free* free* free* free, fused free** free** free* free (high rate) free, fused free** free** free** free* free free** free** free** free** free free** free** free** free** free free** free** free** free* fused fused fused** fused free** free free** free** free** free free free** free* free* free fused fused** fused** fused** fused** free, fused fused fused equivocal free free, fused fused fused fused fused free free** free** free** free** Parsimony Both "full" and "part" Mk1 Likelihood (full) Mk1 Likelihood (part) Mk2 Likelihood (full) Mk2 Likelihood (part) whorled whorled** whorled** whorled* whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** spiral spiral** whorled spiral** whorled whorled whorled** whorled** whorled* whorled* whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled* spiral** whorled* whorled whorled** whorled** spiral** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** spiral** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** spiral** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled, spiral whorled** whorled** spiral** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled whorled** whorled whorled** whorled** whorled** whorled* whorled whorled** whorled** spiral** whorled* whorled whorled** whorled** spiral** whorled* whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** Maximum Likelihood (Mk1 model) Maximum Likelihood (Mk2 model) whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** spiral** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** spiral** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled, spiral whorled** whorled** spiral* whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled whorled** whorled whorled** whorled** whorled** whorled* whorled whorled** whorled** spiral** whorled* whorled whorled** whorled** spiral** whorled* whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** whorled whorled** whorled** whorled** whorled** Parsimony Both "full" and "part" Mk1 Likelihood (full) Mk1 Likelihood (part) Mk2 Likelihood (full) Mk2 Likelihood (part) non-penta non-penta** non-penta** non-penta** non-penta** pentamerous pentamerous** pentamerous** pentamerous** pentamerous* pentamerous pentamerous** pentamerous** pentamerous** pentamerous* non-penta non-penta** non-penta** non-penta** non-penta** non-penta non-penta** non-penta** non-penta** non-penta** pentamerous pentamerous** pentamerous** pentamerous** pentamerous* ? ? ? ? ? pentamerous ? ? ? ? pentamerous pentamerous** pentamerous** pentamerous** pentamerous* pentamerous pentamerous** pentamerous** pentamerous** pentamerous pentamerous pentamerous** pentamerous** pentamerous** pentamerous* non-penta non-penta** non-penta** non-penta* non-penta* non-penta non-penta** non-penta** non-penta** non-penta* pentamerous pentamerous** pentamerous** pentamerous** pentamerous* pentamerous pentamerous** pentamerous** pentamerous** pentamerous* non-penta non-penta** non-penta** non-penta** non-penta** pentamerous pentamerous** pentamerous** pentamerous** pentamerous* pentamerous pentamerous** pentamerous* pentamerous** pentamerous* pentamerous pentamerous** pentamerous* pentamerous** pentamerous* non-penta non-penta** non-penta** non-penta** non-penta** pentamerous pentamerous** pentamerous** pentamerous** pentamerous* pentamerous pentamerous** pentamerous** pentamerous** pentamerous* pentamerous pentamerous** pentamerous** pentamerous** pentamerous* pentamerous pentamerous** pentamerous** pentamerous** pentamerous* non-penta pentamerous pentamerous* pentamerous pentamerous non-penta, pentamerous non-penta* non-penta* non-penta* non-penta* pentamerous pentamerous** pentamerous** pentamerous** pentamerous* pentamerous pentamerous** pentamerous** pentamerous** pentamerous* pentamerous pentamerous** pentamerous* pentamerous** pentamerous* pentamerous pentamerous* pentamerous* pentamerous** pentamerous* pentamerous pentamerous** pentamerous** pentamerous** pentamerous* non-penta non-penta** non-penta** non-penta** non-penta* non-penta non-penta** non-penta** non-penta** non-penta** non-penta non-penta** non-penta** non-penta** non-penta* pentamerous pentamerous** pentamerous** pentamerous** pentamerous* pentamerous pentamerous** pentamerous** pentamerous** pentamerous* pentamerous pentamerous** pentamerous* pentamerous** pentamerous non-penta non-penta** non-penta** non-penta** non-penta* pentamerous pentamerous** pentamerous** pentamerous** pentamerous* non-penta non-penta** non-penta** non-penta** non-penta** pentamerous pentamerous* pentamerous* pentamerous* pentamerous* non-penta non-penta** non-penta** non-penta* non-penta* non-penta non-penta** non-penta** non-penta** non-penta** non-penta non-penta** non-penta** non-penta** non-penta** non-penta, pentamerous non-penta* non-penta** non-penta* non-penta* non-penta non-penta** non-penta** non-penta** pentamerous pentamerous** pentamerous* pentamerous** pentamerous pentamerous* pentamerous* pentamerous** pentamerous pentamerous** pentamerous** pentamerous** pentamerous pentamerous** pentamerous** pentamerous** pentamerous pentamerous** pentamerous** pentamerous** pentamerous pentamerous* pentamerous* pentamerous* non-penta non-penta** non-penta** non-penta** pentamerous pentamerous** pentamerous* pentamerous** pentamerous* differentiated differentiated** differentiated** differentiated** differentiated** non-penta** differentiated differentiated** differentiated* differentiated differentiated* pentamerous* differentiated differentiated** differentiated** differentiated** differentiated** pentamerous* differentiated differentiated** differentiated** differentiated** differentiated** pentamerous* differentiated differentiated** differentiated** differentiated** differentiated** pentamerous* differentiated differentiated** differentiated** differentiated** differentiated** pentamerous* differentiated differentiated** differentiated** differentiated** differentiated* pentamerous differentiated differentiated* differentiated* undifferentiated* undifferentiated non-penta* Maximum Likelihood (Mk1 model) Maximum Likelihood (Mk2 model) pentamerous pentamerous** pentamerous* pentamerous** pentamerous non-penta non-penta pentamerous pentamerous** non-penta non-penta non-penta** non-penta** non-penta** non-penta** pentamerous pentamerous** pentamerous** pentamerous** pentamerous* pentamerous pentamerous** pentamerous** pentamerous** pentamerous* pentamerous pentamerous** pentamerous** pentamerous** pentamerous* pentamerous pentamerous** pentamerous** pentamerous** pentamerous* non-penta non-penta* pentamerous pentamerous non-penta* non-penta, pentamerous non-penta* non-penta* non-penta* non-penta* pentamerous pentamerous** pentamerous* pentamerous** pentamerous pentamerous pentamerous** pentamerous** pentamerous** non-penta pentamerous pentamerous** pentamerous* pentamerous** pentamerous* pentamerous pentamerous* pentamerous* pentamerous** pentamerous* pentamerous pentamerous** pentamerous** pentamerous** pentamerous* non-penta non-penta** non-penta** non-penta** non-penta** non-penta non-penta** non-penta** non-penta** non-penta** non-penta non-penta** non-penta** non-penta** non-penta** pentamerous pentamerous** pentamerous** pentamerous** pentamerous* pentamerous pentamerous** pentamerous* pentamerous** pentamerous pentamerous pentamerous** pentamerous* pentamerous** non-penta non-penta non-penta** non-penta** non-penta** non-penta** pentamerous pentamerous** pentamerous** pentamerous** equivocal non-penta non-penta** non-penta** non-penta** non-penta** pentamerous