Renske E Onstein
email: onsteinre@gmail.com

W Daniel Kissling

Lars W Chatrou

Thomas L P Couvreur

Hélène Morlon

Hervé Sauquet

Which frugivory-related traits facilitated historical long-distance dispersal in the custard apple family (Annonaceae)?

Keywords: Annonaceae, frugivory, functional traits, fruit size, geodispersal, historical biogeography, long-distance dispersal, megafauna, rain forest, vicariance

Aim

Long-distance dispersal has contributed to the disjunct biogeographical distribution of rain forest plants -something that has fascinated biogeographers since Humboldt's time. However, the dispersal 'agent' for these tropical plant lineages remains puzzling. Here, we investigate which frugivory-related traits may have facilitated past intercontinental longdistance dispersal in the custard apple family (Annonaceae), a major vertebrate-dispersed tropical plant family. We hypothesize that long-distance dispersal was associated with the evolution of traits related to dispersal by large-bodied mammals (e.g. large, dull-coloured, 'megafaunal' fruits) and strong-flying, ocean-crossing birds and bats (e.g. dehiscent, moniliform or cauliflorous fruits). Location Global Taxon Annonaceae Methods We used a fossil-calibrated phylogenetic framework to infer the biogeographic history of 234 Annonaceae species (10%, covering nearly all genera) in relation to the evolution of 15 frugivory-related traits, using maximum likelihood and Bayesian inferences. Furthermore, we used linear and generalized linear models and phylogenetic simulations to test whether ancestral fruit traits during intercontinental dispersal were different from those of other lineages not involved in long-distance dispersal.

Results

We inferred the ancestral Annonaceae fruits to be small with a single or few small seeds and a small number of fruitlets. These fruits were most probably apocarpous, indehiscent and/or moniliform (i.e. long beads of fruitlets). Furthermore, most of the long-distance dispersal events in Annonaceae occurred via the expanded tropical forests in the Early Cenozoic ('geodispersal'), and were significantly associated with large (c. 3 cm long), dull-coloured fruits, and short stipes. Additionally, long-distance dispersal was also facilitated by dehiscent, moniliform and non-cauliflorous fruits.

Main conclusions

We suggest that the evolution of frugivory-related traits associated with dispersal by frugivores that frequently move across large distances and/or barriers, such as large-bodied mammals and strong-flying birds, has contributed to the disjunct tropical biogeographical distribution of Annonaceae, and probably of tropical rain forest plants more generally.

Introduction

Since the travels of Alexander von Humboldt (1889), the tropical rain forest biome, its diversity, and the disjunct biogeographic distribution of rain forest families, has fascinated biogeographers. Indeed, rain forests comprise an extraordinary plant diversity even though they cover only ca. 7% of the Earth's surface [START_REF] Morley | Origin and evolution of tropical rain forests[END_REF]. Numerous major plant lineages, such as palms (Arecaeae), custard apples (Annonaceae) or laurels (Lauraceae), are distributed across all major tropical rain forest realms of the world. These lineages are often physiologically dependent on the humid and hot climatic rain forest conditions [START_REF] Morley | Interplate dispersal paths for megathermal angiosperms[END_REF]. Traditionally, it was thought that these intercontinental disjunct distributions of rain forest lineages were the result of 'vicariance' -i.e. the divergence of a once widespread lineage due to the break-up of the Gondwanan supercontinent [START_REF] Raven | Angiosperm biogeography and past continental movements[END_REF]. However, estimates of divergence times using fossil-calibrated phylogenetic trees have shown that the timing of continental break-up often preceded the timing of lineage divergence associated with the colonization of new continents [START_REF] Davis | Laurasian migration explains Gondwanan disjunctions: Evidence from Malpighiaceae[END_REF][START_REF] Renner | Biogeography of the Monimiaceae (Laurales): a role for East Gondwana and long-distance dispersal, but not West Gondwana[END_REF][START_REF] Couvreur | Early evolutionary history of the flowering plant family Annonaceae: steady diversification and boreotropical geodispersal[END_REF][START_REF] Baker | Global biogeography and diversification of palms sheds light on the evolution of tropical lineages. I. Historical biogeography[END_REF]. Long-distance dispersal (e.g. overland dispersal of distances > c. 1000 km and/or across oceans, [START_REF] Pires | Pleistocene megafaunal extinctions and the functional loss of long-distance seed-dispersal services[END_REF] therefore seems the most plausible scenario to explain much of the disjunct distributions of tropical plant lineages. However, it is often unclear by which dispersal mode (e.g. wind, water or animals) tropical plants historically colonized new continents and their rain forests.