pentamerous* pentamerous* pentamerous** pentamerous* non-penta non-penta** non-penta** non-penta* non-penta* non-penta non-penta** non-penta** non-penta** non-penta** non-penta non-penta** non-penta** non-penta** non-penta** non-penta non-penta** non-penta** non-penta* non-penta* non-penta non-penta** non-penta** non-penta** non-penta* non-penta pentamerous* pentamerous* pentamerous** non-penta* non-penta, pentamerous non-penta* pentamerous pentamerous** pentamerous pentamerous pentamerous** pentamerous* pentamerous** non-penta* pentamerous pentamerous* pentamerous* pentamerous** non-penta pentamerous pentamerous** pentamerous** pentamerous** pentamerous* pentamerous pentamerous* pentamerous pentamerous* pentamerous non-penta non-penta** non-penta** non-penta** non-penta** pentamerous pentamerous** pentamerous* pentamerous** pentamerous* Parsimony Both "full" and "part" Mk1 Likelihood (full) Mk1 Likelihood (part) Mk2 Likelihood (full) Mk2 Likelihood (part) undifferentiated differentiated* undifferentiated undifferentiated** undifferentiated differentiated differentiated** differentiated** differentiated** differentiated** differentiated differentiated** differentiated** differentiated** differentiated** undifferentiated, differentiated differentiated* differentiated undifferentiated* differentiated undifferentiated, differentiated differentiated* equivocal undifferentiated** Maximum Likelihood (Mk1 model) Maximum Likelihood (Mk2 model) Parsimony State for q=0.0001 State probability State for q=0.001 State probability State for q=0.01 non-penta non-penta 1 non-penta 1 non-penta pentamerous pentamerous 1 pentamerous 1 pentamerous pentamerous pentamerous 1 pentamerous 1 pentamerous non-penta non-penta 1 non-penta 1 non-penta non-penta non-penta 1 non-penta 1 non-penta pentamerous pentamerous 1 pentamerous 1 pentamerous pentamerous pentamerous 1 pentamerous 1 pentamerous pentamerous pentamerous 0.99 pentamerous 0.94 pentamerous non-penta non-penta 1 non-penta 1 non-penta pentamerous pentamerous 1 pentamerous 1 pentamerous Parsimony State for q=0.0001 State probability State for q=0.001 State probability State for q=0.01 non-penta non-penta 1 non-penta 1 non-penta non-penta non-penta 0.99 non-penta 0.84 pentamerous non-penta, pentamerous non-penta 0.84 non-penta 0.82 non-penta pentamerous pentamerous 1 pentamerous 1 pentamerous pentamerous pentamerous 1 pentamerous 0.99 pentamerous pentamerous pentamerous 1 pentamerous 1 pentamerous pentamerous pentamerous 0.99 pentamerous 0.94 pentamerous non-penta non-penta 1 non-penta 1 non-penta Parsimony State for q=0.0001 State probability State for q=0.001 State probability State for q=0.01 undifferentiated undifferentiated 1 undifferentiated 0.75 differentiated differentiated differentiated 1 differentiated 1 differentiated differentiated differentiated 1 differentiated 1 differentiated undifferentiated, differentiated differentiated 0.74 differentiated 0.81 differentiated undifferentiated, differentiated undifferentiated 0.91 undifferentiated 0.63 differentiated differentiated differentiated 1 differentiated 1 differentiated differentiated differentiated 1 differentiated 1 differentiated differentiated differentiated 1 differentiated 1 differentiated Parsimony State for q=0.0001 State probability State for q=0.001 State probability State for q=0.01 undifferentiated undifferentiated 1 undifferentiated 0.82 differentiated differentiated differentiated 1 differentiated 1 differentiated differentiated differentiated 1 differentiated 1 differentiated Angiosperms ANA+Mangoliidae Monocotyledoneae Basal eudicots Superrosidae+Dillenales 0.95 0.96 0.99 0.98 State probability 0.99 0.96 0.94 0.98 0.64 0.9 State probability 0.99 0.73 0.51 0.86 0.82 0.98 0.61 State probability 0.85 0.98 0.74 0.73 0.87 0.94 0.99 State probability 0.82 0.99 0.98 Superasteridae equivocal (high rate) equivocal (high rate) equivocal (high rate) equivocal (high rate) State for q=0.1 equivocal (high rate) 1 equivocal (high rate) equivocal (high rate) equivocal (high rate) 1 equivocal (high rate) 1 equivocal (high rate) equivocal (high rate) equivocal (high rate) 1 equivocal (high rate) equivocal (high rate) State for q=0.1 equivocal (high rate) equivocal (high rate) equivocal (high rate) equivocal (high rate) equivocal (high rate) equivocal (high rate) equivocal (high rate) 1 equivocal (high rate) State for q=0.1 equivocal (high rate) 1 equivocal (high rate) equivocal (high rate) equivocal (high rate) equivocal (high rate) equivocal (high rate) equivocal (high rate) differentiated (high rate) 0.54 0.5 0.5 0.5 0.5 State probability 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 State probability 0.5 0.5 0.5 0.5 0.5 0.5 0.5 State probability 0.5 0.5 0.5 0.5 0.5 0.5 0.5 State for q=0.1 State probability equivocal (high rate) equivocal (high rate) 0.5 equivocal (high rate) Mixed partions Angiosperms ANA+Mangoliidae Monocotyledoneae Basal eudicots Superrosidae+Dillenales Superasteridae Mixed partions Angiosperms ANA+Mangoliidae Monocotyledoneae Basal eudicots Superrosidae+Dillenales Superasteridae Mixed partitions Angiosperms ANA+Mangoliidae Monocotyledoneae Basal eudicots Superrosidae+Dillenales Superasteridae Mixed partions Angiosperms ANA+Mangoliidae Monocotyledoneae Basal eudicots Superrosidae+Dillenales Superasteridae Mixed partions 0.5 differentiated differentiated 1 differentiated 1 differentiated 0.99 equivocal (high rate) 209 3 40 23 55 88 212 19 38 16 77 61 30 11 0 12 4 3 227 6 1 9 103 107 165 20 43 14 54 33 0.5 differentiated differentiated 1 differentiated 1 differentiated 0.87 equivocal (high rate) 0,0064 0,0008 0,1041 0,2640 0,0043 0,0084 0,0102 7,1730 0,0149 0,0090 0,0717 0,0059 0,0006 0,0035 0,0000 0,0050 0,0002 0,0002 0,0069 0,0024 0,0001 0,0042 0,0117 0,0110 0,0042 0,0139 0,0130 0,0057 0,0037 0,0021 0.5 differentiated differentiated 1 differentiated 1 differentiated 0.94 equivocal (high rate) -691,03 -14,41 -114,34 -68,61 -189,38 -279,59 -666,33 -550,34 -45,05 -93,93 -56,13 -158,64 -176,43 -530,18 -149,96 -35,07 -0,69 -39,30 -23,85 -18,74 -117,65 -658,73 -21,56 -7,43 -34,05 -251,51 -284,84 -599,39 -524,02 -39,05 -104,21 -42,52 -177,89 -132,72 -496,39 0.5 differentiated differentiated 1 differentiated 1 differentiated 0.99 differentiated (high rate) 0.54 1384,06 30,82 230,68 139,22 380,76 561,18 1342,66 1102,68 92,10 189,86 114,26 319,28 354,86 1070,36 301,92 72,14 3,38 80,60 49,70 39,48 245,30 1319,46 45,12 16,86 70,10 505,02 571,68 1208,78 1050,04 80,10 210,42 87,04 357,78 267,44 1002,78 0.5 differentiated differentiated 1 differentiated 1 differentiated 1 equivocal (high rate) 0.5 0,0061 0,0058 0,0663 0,0116 0,0044 0,01 0,0108 4,0140 0,0127 0,0071 0,0717 0,0106 0,0003 0,0034 0,0000 0,0034 0,0008 0,0002 0,0028 0,0041 0,0005 0,0020 0,0250 0,0421 0,0095 0,0144 0,0136 0,0022 0,0106 0,0100 0.5 pentamerous pentamerous 1 pentamerous 1 pentamerous 1 equivocal (high rate) 0.5 pentamerous pentamerous 1 pentamerous 1 pentamerous 0.82 equivocal (high rate) 0.5 differentiated differentiated 1 differentiated 1 differentiated 1 equivocal (high rate) 0.5 differentiated differentiated 1 differentiated 1 differentiated 0.98 equivocal (high rate) 0.5 0,0257 0,1116 0,1294 0,0341 0,0217 0,03 0,0093 7,8470 0,0194 0,0435 0,0709 0,0057 0,0146 0,0030 0,0000 0,0179 0,0719 0,0182 0,0074 0,0224 0,0719 0,0139 0,0136 0,0165 0,0029 0,0136 0,0125 0,0060 0,0036 0,0014 undifferentiated differentiated differentiated** differentiated** differentiated** ? ? ? ? ? ? ? ? ? pentamerous pentamerous 1 pentamerous 1 pentamerous 0.91 equivocal (high rate) 0.5 undifferentiated, differentiated undifferentiated 0.96 undifferentiated 0.59 differentiated 0.79 equivocal (high rate) 0.5 undifferentiated, differentiated differentiated 0.74 differentiated 0.75 differentiated 0.72 equivocal (high rate) 0.5 0,24 0,05 0,51 0,34 0,20 0,28 0,86 0,51 0,65 0,16 0,99 0,54 0,02 0,88 695370,37 0,19 0,01 0,01 0,38 0,18 0,01 0,14 0,54 0,39 0,31 0,94 0,92 0,37 0,34 0,14 differentiated** undifferentiated, differentiated differentiated* equivocal undifferentiated** equivocal differentiated differentiated* differentiated* differentiated* differentiated differentiated differentiated** differentiated** differentiated** differentiated** differentiated differentiated** differentiated** differentiated** differentiated** differentiated differentiated** differentiated** differentiated** differentiated** differentiated differentiated** differentiated** differentiated* differentiated** differentiated differentiated** differentiated undifferentiated** differentiated differentiated differentiated** differentiated** differentiated* undifferentiated differentiated differentiated** differentiated** differentiated** differentiated** differentiated differentiated** differentiated** differentiated differentiated* differentiated differentiated** differentiated** differentiated** differentiated** differentiated differentiated** differentiated** differentiated** differentiated** differentiated differentiated** differentiated** undifferentiated* undifferentiated undifferentiated undifferentiated undifferentiated undifferentiated** undifferentiated differentiated differentiated** differentiated** differentiated** differentiated** differentiated differentiated** differentiated** differentiated** differentiated** differentiated differentiated** differentiated** differentiated** differentiated** differentiated differentiated** differentiated** differentiated* differentiated* undifferentiated undifferentiated* undifferentiated* undifferentiated** undifferentiated* differentiated differentiated** differentiated** differentiated* differentiated* differentiated differentiated** differentiated** differentiated** differentiated** differentiated differentiated** differentiated** differentiated** differentiated** differentiated differentiated* differentiated* equivocal differentiated differentiated differentiated** differentiated** differentiated** differentiated** differentiated differentiated** differentiated** differentiated** differentiated** undifferentiated differentiated* differentiated undifferentiated** equivocal undifferentiated, differentiated differentiated* differentiated* undifferentiated** differentiated undifferentiated differentiated** differentiated* undifferentiated* differentiated differentiated differentiated** differentiated** differentiated** differentiated** differentiated differentiated** differentiated** differentiated** differentiated** differentiated differentiated** differentiated** differentiated** differentiated** undifferentiated differentiated* differentiated undifferentiated** differentiated differentiated differentiated** differentiated** differentiated** differentiated** undifferentiated undifferentiated** undifferentiated* undifferentiated** undifferentiated* differentiated differentiated* differentiated** differentiated* differentiated* differentiated differentiated* differentiated undifferentiated differentiated undifferentiated differentiated undifferentiated undifferentiated** undifferentiated differentiated differentiated** differentiated* undifferentiated** differentiated* differentiated differentiated** differentiated** undifferentiated differentiated** differentiated differentiated** differentiated** undifferentiated* differentiated** pentamerous ? ? ? ? ? ? ? ? pentamerous pentamerous 1 pentamerous 1 pentamerous 0.97 equivocal (high rate) 0.5 pentamerous pentamerous 1 pentamerous 1 pentamerous 0.96 equivocal (high rate) 0.5 pentamerous pentamerous 1 pentamerous 1 pentamerous 0.97 equivocal (high rate) 0.5 non-penta non-penta 1 non-penta 1 non-penta 0.72 equivocal (high rate) 0.5 non-penta non-penta 1 non-penta 1 non-penta 0.95 equivocal (high rate) 0.5 pentamerous pentamerous 1 pentamerous 1 pentamerous 1 equivocal (high rate) 0.5 pentamerous pentamerous 1 pentamerous 1 pentamerous 0.88 equivocal (high rate) 0.5 non-penta non-penta 1 non-penta 1 non-penta 1 equivocal (high rate) 0.5 pentamerous pentamerous 1 pentamerous 1 pentamerous 0.93 equivocal (high rate) 0.5 pentamerous pentamerous 1 pentamerous 1 pentamerous 0.92 equivocal (high rate) 0.5 pentamerous pentamerous 1 pentamerous 1 pentamerous 0.87 equivocal (high rate) 0.5 non-penta non-penta 1 non-penta 1 non-penta 0.96 equivocal (high rate) 0.5 pentamerous pentamerous 1 pentamerous 1 pentamerous 0.97 equivocal (high rate) 0.5 pentamerous pentamerous 1 pentamerous 1 pentamerous 1 equivocal (high rate) 0.5 pentamerous pentamerous 1 pentamerous 0.99 pentamerous 0.93 equivocal (high rate) 0.5 pentamerous pentamerous 1 pentamerous 1 pentamerous 0.98 equivocal (high rate) 0.5 non-penta non-penta 0.99 non-penta 0.89 pentamerous 0.68 equivocal (high rate) 0.5 non-penta, pentamerous non-penta 1 non-penta 0.98 non-penta 0.83 non-penta (high rate) 0.51 pentamerous pentamerous 1 pentamerous 1 pentamerous 0.97 equivocal (high rate) 0.5 pentamerous pentamerous 1 pentamerous 1 pentamerous 0.96 equivocal (high rate) 0.5 pentamerous pentamerous 1 pentamerous 1 pentamerous 0.93 equivocal (high rate) 0.5 pentamerous pentamerous 1 pentamerous 0.97 pentamerous 0.74 equivocal (high rate) 0.5 pentamerous pentamerous 1 pentamerous 1 pentamerous 0.98 equivocal (high rate) 0.5 non-penta non-penta 1 non-penta 1 non-penta 0.99 equivocal (high rate) 0.5 non-penta non-penta 1 non-penta 1 non-penta 0.99 equivocal (high rate) 0.5 non-penta non-penta 1 non-penta 1 non-penta 0.94 equivocal (high rate) 0.5 pentamerous pentamerous 1 pentamerous 1 pentamerous 1 equivocal (high rate) 0.5 pentamerous pentamerous 1 pentamerous 1 pentamerous 0.97 equivocal (high rate) 0.5 pentamerous pentamerous 1 pentamerous 1 pentamerous 0.91 equivocal (high rate) 0.5 non-penta non-penta 1 non-penta 1 non-penta 0.9 equivocal (high rate) 0.5 pentamerous pentamerous 1 pentamerous 1 pentamerous 0.98 equivocal (high rate) 0.5 non-penta non-penta 1 non-penta 1 non-penta 0.96 equivocal (high rate) 0.5 pentamerous pentamerous 1 pentamerous 0.96 pentamerous 0.71 equivocal (high rate) 0.5 non-penta non-penta 1 non-penta 1 non-penta 0.87 equivocal (high rate) 0.5 non-penta non-penta 1 non-penta 1 non-penta 0.96 equivocal (high rate) 0.5 non-penta non-penta 1 non-penta 1 non-penta 1 equivocal (high rate) 0.5 non-penta, pentamerous non-penta 0.97 non-penta 0.97 non-penta 0.8 equivocal (high rate) 0.5 non-penta non-penta 1 non-penta 1 non-penta 0.95 equivocal (high rate) 0.5 pentamerous pentamerous 1 pentamerous 1 pentamerous 0.92 equivocal (high rate) 0.5 non-penta non-penta 1 non-penta 1 non-penta 0.94 equivocal (high rate) 0.5 non-penta non-penta 1 non-penta 1 non-penta 1 equivocal (high rate) 0.5 pentamerous pentamerous 1 pentamerous 1 pentamerous 0.99 equivocal (high rate) 0.5 ? ? ? ? ? ? ? ? ? non-penta, pentamerous ? ? ? ? ? ? ? ? pentamerous pentamerous 1 pentamerous 1 pentamerous 0.97 equivocal (high rate) 0.5 pentamerous pentamerous 1 pentamerous 1 pentamerous 0.85 equivocal (high rate) differentiated differentiated 0.99 differentiated 0.92 differentiated 0.58 equivocal (high rate) 0.5 differentiated differentiated 1 differentiated 1 differentiated 0.99 equivocal (high