Up to 94% of extant woody tropical rain forest plant species depend on fruit-eating animals ('frugivores') for their seed dispersal [START_REF] Jordano | Fruits and frugivory. Seeds: the ecology of regeneration in plant communities 2[END_REF], in which frugivores are rewarded by obtaining important nutrients from the fruits they feed on. Rain forest taxa often show high degrees of continental endemism (at species and genus levels) (e.g. palms, [START_REF] Kissling | Cenozoic imprints on the phylogenetic structure of palm species assemblages worldwide[END_REF], because intercontinental dispersal by animals, as compared to wind or water, is relatively rare. Indeed, seed dispersal distances, the geographic pattern of seed rain, and the frequency of long-distance dispersal of animal-dispersed taxa are determined by frugivores and their movement behaviours [START_REF] Nathan | Mechanisms of long-distance seed dispersal[END_REF][START_REF] Pires | Pleistocene megafaunal extinctions and the functional loss of long-distance seed-dispersal services[END_REF], which may in turn influence the diversification of fleshy-fruited plants [START_REF] Onstein | Frugivory-related traits promote speciation of tropical palms[END_REF]. Long-distance dispersal is typically rare ("fat-tailed dispersal kernels", [START_REF] Nathan | Spatial patterns of seed dispersal, their determinants and consequences for recruitment[END_REF] and mostly depends on dispersal by large-bodied and wide-ranging frugivorous megafauna (e.g. tapirs [Tapiridae], elephants [Elephantidae]) or strong-flying volant frugivores (e.g. hornbills [Bucerotidae], toucans [Ramphastidae] and fruit bats [Pteropodidae]) [START_REF] Shanahan | Colonization of an island volcano, Long Island, Papua New Guinea, and an emergent island, Motmot, in its caldera lake. V. colonization by figs (Ficus spp.), their dispersers and pollinators[END_REF][START_REF] Holbrook | Implications of long-distance movements of frugivorous rain forest hornbills[END_REF][START_REF] Nathan | Mechanisms of long-distance seed dispersal[END_REF][START_REF] Schurr | Longdistance seed dispersal[END_REF][START_REF] Pires | Pleistocene megafaunal extinctions and the functional loss of long-distance seed-dispersal services[END_REF]. It is therefore expected that the largest and most widespread frugivores have been most important for the historical dispersal of tropical plant lineages across continents, but this remains largely untested.

We take a trait-based approach to identify frugivory-related plant traits associated with long-distance seed dispersal, in order to understand which fruits and frugivores may have been most important for historical long-distance dispersal. Large-bodied frugivores, for example, are more likely to perform long-distance seed dispersal and often prefer the largest fruits [START_REF] Jordano | Fruits and frugivory. Seeds: the ecology of regeneration in plant communities 2[END_REF][START_REF] Herrera | Seed dispersal by vertebrates. Plant-animal interactions: an evolutionary approach[END_REF], thereby increasing the probability of long-distance dispersal for plant species with large fruits compared to those with smaller fruits. Similarly, primates [Primates] disperse seeds over long distances and in multiple habitats due to their large home ranges, and often prefer dull-coloured fruits [START_REF] Gautier-Hion | Fruit characters as a basis of fruit choice and seed dispersal in a tropical forest vertebrate community[END_REF][START_REF] Lomáscolo | Signal convergence in fruits: a result of selection by frugivores[END_REF], thus increasing the probability of long-distance dispersal for plants with dull-coloured fruits compared to those with bright-coloured fruits. Furthermore, strong-flying, volant frugivores, such as certain species of birds (e.g. hornbills) and bats (e.g. fruit bats), are able to cross barriers (e.g. water) and thereby increase the chance for longdistance dispersal [START_REF] Onstein | Frugivory-related traits promote speciation of tropical palms[END_REF]. Small-seeded fruits with a smooth exocarp, dehiscent or moniliform fruits (i.e. fruits constricted between the seeds, like a necklace) or cauliflory, have been associated with bird-or bat-dispersal, potentially increasing the probability of longdistance dispersal for these fruits [START_REF] Van Der Pijl | Principles of dispersal in higher plants[END_REF][START_REF] Janson | Adaptation of fruit morphology to dispersal agents in a Neotropical forest[END_REF][START_REF] Gautier-Hion | Fruit characters as a basis of fruit choice and seed dispersal in a tropical forest vertebrate community[END_REF]Lomáscolo et al., 2010). Thus, certain frugivory-related 'trait syndromes' (i.e. sets of correlated traits) [START_REF] Van Der Pijl | Principles of dispersal in higher plants[END_REF][START_REF] Janson | Adaptation of fruit morphology to dispersal agents in a Neotropical forest[END_REF][START_REF] Gautier-Hion | Fruit characters as a basis of fruit choice and seed dispersal in a tropical forest vertebrate community[END_REF]Lomáscolo et al., 2010) may have predisposed plants for long-distance seed dispersal. However, the role of these traits in relation to the disjunct biogeographical distribution of vertebrate-dispersed plant lineages remains puzzling.