rate) 0.5 differentiated differentiated 1 differentiated 1 differentiated 1 equivocal (high rate) 0.5 differentiated differentiated 1 differentiated 1 differentiated 0.97 equivocal (high rate) 0.5 differentiated differentiated 1 differentiated 1 differentiated 0.83 equivocal (high rate) 0.5 differentiated differentiated 0.85 differentiated 0.65 differentiated 0.9 equivocal (high rate) 0.5 differentiated differentiated 1 differentiated 1 differentiated 0.9 equivocal (high rate) 0.5 undifferentiated, differentiated undifferentiated 0.91 undifferentiated 0.7 differentiated 0.68 equivocal (high rate) 0.5 differentiated differentiated 1 differentiated 1 differentiated 1 equivocal (high rate) -612,85 -11,91 -105,67 -64,78 -169,21 -248,46 -600,03 -549,44 -41,60 -91,99 -46,02 -158,63 -174,69 -512,93 -123,39 -36,06 0,00 -34,50 -22,24 -17,22 -646,16 -19,90 -6,08 -29,38 -241,21 -261,06 -557,63 -501,41 -39,03 -104,14 -41,91 -173,76 -124,44 -483,28 -110,02 0.5 undifferentiated undifferentiated 0.97 undifferentiated 0.68 differentiated 0.78 equivocal (high rate) 1229,70 27,82 215,34 133,56 342,42 500,92 1220,06 1102,88 87,20 187,98 96,04 321,26 353,38 1045,86 250,78 76,12 4,00 73,00 48,48 38,44 240,04 1296,32 43,80 16,16 62,76 486,42 526,12 1135,26 1006,82 82,06 212,28 87,82 351,52 252,88 986,56 0.5 differentiated differentiated 0.99 differentiated 0.92 differentiated 0.58 equivocal (high rate) 154,36 3,00 15,34 5,66 38,34 60,26 122,60 0,20 4,90 1,88 18,22 1,98 1,48 24,50 51,14 3,98 0,62 7,60 1,22 1,04 5,26 23,14 1,32 0,70 7,34 18,60 45,56 73,52 43,22 1,96 1,86 0,78 6,26 14,56 16,22 0.5 differentiated differentiated 1 differentiated 1 differentiated 0.99 equivocal (high rate) Delta AIC Angio-mixed (Mk1)= 32,32 Delta AIC Angio-mixed (Mk1)= 56,62 Delta AIC Angio-mixed (Mk1)= 110,68 Delta AIC Angio-mixed (Mk1)= 47,26 0.5 Brassicales differentiated differentiated 1 differentiated 1 differentiated 1 equivocal (high rate) Delta AIC angio-mixed (Mk2)= 9,64 Delta AIC Angio-mixed (Mk2)= 57,02 Delta AIC Angio-mixed (Mk2)= 10,74 Delta AIC Angio-mixed (Mk2)= 161,06 Delta AIC Angio-mixed (Mk2)= 20,26 0.5 Bruniales differentiated differentiated 1 differentiated 1 differentiated 0.97 equivocal (high rate) 0.5 too high for state inferrence too high for state inferrence no state changes in clade 0.5 Bruniales pentamerous pentamerous 1 pentamerous 1 pentamerous 0.97 equivocal (high rate) 0.5 Buxales non-penta non-penta 1 non-penta 1 non-penta 0.74 equivocal (high rate) Celastrales differentiated differentiated 1 differentiated 1 differentiated 0.95 equivocal (high rate) 0.5 Commelinales differentiated differentiated 1 differentiated 1 differentiated 0.97 equivocal (high rate) 0.5 Buxales differentiated differentiated 1 differentiated 1 differentiated 0.82 equivocal (high rate) 0.5 Canellales differentiated differentiated 0.85 differentiated 0.58 differentiated 0.88 equivocal (high rate) 0.5 ORIGINAL DATA Angiosperms ANA+Mangoliidae Monocotyledoneae Basal eudicots Superrosidae+Dillenales Superasteridae Mixed total ORIGINAL DATA Angiosperms ANA+Mangoliidae Monocotyledoneae Basal eudicots Superrosidae+Dillenales Superasteridae Mixed partions ORIGINAL DATA Angiosperms ANA+Mangoliidae Monocotyledoneae Basal eudicots Superrosidae+Dillenales Superasteridae Mixed partitions ORIGINAL DATA Angiosperms ANA+Mangoliidae Monocotyledoneae Basal eudicots Superrosidae+Dillenales Superasteridae Mixed partions ORIGINAL DATA Angiosperms ANA+Mangoliidae Monocotyledoneae Basal eudicots Superrosidae+Dillenales Superasteridae Mixed partions 0.5 Canellales non-penta non-penta 1 non-penta 1 non-penta 0.97 equivocal (high rate) Cornales differentiated differentiated 1 differentiated 1 differentiated 0.98 equivocal (high rate) 0.5 Caryophyllales differentiated differentiated 1 differentiated 1 differentiated 0.9 equivocal (high rate) 0.5 Parsi steps 190 3 38 20 54 75 Parsi steps 154 13 34 6 53 47 Parsi steps 28 11 0 11 3 3 Parsi steps 199 3 1 7 89 98 Parsi steps 161 19 42 14 53 32 0.5 Caryophyllales pentamerous pentamerous 1 pentamerous 1 pentamerous 0.99 equivocal (high rate) 0.5 Celastrales pentamerous pentamerous 1 pentamerous 1 pentamerous 0.86 equivocal (high rate) 0.5 Commelinales non-penta non-penta 1 non-penta 1 non-penta 1 equivocal (high rate) 0.5 Cornales pentamerous pentamerous 1 pentamerous 0.97 pentamerous 0.86 equivocal (high rate) 0.5 Crossosomatales pentamerous pentamerous 1 pentamerous 1 pentamerous 0.91 equivocal (high rate) 0.5 Cucurbitales non-penta non-penta 0.98 non-penta 0.86 equivocal 0.5 equivocal (high rate) 0.5 Dioscoreales non-penta non-penta 1 non-penta 1 non-penta 0.96 equivocal (high rate) 0.5 Dipsacales pentamerous pentamerous 1 pentamerous 1 pentamerous 0.97 equivocal (high rate) 0.5 Ericales pentamerous pentamerous 1 pentamerous 1 pentamerous 0.99 equivocal (high rate) 0.5 Escalloniales pentamerous pentamerous 1 pentamerous 0.99 pentamerous 0.93 equivocal (high rate) 0.5 Fabales pentamerous pentamerous 1 pentamerous 1 pentamerous 0.95 equivocal (high rate) 0.5 Fagales non-penta non-penta 1 non-penta 0.99 pentamerous 0.53 equivocal (high rate) 0.5 Garryales non-penta, pentamerous non-penta 1 non-penta 0.98 non-penta 0.83 non-penta (high rate) 0.51 Gentianales pentamerous pentamerous 1 pentamerous 1 pentamerous 0.94 equivocal (high rate) Geraniales pentamerous pentamerous 1 pentamerous 1 pentamerous 0.9 equivocal (high rate) Huerteales pentamerous pentamerous 1 pentamerous 1 pentamerous 0.88 equivocal (high rate) Icacinales pentamerous pentamerous 1 pentamerous 0.97 pentamerous 0.74 equivocal (high rate) Lamiales pentamerous pentamerous 1 pentamerous 1 pentamerous 0.96 equivocal (high rate) Laurales non-penta non-penta 1 non-penta 1 non-penta 0.99 equivocal (high rate) Liliales non-penta non-penta 1 non-penta 1 non-penta 0.99 equivocal (high rate) Magnoliales non-penta non-penta 1 non-penta 1 non-penta 0.95 equivocal (high rate) Malpighiales pentamerous pentamerous 1 pentamerous 1 pentamerous 1 equivocal (high rate) Malvales pentamerous pentamerous 1 pentamerous 1 pentamerous 0.89 equivocal (high rate) Myrtales pentamerous pentamerous 1 pentamerous 1 pentamerous 0.79 equivocal (high rate) Nymphaeales non-penta non-penta 1 non-penta 1 non-penta 0.9 equivocal (high rate) Oxalidales pentamerous pentamerous 1 pentamerous 1 pentamerous 0.93 equivocal (high rate) Pandanales non-penta non-penta 1 non-penta 1 non-penta 0.96 equivocal (high rate) Paracryphiales pentamerous pentamerous 1 pentamerous 0.96 pentamerous 0.71 equivocal (high rate) Petrosaviales non-penta non-penta 1 non-penta 1 non-penta 0.87 equivocal (high rate) Piperales non-penta non-penta 1 non-penta 1 non-penta 0.97 equivocal (high rate) Santalales differentiated differentiated 1 differentiated 1 differentiated 0.98 equivocal (high rate) 0.5 Proteales differentiated differentiated 1 differentiated 1 differentiated 0.97 equivocal (high rate) 0.5 0.5 Rosales differentiated differentiated 1 differentiated 0.96 differentiated 0.78 equivocal (high rate) 0.5 Poales differentiated differentiated 1 differentiated 0.95 differentiated 0.83 equivocal (high rate) 0.5 0.5 Ranunculales differentiated differentiated 1 differentiated 1 differentiated 0.98 equivocal (high rate) 0.5 Piperales undifferentiated undifferentiated 0.98 undifferentiated 0.82 differentiated 0.62 equivocal (high rate) 0.5 0.5 Proteales differentiated differentiated 1 differentiated 1 differentiated 0.97 equivocal (high rate) 0.5 Petrosaviales differentiated differentiated 0.97 differentiated 0.8 differentiated 0.77 equivocal (high rate) 