Here, we investigate which frugivory-related functional traits may have facilitated intercontinental long-distance dispersal (i.e. overland dispersal across large distances > c. 1000 km and/or across oceans, [START_REF] Pires | Pleistocene megafaunal extinctions and the functional loss of long-distance seed-dispersal services[END_REF]. First, we hypothesize that long-distance dispersal was associated with relatively large fruits with dull colours (i.e. brown, green), and / or large, (pseudo-)syncarpous fruits (in some species described as "megafaunal fruits", [START_REF] Guimarães | Seed dispersal anachronisms: rethinking the fruits extinct megafauna ate[END_REF] (see Figure 1 for examples). These 'mammal' trait syndromes (Figure 2, [START_REF] Janson | Adaptation of fruit morphology to dispersal agents in a Neotropical forest[END_REF] may have enhanced overland long-distance seed dispersal by large-bodied megafauna (e.g. primates, elephants, tapirs, or extinct giant sloths [Megatheriidae] and gomphotheres [Gomphotheriidae]) and thus increase the probability of long-distance dispersal, as compared to small, bright-coloured and / or apocarpous fruits. Second, we expect small seeds, a smooth exocarp, conspicuous, dehiscent or moniliform fruits and / or cauliflorous fruits to be associated with long-distance dispersal (see Figure 1 for examples). These 'bird/bat' trait syndromes (Figure 2, [START_REF] Janson | Adaptation of fruit morphology to dispersal agents in a Neotropical forest[END_REF] may have increased the opportunity for long-distance dispersal by strong-flying, ocean-crossing, volant frugivores as compared to large-seeded, warty or pubescent, indehiscent, non-moniliform and / or non-cauliflorous fruits. As some of these traits may be correlated to other plant traits (e.g. plant height) or present a resource-allocation trade-off (e.g. number vs. size of fruits/seeds and stipe length, Table 1) we also included plant height, growth form, stipe length, fruit and seed number in our analysis.

We test these hypotheses in the custard apple family (Annonaceae, Magnoliales), a major vertebrate-dispersed, globally-distributed plant family, typically confined to the rain forest biome [START_REF] Keßler | Annonaceae. The families and genera of vascular plants, Vol. 2. Magnoliid, Hamamelid and Caryophyllid families[END_REF]. Annonaceae comprises c. 2400 species and has been well studied from phylogenetic [START_REF] Chatrou | A new subfamilial and tribal classification of the pantropical flowering plant family Annonaceae informed by molecular phylogenetics[END_REF]Guo et al., 2017a), evolutionary [START_REF] Couvreur | Early evolutionary history of the flowering plant family Annonaceae: steady diversification and boreotropical geodispersal[END_REF][START_REF] Pirie | Parallel diversifications of Cremastosperma and Mosannona (Annonaceae), tropical rainforest trees tracking Neogene upheaval of South America[END_REF] and biogeographical [START_REF] Doyle | Phylogeny, molecular and fossil dating, and biogeographic history of Annonaceae and Myristicaceae (Magnoliales)[END_REF][START_REF] Couvreur | Early evolutionary history of the flowering plant family Annonaceae: steady diversification and boreotropical geodispersal[END_REF][START_REF] Zhou | Out-of-Africa' dispersal of tropical floras during the Miocene climatic optimum: evidence from Uvaria (Annonaceae)[END_REF][START_REF] Thomas | The historical origins of palaeotropical intercontinental disjunctions in the pantropical flowering plant family Annonaceae[END_REF] points of view. Furthermore, almost all Annonaceae species are dispersed by animals, ranging from birds, bats, primates, small-bodied mammals (e.g. rodents), and, in some cases, fish [START_REF] Keßler | Annonaceae. The families and genera of vascular plants, Vol. 2. Magnoliid, Hamamelid and Caryophyllid families[END_REF]. Consequently, the family shows a spectacular diversity of fruit types (Figure 1). We use a newly generated fossil-calibrated phylogenetic framework of Annonaceae, on which we identify long-distance dispersal events using historical biogeographical inference. Furthermore, we reconstruct the ancestral states of fifteen frugivory-related functional traits and use linear and generalized linear models and phylogenetic simulations to identify which fruit traits are significantly associated with longdistance seed dispersal events, as compared to other lineages not involved in long-distance dispersal.

Materials and Methods

Molecular dataset

We sampled 234 Annonaceae species (c. 10% of total) representing 105 (c. 97% of total) genera and all four subfamilies, and seven outgroup taxa from related families (Annonaceae was constrained to be monophyletic). For these species, we generated a molecular supermatrix of eight plastid markers as assembled by [START_REF] Chatrou | A new subfamilial and tribal classification of the pantropical flowering plant family Annonaceae informed by molecular phylogenetics[END_REF] supplemented with 157 additional sequences for 37 species. For details on the methods, see [START_REF] Chatrou | A new subfamilial and tribal classification of the pantropical flowering plant family Annonaceae informed by molecular phylogenetics[END_REF], GenBank numbers for the new sequences are provided in Appendix S1.

Phylogeny and dating

We reconstructed and dated the Annonaceae phylogenetic tree in BEAST 1.8.2 [START_REF] Drummond | BEAST: bayesian evolutionary analysis by sampling trees[END_REF]. We used the uncorrelated lognormal clock model and a Yule birth prior, but both the Yule and birth-death models inferred similar divergence times (Figure S1). Substitution rates of markers were linked, because all markers are located on the chloroplast and linkage allowed the analyses to reach convergence. We used the GTR + gamma + invariant sites substitution rate model. To date the Annonaceae, we used the fossils Endressinia (most-recent common ancestor of Magnoliaceae and Annonaceae; 113 Ma, [START_REF] Mohr | Endressinia brasiliana, a Magnolialean Angiosperm from the Lower Cretaceous Crato Formation (Brazil)[END_REF]Massoni et al., 2015a) for the split between Magnoliaceae and Annonaceae, and Futabanthus (89 Ma, [START_REF] Takahashi | Floral Evidence of Annonaceae from the Late Cretaceous of Japan[END_REF] for the Annonaceae crown node (for more details, see Appendix S2).

Fruit traits

We collected data on 15 frugivory-related functional traits (six continuous traits and nine binary traits) for the same Annonaceae species for which sequence data were available, excluding seven species because of lack of fruit trait data (i.e. total trait data for n = 228 species, n = 3680 data records scored from 197 sources). These species cover the taxonomic and functional variation in the family (Table 1). Data were gathered from scientific articles, monographs, books, and herbaria in Zurich and Paris (Z, ZT and P) and in the field (Sabah, Borneo, Malaysia, for details see Appendix S1). All traits were assembled in the PROTEUS database [START_REF] Sauquet | PROTEUS: A database for recording morphological data and creating NEXUS matrices[END_REF], and the data and data sources are available from Appendix S1 and Dryad XXX.