0.5 0.5 Poales differentiated differentiated 1 differentiated 0.99 differentiated 0.88 equivocal (high rate) 0.5 Paracryphiales differentiated differentiated 1 differentiated 0.96 differentiated 0.72 equivocal (high rate) 0.5 0.5 Piperales undifferentiated undifferentiated 0.98 undifferentiated 0.77 differentiated 0.63 equivocal (high rate) 0.5 Pandanales undifferentiated undifferentiated 1 undifferentiated 1 undifferentiated 0.85 equivocal (high rate) 0.5 0.5 Petrosaviales differentiated differentiated 0.97 differentiated 0.82 differentiated 0.79 equivocal (high rate) 0.5 Oxalidales differentiated differentiated 1 differentiated 1 differentiated 0.99 equivocal (high rate) 0.5 0.5 Paracryphiales differentiated differentiated 1 differentiated 0.96 differentiated 0.72 equivocal (high rate) 0.5 Nymphaeales undifferentiated undifferentiated 0.97 undifferentiated 0.66 differentiated 0.79 equivocal (high rate) 0.5 0.5 Pandanales undifferentiated undifferentiated 1 undifferentiated 1 undifferentiated 0.84 equivocal (high rate) 0.5 Myrtales differentiated differentiated 1 differentiated 1 differentiated 0.99 equivocal (high rate) 0.5 0.5 Oxalidales differentiated differentiated 1 differentiated 1 differentiated 0.99 equivocal (high rate) 0.5 Malvales differentiated differentiated 1 differentiated 1 differentiated 0.96 equivocal (high rate) 0.5 0.5 Nymphaeales undifferentiated undifferentiated 0.96 undifferentiated 0.57 differentiated 0.8 equivocal (high rate) 0.5 Malpighiales differentiated differentiated 1 differentiated 1 differentiated 1 equivocal (high rate) 0.5 0.5 Myrtales differentiated differentiated 1 differentiated 1 differentiated 0.99 equivocal (high rate) 0.5 Magnoliales undifferentiated undifferentiated 0.95 undifferentiated 0.57 differentiated 0.86 equivocal (high rate) 0.5 0.5 Malvales differentiated differentiated 1 differentiated 1 differentiated 0.96 equivocal (high rate) 0.5 Liliales undifferentiated, differentiated undifferentiated 0.94 undifferentiated 0.69 differentiated 0.78 equivocal (high rate) 0.5 0.5 Malpighiales differentiated differentiated 1 differentiated 1 differentiated 1 equivocal (high rate) 0.5 Laurales undifferentiated undifferentiated 0.96 undifferentiated 0.64 differentiated 0.76 equivocal (high rate) 0.5 0.5 Magnoliales undifferentiated undifferentiated 0.93 differentiated 0.53 differentiated 0.87 equivocal (high rate) 0.5 Lamiales differentiated differentiated 1 differentiated 1 differentiated 0.99 equivocal (high rate) 0.5 0.5 Liliales undifferentiated, differentiated undifferentiated 0.93 undifferentiated 0.61 differentiated 0.82 equivocal (high rate) 0.5 Icacinales differentiated differentiated 1 differentiated 1 differentiated 0.9 equivocal (high rate) 0.5 0.5 Laurales undifferentiated undifferentiated 0.94 undifferentiated 0.53 differentiated 0.8 equivocal (high rate) 0.5 Huerteales differentiated differentiated 0.99 differentiated 0.88 differentiated 0.61 equivocal (high rate) 0.5 0.5 Crossosomatales differentiated differentiated 1 differentiated 1 differentiated 0.92 equivocal (high rate) 0.5 Cucurbitales differentiated differentiated 0.99 differentiated 0.99 differentiated 0.86 equivocal (high rate) 0.5 Dioscoreales undifferentiated undifferentiated 1 undifferentiated 0.91 differentiated 0.59 equivocal (high rate) 0.5 Dipsacales differentiated differentiated 1 differentiated 1 differentiated 0.99 equivocal (high rate) 0.5 Ericales differentiated differentiated 1 differentiated 1 differentiated 1 equivocal (high rate) 0.5 Escalloniales differentiated differentiated 1 differentiated 1 differentiated 0.97 equivocal (high rate) 0.5 Fabales differentiated differentiated 1 differentiated 1 differentiated 0.97 equivocal (high rate) 0.5 Fagales undifferentiated undifferentiated 0.99 undifferentiated 0.89 differentiated 0.63 equivocal (high rate) 0.5 Garryales differentiated differentiated 1 differentiated 0.98 differentiated 0.82 equivocal (high rate) 0.5 Gentianales differentiated differentiated 1 differentiated 1 differentiated 0.99 equivocal (high rate) 0.5 Geraniales differentiated differentiated 1 differentiated 1 differentiated 0.98 equivocal (high rate) 0.5 Huerteales differentiated differentiated 0.99 differentiated 0.88 differentiated 0.61 equivocal (high rate) 0.5 Icacinales differentiated differentiated 1 differentiated 1 differentiated 0.9 equivocal (high rate) 0.5 Lamiales differentiated differentiated 1 differentiated 1 differentiated 0.99 equivocal (high rate) 0.5 Celastrales differentiated differentiated 1 differentiated 1 differentiated 0.95 equivocal (high rate) 0.5 Commelinales differentiated differentiated 1 differentiated 1 differentiated 0.96 equivocal (high rate) Mk1 q 0,0055 0,0008 0,1261 0,0305 0,0042 0,0064 Mk1 q 0,0072 0,0058 0,0120 0,0026 0,0112 0,0057 Mk1 q 0,0005 0,0036 0,0000 0,0045 0,0002 Mk1 q 0,0064 0,0012 0,0001 0,0032 0,0119 0,0107 Mk1 q 0,0042 0,0139 0,0130 0,0057 0,0036 0,0020 0,0002 0.5 Cornales differentiated differentiated 1 differentiated 1 differentiated 0.98 equivocal (high rate) Mk1 logLik -643,88 -14,32 -112,28 -65,35 -186,83 -248,54 -627,32 Mk1 logLik -429,57 -37,00 -85,49 -31,30 -128,23 -141,02 -423,04 Mk1 logLik -139,04 -34,08 -0,69 -35,69 -18,37 -18,74 Mk1 logLik -584,45 -13,04 -7,43 -29,16 -216,12 -256,56 -522,31 Mk1 logLik -514,86 -37,05 -102,44 -42,52 -175,52 -129,59 -487,12 -107,57 0.5 Crossosomatales differentiated differentiated 1 differentiated 1 differentiated 0.89 equivocal (high rate) Mk1 AIC 1289,76 30,64 226,56 132,70 375,66 499,08 1264,64 Mk1 AIC 861,14 76,00 172,98 64,60 258,46 284,04 856,08 Mk1 AIC 280,08 70,16 3,38 73,38 38,74 39,48 225,14 Mk1 AIC 1170,90 28,08 16,86 60,32 434,24 515,12 1054,62 Mk1 AIC 1031,72 76,10 206,88 87,04 353,04 261,18 984,24 0.5 Cucurbitales differentiated differentiated 1 differentiated 0.99 differentiated 0.86 equivocal (high rate) 0.5 Dioscoreales undifferentiated undifferentiated 1 undifferentiated 0.93 differentiated 0.56 equivocal (high rate) 0.5 Dipsacales differentiated differentiated 1 differentiated 1 differentiated 0.99 equivocal (high rate) 0.5 Ericales differentiated differentiated 1 differentiated 1 differentiated 1 equivocal (high rate) 0.5 Escalloniales differentiated differentiated 1 differentiated 1 differentiated 0.97 equivocal (high rate) 0.5 Fabales differentiated differentiated 1 differentiated 1 differentiated 0.96 equivocal (high rate) 0.5 Fagales undifferentiated undifferentiated 0.99 undifferentiated 0.89 differentiated 0.62 equivocal (high rate) 0.5 Garryales differentiated differentiated 1 differentiated 0.98 differentiated 0.82 equivocal (high rate) 0.5 Gentianales differentiated differentiated 1 differentiated 1 differentiated 0.99 equivocal (high rate) 0.5 Geraniales differentiated differentiated 1 differentiated 1 differentiated 0.98 equivocal (high rate) 0.5 Mk2 q01 0,0056 0,0060 0,0992 0,0080 0,0041 0,0074 Mk2 q10 0,0247 0,1104 0,2400 0,0314 0,0211 0,0280 symmetry ratio 0,23 0,05 0,41 0,25 0,19 0,26 Mk2 logLik -577,57 -11,80 -102,41 -59,42 -166,75 -225,53 -565,91 Mk2 AIC 1159,14 27,60 208,82 122,84 337,50 455,06 1151,82 delta AIC 130,62 3,04 17,74 9,86 38,16 44,02 112,82 Delta AIC Angio-mixed (Mk1)= 25,12 Delta AIC Angio-mixed (Mk2)= 7,32 too high for state inferrence Mk2 q01 0,0069 0,3555 0,0121 0,0028 0,0306 0,0096 Mk2 q10 0,0084 0,9481 0,0222 0,0506 0,0470 0,0028 symmetry ratio 0,82 0,37 0,55 0,06 0,65 0,29 Mk2 logLik -428,80 -32,23 -81,91 -22,80 -125,76 -138,92 -401,62 Mk2 AIC 861,60 68,46 167,82 49,60 255,52 281,84 823,24 delta AIC 0,46 7,54 5,16 15,00 2,94 