The fruit measurements relate to the dispersal unit of the plant (Figure 1), because we are interested in the functional role of the fruit in relation to seed dispersal (Table 1), i.e. how the fruit appears to frugivores. For most Annonaceae the dispersal unit is the separate fruitlet ('monocarp'), developed from a carpel that is free in flower (i.e. n = 205 apocarpous Annonaceae species in our dataset). In some genera (Annona, Anonidium, and genera in tribe Duguetieae) the carpels that are free in flower fuse postgenitally during fruit development [START_REF] Chatrou | Studies in Annonaceae XXXIII. A revision of Fusaea (Baill.) Saff[END_REF]. In Isolona and Monodora, carpels are fused both in flower and fruit stage [START_REF] Couvreur | Monograph of the syncarpous African genera Isolona and Monodora (Annonaceae)[END_REF]. Despite the distinction in morphology and development, we treat the latter two fruit types similarly, as both produce fleshy fruits that are equivalent from the perspective of fruit dispersal (i.e. n = 23 [pseudo-]syncarpous Annonaceae species in our dataset). We calculated species averages when more than one observation for a trait was recorded. Furthermore, fruit length, fruit number, seed number and maximum plant height were log-transformed to gain normality in the data and to reduce the effect of outliers in the analyses. We performed a principal component analysis (PCA) to evaluate whether the correlation between frugivory-related traits allows us to define trait-syndromes potentially associated with particular frugivores using the 'mix.dudi' function in the 'ade4' package in R [START_REF] Dray | The ade4 Package: Implementing the duality diagram for ecologists[END_REF]. In addition, Phylogenetic Generalized Least Squares (PGLS) regressions were performed to further evaluate correlations between these traits [START_REF] Martins | Phylogenies and the comparative method: a general approach to incorporating phylogenetic information into the analysis of interspecific data[END_REF], resulting in 45 pairwise trait PGLS regressions. The PGLS method estimates phylogenetic signal and regression parameters simultaneously, adjusted for the phylogenetic signal in the model residuals. This was done using the 'pgls' function in the 'caper' R package [START_REF] Orme | Caper: comparative analyses of phylogenetics and evolution in R. R package version 1[END_REF].

Biogeographical inference

Ancestral geographic ranges of Annonaceae were inferred using the maximum-likelihood approach implemented in BioGeoBEARS [START_REF] Matzke | Probabilistic historical biogeography: new models for founder-event speciation, imperfect detection, and fossils allow improved accuracy and modeltesting[END_REF]). An unconstrained dispersalextinction-cladogenesis model (DEC), which allows for probabilistic inference of models of range expansion [START_REF] Ree | A likelihood framework for inferring the evolution of geographic range on phylogenetic trees[END_REF][START_REF] Ree | Maximum likelihood inference of geographic range evolution by dispersal, local extinction, and cladogenesis[END_REF], as well as a model which additionally allows for cladogenetic dispersal outside the parental areas ('founder-event speciation', DEC+J) were fit to the Annonaceae maximum clade credibility (MCC) tree, and compared using a likelihood ratio-test. All species were coded as present / absent in six geographical regions [START_REF] Couvreur | Early evolutionary history of the flowering plant family Annonaceae: steady diversification and boreotropical geodispersal[END_REF]: North America (including Central America), South America, Asia, Afrotropics, Madagascar and Oceania (including the Pacific islands). We set the maximum number of areas to three to reflect the maximum number of areas occupied by any extant Annonaceae species. The dispersal probability through time between areas was set to equal, to avoid making subjective assumptions on the historical connectivity between continents (but see section on 'classification of long-distance dispersal routes'). The biogeographical reconstructions obtained from the best model were visualized on the MCC tree. These reconstructions were used to identify long-distance dispersal events, i.e. changes in the most likely ancestral area between nodes in the tree. By only evaluating biogeographical reconstructions in the Cenozoic, we excluded vicariance as a possibility to explain biogeographical shifts between ascending and descending nodes.

Classification of long-distance dispersal routes

We classified long-distance dispersal events of Annonaceae based on the timing and the direction of the events into five routes (for more details see Appendix S2): (1) 'Laurasian geodispersal' (ca. 66-45 Ma) across land bridges during times when the climate was favourable for rain forest taxa at higher latitudes [START_REF] Van Steenis | The land-bridge theory in botany with particular reference to tropical plants[END_REF][START_REF] Thorne | Major disjunctions in the geographic ranges of seed plants[END_REF][START_REF] Morley | Origin and evolution of tropical rain forests[END_REF][START_REF] Morley | Interplate dispersal paths for megathermal angiosperms[END_REF]. 'Geodispersal' refers to the process whereby species can expand their geographical ranges due to geological or climatic changes [START_REF] Lieberman | Geobiology and paleobiogeography: tracking the coevolution of the Earth and its biota[END_REF]; (2) 'Afro-Asian land bridge' enabling migration from Africa to Asia across Arabia via the expanded tropical forests during the Miocene (23-5.3 Ma) [START_REF] Zachos | Trends, rhythms, and aberrations in global climate 65 Ma to present[END_REF]; (3) 'South America-Africa (SA-A) stepping stones' supporting stepping stone dispersal across islands of the Rio-Grande Rise and the Walvis Ridge, connecting South America and Africa up until the Oligocene (66-33.9 Ma) [START_REF] Morley | Interplate dispersal paths for megathermal angiosperms[END_REF]; (4) 'Pacific island hopping' enabling dispersal between Southeast Asia, Australia and the Pacific islands from the late Miocene-Pliocene onward (ca. 10 Ma), when Australia and the Asian Plate collided; (5) 'remaining longdistance dispersal' events that could not be assigned to any of the dispersal routes.