2,20 32,84 Delta AIC Angio-mixed (Mk1)= 5,06 Delta AIC Angio-mixed (Mk2)= 38,36 no state changes in clade too high for state inferrence Mk2 q01 0,0002 0,0035 0,0000 0,0035 0,0005 Mk2 q01 0,0018 0,0041 0,0005 0,0013 0,0170 0,0283 Mk2 q01 0,0091 0,0143 0,0133 0,0022 0,0098 0,0090 0,0002 Mk2 q10 0,0152 0,0030 0,0000 0,0222 0,0663 Mk2 q10 0,0077 0,0537 0,0719 0,0120 0,0113 0,0128 Mk2 q10 0,0029 0,0137 0,0123 0,0060 0,0035 0,0015 0,0182 symmetry ratio 0,01 0,86 695370,37 0,16 0,01 symmetry ratio 0,23 0,08 0,01 0,11 0,66 0,45 symmetry ratio 0,32 0,96 0,92 0,37 0,36 0,17 0,01 Mk2 logLik -114,17 -34,07 0,00 -30,95 -17,53 -17,22 Mk2 logLik -563,30 -10,85 -6,08 -24,38 -213,30 -244,00 -498,61 Mk2 logLik -493,56 -37,04 -102,42 -41,91 -171,74 -122,76 -475,87 -99,77 Mk2 AIC 232,34 72,14 4,00 65,90 39,06 38,44 Mk2 AIC 1130,60 25,70 16,16 52,76 430,60 492,00 1017,22 Mk2 AIC 991,12 78,08 208,84 87,82 347,48 249,52 971,74 219,54 delta AIC 47,74 1,98 0,62 7,48 0,32 1,04 delta AIC 40,30 2,38 0,70 7,56 3,64 23,12 37,40 delta AIC 40,60 1,98 1,96 0,78 5,56 11,66 12,50 5,60 Delta AIC Angio-mixed (Mk1)= 116,28 Delta AIC Angio-mixed (Mk1)= 47,48 Delta AIC Angio-mixed (Mk1)= 54,94 Delta AIC Angio-mixed (Mk2)= 12,80 Delta AIC Angio-mixed (Mk2)= 113,38 Delta AIC Angio-mixed (Mk2)= 19,38
	ORIGINAL DATA ORIGINAL DATA	Parsimony Parsimony	Maximum Likelihood (Mk1 model) Maximum Likelihood (Mk1 model)	Maximum Likelihood (Mk2 model) Maximum Likelihood (Mk2 model)
	ORIGINAL DATA ORIGINAL DATA ORIGINAL DATA	Both "full" and "part" Parsimony Parsimony Parsimony Both "full" and "part"	Mk1 Likelihood (full) Mk1 Likelihood (part) Mk2 Likelihood (full) Mk2 Likelihood (part) Maximum Likelihood (Mk1 model) Maximum Likelihood (Mk2 model) Maximum Likelihood (Mk1 model) Maximum Likelihood (Mk2 model) Maximum Likelihood (Mk1 model) Maximum Likelihood (Mk2 model) Mk1 Likelihood (full) Mk1 Likelihood (part) Mk2 Likelihood (full) Mk2 Likelihood (part)
	Alismatales Alismatales	actinomorphic Both "full" and "part" Both "full" and "part" Both "full" and "part" undifferentiated	actinomorphic** Mk1 Likelihood (full) Mk1 Likelihood (full) Mk1 Likelihood (full) differentiated*	equivocal (high rate) actinomorphic* Mk1 Likelihood (part) Mk2 Likelihood (full) Mk1 Likelihood (part) Mk2 Likelihood (full) Mk1 Likelihood (part) Mk2 Likelihood (full) undifferentiated undifferentiated**	actinomorphic (high rate) Mk2 Likelihood (part) Mk2 Likelihood (part) Mk2 Likelihood (part) undifferentiated
	Apiales Alismatales Alismatales Alismatales Apiales	actinomorphic free whorled non-penta differentiated	actinomorphic** free** whorled** non-penta** differentiated**	actinomorphic** free** whorled** non-penta** differentiated**	actinomorphic* free** whorled* non-penta** differentiated**		actinomorphic* free* whorled** non-penta** differentiated**
	Aquifoliales Apiales Apiales Apiales Aquifoliales	actinomorphic free whorled pentamerous differentiated	actinomorphic** free whorled** pentamerous** differentiated**	actinomorphic** free whorled** pentamerous** differentiated**	actinomorphic* fused whorled** pentamerous** differentiated**		actinomorphic* free** whorled** pentamerous* differentiated**
	Arecales Aquifoliales Aquifoliales Aquifoliales Arecales	actinomorphic fused whorled pentamerous undifferentiated, differentiated	actinomorphic** fused* whorled** pentamerous** differentiated*	equivocal (high rate) actinomorphic* fused** fused** whorled** whorled** pentamerous** pentamerous** differentiated undifferentiated*		actinomorphic (high rate) free** whorled** pentamerous* differentiated
	Asparagales Arecales Arecales Arecales Asparagales	actinomorphic free whorled non-penta undifferentiated, differentiated	actinomorphic** free** whorled** non-penta** differentiated*	equivocal (high rate) zygomorphic free* free** whorled** whorled** non-penta** non-penta** undifferentiated undifferentiated**	actinomorphic (high rate) free* whorled** non-penta** undifferentiated
	Asterales Asparagales Asparagales Asparagales Asterales	actinomorphic free whorled non-penta differentiated	actinomorphic** free** whorled** non-penta** differentiated**	actinomorphic** free** whorled** non-penta** differentiated**	actinomorphic* free** whorled** non-penta** differentiated**		actinomorphic* free* whorled** non-penta** differentiated**
	Austrobaileyales Asterales Asterales Asterales Austrobaileyales	actinomorphic fused whorled pentamerous undifferentiated	actinomorphic** fused** whorled** pentamerous** differentiated*	actinomorphic** fused** whorled** pentamerous** undifferentiated	actinomorphic* fused** whorled** pentamerous** undifferentiated**	actinomorphic** fused whorled** pentamerous* undiffrentiated
	Berberidopsidales Austrobaileyales Austrobaileyales Austrobaileyales Berberidopsidales	actinomorphic free spiral ? differentiated	actinomorphic** free** spiral** ? differentiated*	actinomorphic** free** whorled ? differentiated*	actinomorphic** free** spiral** ? differentiated*		actinomorphic** free (high rate) whorled ? differentiated
	Boraginales Berberidopsidales Berberidopsidales Berberidopsidales Boraginales	actinomorphic free whorled non-penta, pentamerous differentiated	actinomorphic** free** whorled** ? differentiated**	actinomorphic** free** whorled** ? differentiated**	zygomorphic free** whorled* ? differentiated**		actinomorphic free** whorled* ? differentiated**
	Brassicales Boraginales Boraginales Boraginales Brassicales	actinomorphic fused whorled pentamerous differentiated	actinomorphic** fused** whorled** pentamerous** differentiated**	actinomorphic** fused** whorled** pentamerous** differentiated**	actinomorphic* fused** whorled** pentamerous** differentiated**		actinomorphic fused** whorled** pentamerous* differentiated**
	Bruniales Brassicales Brassicales Brassicales Bruniales	actinomorphic free whorled pentamerous differentiated	actinomorphic** free** whorled** pentamerous** differentiated**	actinomorphic** free** whorled** pentamerous* differentiated**	actinomorphic* free** whorled** pentamerous** differentiated**		actinomorphic* free* whorled** non-penta differentiated**
	Buxales Bruniales Bruniales Bruniales Buxales	actinomorphic free, fused whorled pentamerous differentiated	actinomorphic** fused* whorled** pentamerous** differentiated**	actinomorphic fused* whorled** pentamerous** differentiated**	actinomorphic* fused* whorled** pentamerous** differentiated*		actinomorphic* free** whorled** pentamerous* differentiated**
	Canellales Buxales Buxales Buxales Canellales	actinomorphic free whorled non-penta differentiated	actinomorphic** free** whorled** non-penta* differentiated*	actinomorphic** free** whorled** non-penta** differentiated	actinomorphic* free** whorled* non-penta* undifferentiated**	actinomorphic** free** whorled* non-penta** differentiated
	Caryophyllales Canellales Canellales Canellales Caryophyllales	actinomorphic free, fused whorled non-penta differentiated	actinomorphic** free** whorled** non-penta** differentiated**	actinomorphic** free** whorled** non-penta** differentiated**	actinomorphic** free** spiral** non-penta** differentiated*		actinomorphic** free (high rate) whorled** non-penta** differentiated
	Celastrales Caryophyllales Caryophyllales Caryophyllales Celastrales	actinomorphic free, fused whorled pentamerous differentiated	actinomorphic** free** whorled** pentamerous** differentiated**	actinomorphic** fused* whorled** pentamerous** differentiated**	actinomorphic** free* whorled** pentamerous** differentiated**		actinomorphic** free** whorled** pentamerous* differentiated**