Importantly, long-distance dispersal of Annonaceae lineages may have occurred any time along a branch, and the uncertainties in estimated divergence times were therefore taken into account when assigning long-distance dispersal events to dispersal routes (Table S1).

Ancestral fruit trait reconstructions

To evaluate which traits may have facilitated historical long-distance dispersal in Annonaceae, we reconstructed ancestral states for the fifteen frugivory-related traits on 100 phylogenetic trees randomly sampled from the posterior of the BEAST analyses, and summarized them on the MCC tree. Inferred probabilities for trait states therefore take topological and divergence time uncertainties into account.

For the binary traits, we used maximum likelihood as well as Bayesian inferences to perform the ancestral state reconstructions. We used the 'multistate' function in BAYESTRAITS v.2 [START_REF] Pagel | Bayesian analysis of correlated evolution of discrete characters by reversible jump Markov Chain Monte Carlo[END_REF] using the 'addMRCA' command followed by a list of species descending from a particular node for which we aimed to infer the ancestral trait state. These descending species do not necessarily have to form a clade in all 100 trees. For the maximum likelihood analysis, we evaluated support for an equal or unequal transition rate model; the unequal transition rate model was supported for six out of nine discrete traits (Table S2). For the Bayesian Markov chain Monte Carlo (MCMC), we used a reversible jump (rjMCMC) hyper prior with an exponential prior between 0 and 100 for 10 x 10 6 iterations, with a 10% burn-in. The rjMCMC approach integrates results over the model space and visits models (e.g. equal and unequal transition rate models) and parameters (e.g. RateDev parameter, to get an acceptance rate of changes between 20 -40%) in proportion to their posterior probability. The hyper prior provides a distribution from which values are drawn to seed the exponential prior [START_REF] Pagel | Bayesian estimation of ancestral character states on phylogenies[END_REF][START_REF] Pagel | Bayesian analysis of correlated evolution of discrete characters by reversible jump Markov Chain Monte Carlo[END_REF]; see [START_REF] Sauquet | Zygomorphy evolved from disymmetry in Fumarioideae (Papaveraceae, Ranunculales): new evidence from an expanded molecular phylogenetic framework[END_REF][START_REF] Onstein | Beyond climate: convergence in fast evolving sclerophylls in Cape and Australian Rhamnaceae predates the mediterranean climate[END_REF] for empirical examples).

For the continuous traits, we used the two-step approach in BAYESTRAITS, in which 'random-walk' models (i.e., Brownian motion) for each trait were run on 100 Annonaceae phylogenetic trees, and the average trait value was estimated subsequently for each internal node. Again, the 'addMRCA' command indicated the common ancestor of a group of species, and the MCMC was run for 10 x 10 6 iterations, with a 10% burn-in.

Inferring trait-related long-distance dispersal

To evaluate whether frugivory-related traits involved in historical long-distance dispersal of Annonaceae deviated from ancestral fruits not involved in long-distance dispersal, we combined the data from the biogeographical inference with the reconstructed traits. First, we tested whether fruit traits were different for ancestral lineages involved in long-distance dispersal compared to those not involved in long-distance dispersal, using Welch Two Sample t-tests. It is important to note that the geographical distribution of some of our characters is highly skewed. For example, (pseudo-)syncarpous fruits do not occur in Asia, some occur in Africa, whereas they are abundant in the Neotropics. Moniliform fruits only occur in Africa, Madagascar and Asia, and are totally absent in the Neotropics. Furthermore, as nodes (and inferred trait values on nodes) are correlated in phylogenies, we expect long-distance dispersal events to be non-randomly distributed across the Annonaceae tree (conditional on the presence of frugivory-related character states as opposed to, for example, 'random' opportunities for dispersal). In addition, it is possible that we detect an association between traits and long-distance dispersal using our method when it is not truly there (i.e. type II error) [START_REF] Maddison | The unsolved challenge to phylogenetic correlation tests for categorical characters[END_REF]. To address these issues, we compared the empirical results against 1000 simulations of long-distance dispersal events across the Annonaceae tree. In each simulation we randomly assigned long-distance dispersal events to branches within the Annonaceae tree (without replacement, and keeping the total number of long-distance dispersal events the same as empirically inferred), and repeated the t-test as described above (i.e. to test for an association between traits and long-distance dispersal). For these 'random' long-distance dispersals we expected no significant association with frugivory-related traits, and thus we evaluated whether our observed t-value fell outside the 95% distribution of simulated t-values.

Second, we tested whether fruit traits were different for ancestral lineages involved in the different dispersal routes (Laurasian geodispersal, Afro-Asian land bridge, SA-A stepping stones, Pacific island hopping and the remaining long-distance dispersal). To this end, linear models (LM) were performed, regressing the continuous fruit traits against the dispersal routes. We evaluated whether the model met the model requirements, i.e. normality of residuals and presence or absence of a relationship between the fitted values and, respectively, the observed and residual values. For the discrete traits, generalized linear models (GLM) using a quasibinomial family with a logit link function were performed, using the probability (between 0 and 1) of presence of the traits as the response variables. The quasibinomial family was used in order to adjust the dispersion parameter to match the degrees of freedom in the data. Similarly, as done for the t-tests, we evaluated the effect of type II error rates on our results by repeating the LMs and GLMs after simulating random long-distance dispersal events 1000 times on the Annonaceae phylogeny.

Results

Phylogeny

The Annonaceae crown node was estimated to be 96.8 Ma (89.0 -104.6 Ma [ranges reflect the 95% HPD]), the Ambavioideae 69.9 (50.6 -86 Ma), the Annonoideae 74.6 Ma (65.6 -84.3 Ma) and the Malmeoideae 38.2 Ma (27.9 -49.8 Ma). More details are available from the MCC tree (Dryad XXX).

Biogeographical inference and dispersal routes

The DEC+J model fitted the data significantly better than the DEC model (Log Likelihood of -233 for DEC+J vs. -259 for DEC), indicating that (founder-event) jump dispersal may have been an important process in the biogeographical history of Annonaceae. However, due to issues related to estimation of the +J parameter [START_REF] Ree | Conceptual and statistical problems with the DEC+J model of founder-event speciation and its comparison with DEC via model selection[END_REF], we present results consistent across both models here (both models gave qualitatively similar results and are presented in the Supporting tables and figures). Both models identified 24 long-distance dispersal events during Annonaceae evolution, which took place throughout the Late Cretaceous and Cenozoic, possibly from c. 70 Ma until as recent as 0.5 Ma (Figure 3, Figure S2, Table S1). These long-distance dispersals took place within all four Annonaceae subfamilies (Anaxagoreoideae, Ambavioideae, Annonoideae and Malmeoideae), and include shifts within the tribes Bocageeae, Xylopieae, Duguetieae, Guatterieae, Annoneae, Uvarieae, Malmeeae and Miliuseae. Our biogeographical inference also shows that the ancestral area for the Annonaceae crown node cannot be reconstructed with confidence, but Africa is the most probable ancestral area for Annonaceae excl. Anaxagoreoideae (Figure 3, Figure S2).

Ancestral fruit trait reconstruction and trait ordination

The maximum likelihood and Bayesian ancestral state reconstructions of the frugivory-related traits gave qualitatively similar results, and only the Bayesian reconstructions were therefore used in the subsequent analyses. Based on these reconstructions, we inferred the ancestral Annonaceae fruits to be small, placed on short stipes, with a single or a few small seeds and a small number of fruitlets. These fruits were most probably apocarpous, indehiscent and/or moniliform. Colour, conspicuousness, exocarp, pubescence and cauliflory showed ambiguous (equivocal) reconstructions at the ancestral nodes. All ancestral state reconstructions are illustrated in Figure S3.

The PCA shows that the frugivory-related traits we hypothesized to be associated to bird, bat or mammal 'syndromes' (see hypotheses) are clustered in trait space, and thus explain distinct parts of the total frugivory-related functional trait variation in Annonaceae (Figure 2). Similar frugivory-related trait syndromes were also recovered with PGLS, i.e. mammal syndromes of (1) few, syncarpous fruits with many seeds, large fruits, large seeds; bird syndromes of (2) many, bright-coloured, small fruits with few, small seeds and long stipes, and (3) dehiscent fruits with small seeds; and a bat syndrome of (4) dull-coloured, cauliflorous fruits (Table S3). This suggests that frugivory-related traits do not evolve independently from each other and that 'dispersal syndromes' may indeed exist, i.e. sets of co-occurring fruit traits that match the behaviour, feeding preferences and morphology of particular types of frugivores.