Table IV .

 IV S1: Number of changes in inferred most likely ancestral state between models and tree types in the key node series. Each column compares the results of two of the model and tree type combinations and reports the number of nodes that change most likely state in each case. Mk1= one rate maximum likelihood model; Mk2= two-rate maximum likelihood model;

	full= full tree; part= partitioned tree.
	15 nodes (full)	Mk1	Mk2	(full)	(part)
	13 nodes (part)	(full) ≠ (part)	(full) ≠ (part)	Mk1 ≠ Mk2	Mk1 ≠ Mk2
	fusion	2	2	0	4
	symmetry	0	0	1	0
	phyllotaxy	0	4	5	0
	pentamery	0	4	0	4
	differentiation	3	2	6	0

Table IV .

 IV S2: Number of changes in inferred most likely ancestral state between models and tree types in the order series. Each column compares the results of two of the model and tree type combinations and reports the number of nodes that change most likely state in each case.Mk1= one rate maximum likelihood model; Mk2= two-rate maximum likelihood model; full= full tree; part= partitioned tree.

	54 nodes	Mk1 (full) ≠ (part)	Mk2 (full) ≠ (part)	(full) Mk1 ≠ Mk2	(part) Mk1 ≠ Mk2
	fusion	1	7	1	6
	symmetry	0	2	6	2
	phyllotaxy	1	7	6	0
	pentamery	3	10	4	9
	differentiation	5	8	15	2

Table IV .

 IV .S3). At order node level, fusion, phyllotaxy and pentamery all have fewer state-changing node than differentiation, while symmetry has none (Table IV.S4). Table IV.S3: Number of nodes confirmed or suspected to state changes under different Mk1 rates (Key nodes). Confirmed: observed change in most probable state. Suspected: state change not observed, but shared evolution pattern. S4: Number of nodes confirmed or suspected to state changes under different Mk1 rates (Order nodes). Confirmed: observed change in most probable state. Suspected: state change not observed, but shared evolution pattern.

	15 nodes	Total	Confirmed	Suspected
	fusion	0	0	0
	symmetry	0	0	0
	phyllotaxy	0	0	0
	pentamery	0	0	0
	differentiation	5	4	1
	54 nodes	Total	Confirmed	Suspected
	fusion	2	2	0
	symmetry	0	0	0
	phyllotaxy	1	1	0
	pentamery	2	2	0
	differentiation	12	10	2

Table IV .

 IV S5: Number of changes in inferred most likely ancestral state between models and tree types in the key node series. Each column compares the results of two of the model and tree type combinations and reports the number of nodes that change most likely state between rescored and original data in each case. Mk1= one rate maximum likelihood model; Mk2= two-rate maximum likelihood model; full= full tree; part= partitioned tree; rescor= rescored used in article; orig= data as it was entered in PROTEUS.

	15 nodes (full)	Mk1 (full)
	12 nodes (part)	(rescor) ≠ (orig)

ACKNOWLEDGEMENTS

I thank my thesis supervisors Sophie and Hervé for their help, as well as the other members of the EVA team, but most particularly the people I saw regularly such as Julien, Frank, Stefan, Laetitia, Renske, Qian, Charlotte, James, Véronique and Thierry. I also thank people from outside the team that have contributed to my papers such as Hélène Morlon, Jürg Schönenberger and Maria von Balthazar. I thank the jury Louis Ronse de Craene, Félix Forest, Catherine Damerval, Porter Lowry, and Thomas Haevermans to have taken time to evaluate my thesis and participate in the defense. I thank the member of my thesis committee for advising me: Susana Magallón, Marianne Elias, Jean-Yves Dubuisson.

I also thank Jacqui and Martine for having helped me with my various paperwork worries and the other people I got to meet during my stay in this lab.

I thank my parents and officemates Roxane, Julie and Angeline for their moral support.

ACKNOWLEDGEMENTS

We thank Sophie Nadot, Peter Weston, and Nathalie Nagalingum for helpful comments on earlier drafts of this paper. Mark Rausher and three anonymous reviewers are also thanked for their constructive comments on this paper. This work was funded by ANR-CHEX grant ECOEVOBIO attributed to H.M.

ACKNOWLEDGMENTS

We thank Jürg Schönenberger and University of Vienna for hosting the PROTEUS database. We also thank the following PROTEUS users for contributing to the data used in this paper: Charlotte Prieu, Maria von Balthazar, Julien Massoni, Laetitia Carrive, Kristel Schoonderwoerd, Mario Coiro, Stefan Löfstrand, Florian Jabbour, Patrícia dos Santos and Jürg Schönenberger. Domingos Cardoso and an anonymous reviewer provided constructive comments that helped to improve this paper. modifie également la distribution des états, tout en améliorant la résolution des reconstructions d'états ancestraux. Ce facteur a baissé les taux de transition estimés par maximum de vraisemblance comparé à l'arbre montrant uniquement la symétrie et m'a permis de l'utiliser pour des reconstructions d'états ancestraux prenant la longueur des branches en compte. Pour évaluer la portée de l'hétérogénéité des taux à l'intérieur des Angiospermes, j'ai comparé les taux estimés quand le même modèle était suivi par tous les Angiospermes à ceux qui étaient estimés quand différentes sous-sections de l'arbre suivaient un modèle différent. viii Pour cela, l'arbre a été divisé en cinq partitions, sur lesquelles l'évolution de chacun des cinq caractères a été optimisée séparément : un grade d'Angiospermes basales (le grade ANA et les Magnoliidae), les Monocotyledoneae, les Eudicotyledoneae basales (Ranunculales à Buxales), les Superrosideae (Dilleniales incluses) et les Superasteridae. La parcimonie et le maximum de vraisemblance avec les modèles Mk1 et Mk2 ont été utilisés pour reconstruire les états ancestraux aussi bien sur l'arbre complet des Angiospermes que sur les partitions (collectivement appelées arbre partitionné). Ici, la plupart des taux de transition estimés étaient assez bas pour que chaque noeud ait des probabilités d'état distinctes, contrairement à l'artéfact induit par des taux de transition trop élevés dans le précédent chapitre. Pour tester l'impact du changement du modèle d'optimisation entre Mk1 et Mk2 et les optimisations sur l'arbre complet et l'arbre partitionné, j'ai comparé les états ancestraux inférés par les diverses optimisations sur deux jeux de noeuds. L'un de ces jeux consistait en quinze noeuds définissant les plus grands clades communément acceptés de l'arbre : les

Commelinales actinomorphic, zygomorphic zygomorphic equivocal (high rate) zygomorphic** actinomorphic (high rate) Cornales actinomorphic actinomorphic** actinomorphic** actinomorphic** actinomorphic* Crossosomatales actinomorphic actinomorphic** actinomorphic** actinomorphic** actinomorphic** Cucurbitales actinomorphic actinomorphic** actinomorphic** actinomorphic** actinomorphic** Dioscoreales actinomorphic actinomorphic** equivocal (high rate) actinomorphic* actinomorphic (high rate) Dipsacales actinomorphic actinomorphic* actinomorphic* actinmorphic actinomorphic* Ericales actinomorphic actinomorphic** actinomorphic** actinomorphic** actinomorphic** Escalloniales actinomorphic actinomorphic** actinomorphic** actinomorphic* actinomorphic* Fabales actinomorphic actinomorphic* actinomorphic* actinomorphic* actinomorphic Fagales actinomorphic actinomorphic** actinomorphic** actinomorphic** actinomorphic** Garryales actinomorphic actinomorphic** actinomorphic** actinomorphic** actinomorphic** Gentianales actinomorphic actinomorphic** actinomorphic** actinomorphic* actinomorphic* Geraniales actinomorphic actinomorphic** actinomorphic** actinomorphic* actinomorphic* Huerteales actinomorphic actinomorphic** actinomorphic** actinomorphic** actinomorphic** Icacinales actinomorphic actinomorphic** actinomorphic** actinomorphic* actinomorphic* Lamiales actinomorphic, zygomorphic actinomorphic* actinomorphic* zygomorphic* zygomorphic* Laurales actinomorphic actinomorphic** actinomorphic** actinomorphic** actinomorphic** Liliales actinomorphic actinomorphic** equivocal (high rate) actinomorphic actinomorphic (high rate) Magnoliales actinomorphic actinomorphic** actinomorphic** actinomorphic** actinomorphic** Malpighiales actinomorphic actinomorphic** actinomorphic** actinomorphic** actinomorphic** Malvales actinomorphic actinomorphic** actinomorphic** actinomorphic** actinomorphic** Myrtales actinomorphic actinomorphic** actinomorphic** actinomorphic* actinomorphic** Nymphaeales actinomorphic actinomorphic** actinomorphic** actinomorphic* actinomorphic** Oxalidales actinomorphic actinomorphic** actinomorphic** actinomorphic** actinomorphic** Pandanales actinomorphic actinomorphic** equivocal (high rate) actinomorphic* actinomorphic (high rate) Paracryphiales actinomorphic actinomorphic** actinomorphic** actinomorphic* actinomorphic* Petrosaviales actinomorphic actinomorphic** equivocal (high rate) actinomorphic* actinomorphic (high rate) Piperales actinomorphic actinomorphic** actinomorphic** actinomorphic* actinomorphic** Poales actinomorphic actinomorphic** equivocal (high rate) zygomorphic* actinomorphic (high rate) Proteales actinomorphic actinomorphic** actinomorphic actinomorphic* actinomorphic* Ranunculales actinomorphic actinomorphic** actinomorphic actinomorphic* actinomorphic* Rosales actinomorphic actinomorphic** actinomorphic** actinomorphic** actinomorphic** Santalales actinomorphic actinomorphic** actinomorphic** actinomorphic** actinomorphic* Sapindales actinomorphic actinomorphic** actinomorphic** actinomorphic** actinomorphic** Saxifragales actinomorphic actinomorphic** actinomorphic** actinomorphic** actinomorphic** Solanales actinomorphic actinomorphic** actinomorphic** zygomorphic actinomorphic Vitales actinomorphic actinomorphic** actinomorphic** actinomorphic* actinomorphic** Zingiberales zygomorphic zygomorphic** equivocal (high rate) zygomorphic** actinomorphic (high rate) Zygophyllales actinomorphic actinomorphic* actinomorphic* actinomorphic* actinomorphic* Commelinales differentiated differentiated** differentiated** differentiated* differentiated* Cornales differentiated differentiated** differentiated** differentiated** differentiated** Crossosomatales differentiated differentiated** differentiated** differentiated** differentiated** Cucurbitales differentiated differentiated** differentiated** undifferentiated undifferentiated Dioscoreales undifferentiated undifferentiated undifferentiated undifferentiated** undifferentiated Dipsacales differentiated differentiated** differentiated** differentiated** differentiated** Ericales differentiated differentiated** differentiated** differentiated** differentiated** Escalloniales differentiated differentiated** differentiated** differentiated** differentiated** Fabales differentiated differentiated** differentiated** differentiated** differentiated** Fagales undifferentiated undifferentiated* undifferentiated* undifferentiated** undifferentiated* Garryales differentiated differentiated** differentiated** differentiated* differentiated* Gentianales differentiated differentiated** differentiated** differentiated** differentiated** Geraniales differentiated differentiated** differentiated** differentiated** differentiated** Huerteales differentiated differentiated* differentiated* equivocal differentiated Icacinales differentiated differentiated** differentiated** differentiated** differentiated** Lamiales differentiated differentiated** differentiated** differentiated** differentiated** Laurales undifferentiated differentiated* undifferentiated undifferentiated** undifferentiated Liliales undifferentiated, differentiated differentiated* differentiated undifferentiated** differentiated Magnoliales undifferentiated differentiated* differentiated undifferentiated* differentiated Malpighiales differentiated differentiated** differentiated** differentiated** differentiated** Malvales differentiated differentiated** differentiated** differentiated** differentiated** Myrtales differentiated differentiated** differentiated** differentiated** differentiated** Nymphaeales undifferentiated differentiated* equivocal undifferentiated** equivocal Oxalidales differentiated differentiated** differentiated** differentiated** differentiated** Pandanales undifferentiated undifferentiated** undifferentiated* undifferentiated** undifferentiated* Paracryphiales differentiated differentiated* differentiated** differentiated* differentiated* Petrosaviales differentiated differentiated* differentiated undifferentiated* differentiated Piperales undifferentiated undifferentiated undifferentiated undifferentiated** undifferentiated Poales differentiated differentiated* differentiated* undifferentiated** differentiated Proteales differentiated differentiated** differentiated** undifferentiated differentiated** Ranunculales differentiated differentiated** differentiated** undifferentiated* differentiated** Rosales differentiated differentiated* differentiated* undifferentiated* undifferentiated* Santalales differentiated differentiated** differentiated** differentiated** differentiated* Sapindales differentiated differentiated** differentiated** differentiated** differentiated** Saxifragales differentiated differentiated** differentiated** differentiated** differentiated** Solanales differentiated differentiated** differentiated** differentiated** differentiated** Vitales differentiated differentiated** differentiated** differentiated** differentiated** Zingiberales differentiated differentiated** differentiated* differentiated* differentiated* Zygophyllales differentiated differentiated** differentiated** differentiated** differentiated**

Reconstructing ancestral states using model-based methods often involves estimating transition rates among character states. However, the estimated value of these transition rates may change according to the conditions in which they are estimated, such as taxon sampling and taxonomic scale. These variations may in turn impact the probability of the state at a given node. Here, we test the influence of maximum likelihood methods on five binary floral characters in which one of the states is a candidate key innovation (perianth symmetry, fusion, phyllotaxy, pentamery and differentiation) optimized on a phylogenetic tree of angiosperms including 1232 species sampled from all 424 currently recognized families. We compare the states reconstructed by an equal-rate (Mk1) and two-rate (Mk2) models fitted either with a single set of rates for the whole tree or as a partitioned model, with different rates for each of five partitions of the tree. We also test the impact of four different arbitrary transition rates under the Mk1 model. We focus our comparisons on both a set of 15 key nodes and a set of 54 nodes corresponding to the most recent common ancestors of all orders with more than one species. We found a strong signal for rate heterogeneity among the five subdivisions for all five characters. However, our results suggest that the choice of a model has little overall impact on reconstructed ancestral states for these characters in angiosperms, albeit with some variation depending on the character. Our results also show that the derived states from our characters are usually absent at both key node and order node level and evolved many times independently, except for pentamery and differentiation in Pentapetalae and fusion in Superasteridae.

There is a general tendency for full trees and partitions that have a high symmetry ratio under Mk2 to be best fitted by Mk1 or have neither model fit better than the other, and for those that have a high symmetry ratio to be best fitted by Mk2. When Mk1 rates are imposed on the tree, fusion, symmetry, pentamery and differentiation have their lowest AIC at q= 0.0100. Phyllotaxy has its lowest AIC at q=0.0010.

Character optimization results

Appendix IV.8 shows the character state data that we have for all the species of our tree.

Overall, most of the nodes tested are not very sensitive to model changes, although we observed more differences in shallow nodes (such as most recent common ancestors of orders; Appendices IV.3 and IV.5) than in deep nodes (the 15 key clades; Appendices IV.2 and IV.4) of the phylogeny. Moreover, model sensitivity was greater for perianth differentiation than for the other four characters considered in this study.

Full tree and partitions under Mk1 and Mk2. Changes in the most-likely state induced by going from the full tree model to a partition model are more frequent under Mk2 than under Mk1. The partitioned tree is less affected by a change from Mk1 to Mk2 than the full tree.

To simplify the interpretation of results, we chose to classify the proportional marginal likelihoods of character states in three categories. Those with a probability of 0.90 or higher (the default threshold used by Mesquite) are considered to have strong support and are indicated by two asterisks in the appendices in which the results are compiled (Appendices IV.2 and IV.3) and Table IV.1. Values higher than 0.60 and lower than 0.90 are considered to have moderate support and are indicated by a single asterisk in the appendices. Those not exceeding 0.60 are considered too close to 0.50 and are thus regarded to have weak support (no asterisk). While the term "equivocal" is commonly used for probabilities that are covered by weak and moderate support in this study, we use it for state probabilities of exactly 0.5. Table IV.1 summarizes the results for Caryophyllales, as an example of a node subject to changes in both fusion state and differentiation state. Appendix IV.8. Tree used for the reconstructions, with a breakdown of the character states that were available for each taxon at the tips.

SUPPORTING INFORMATION FOR CHAPTER 1: PRESENCE IN MEDITERRANEAN HOTSPOTS AND FLORAL SYMMETRY AFFECT SPECIATION AND EXTINCTION RATES IN PROTEACEAE