Trait-related long-distance dispersal

Taking all Annonaceae long-distance dispersal events together, we found that five (out of 15) of the frugivory-related traits were significantly associated with long-distance dispersal as compared to those lineages not involved in long-distance dispersal (based on p < 0.05, for test statistics see Table S4). These long-distance dispersal fruits were, on average, relatively large (c. 3 cm long) and were subtended by short stipes (c. 0.6 cm long). Fruits were also more likely to be dull-coloured, moniliform and/or non-cauliflorous (Figure 4, Table S4). Several of these traits are associated with our hypothesized dispersal syndromes (i.e. a mammal syndrome of large fruits, short stipes, dull colours and a bird syndrome consisting of moniliform fruits). Our simulations show that these results are unlikely explained by type II error rates, because our observed t-value linking frugivory-related traits to long-distance dispersal (for those traits that showed empirical significance) falls outside the 95% distribution of simulated t-values (i.e. after randomly reshuffling long-distance dispersal events across the Annonaceae phylogenetic tree) (Figure S4).

When testing fruit trait associations with any of the five Cenozoic dispersal routes in particular (Laurasian geodispersal, Afro-Asian land bridge, SA-A stepping stones, Pacific island hopping and remaining long-distance dispersal events), we found that nine (out of 15) traits showed a significant association with at least one of these routes (Figure 4, Tables S5 andS6). These traits were few, viz. large fruits on short stipes and a high probability of being syncarpous (associated with Laurasian geodispersal, SA-A stepping stones), dehiscent or moniliform fruits (associated with Laurasian geodispersal, Afro-Asian land bridge, SA-A stepping stones), non-cauliflorous fruits (associated with Pacific island hopping) and dullcoloured fruits (associated with remaining long-distance dispersal events, but only in the DEC+J inference). Seed length and seed number may also be associated with long-distance dispersal, but results were inconsistent between biogeographical models (i.e. DEC+J vs. DEC). For example, small seeds were associated with Pacific island hopping when following inferences from the DEC+J model, but the DEC model associated seed length with Afro-Asian land bridge and SA-A stepping stone dispersal. Similarly, seed number was positively associated with Early Cenozoic geodispersal and stepping stone dispersal following the DEC+J model, but was associated with remaining long-distance dispersal events when following inferences from the DEC model (Figure 4, Table S5).

Again, several of these traits could be linked to the hypothesized dispersal syndromes (i.e. a mammal syndrome of large, [pseudo-]syncarpous fruits and dull colours; a bird syndrome consisting of dehiscent or moniliform fruits, Figure 2). Furthermore, these results are unlikely to be driven by 'random' opportunities for long-distance dispersal as shown by our simulations, although some uncertainty exists for seed number, seed length, fruit colour, and dehiscent fruits (Figure S5).

Discussion

In this study, we combined a comprehensive trait database with a comparative phylogenetic approach to identify frugivory-related traits associated with past intercontinental longdistance dispersal in Annonaceae, a major vertebrate-dispersed tropical plant family (Figure 1). We show that most long-distance dispersal occurred in the Early Cenozoic (Figure 3) when climates were warm and rain forests were extended beyond their current ranges [START_REF] Morley | Interplate dispersal paths for megathermal angiosperms[END_REF]. These long-distance dispersal events may have been facilitated by the evolution of few, large fruits, short stipes, dull colours, (pseudo-)syncarpy, dehiscent and/or moniliform fruits (Figures 2 and4). The recurrent evolution of these traits may have predisposed Annonaceae to colonize (new) continents or islands throughout the Cenozoic, through their interactions with wide-ranging and/or ocean-crossing frugivores.

Frugivory-related traits influence long-distance dispersal

We show that (pseudo-)syncarpous fruits have been associated with long-distance dispersal of Annonaceae in the Early Cenozoic (c. 45-65 Ma), with dispersals from Africa to South America and Asia (Figure 1d, e, Figure 3, Figure 4f). Some of these (pseudo-)syncarpous fruits have been described as 'megafaunal' fruits, as they are >10 cm in size and contain several seeds in a juicy, fleshy pulp [START_REF] Guimarães | Seed dispersal anachronisms: rethinking the fruits extinct megafauna ate[END_REF]), similar to for example durians and jackfruits. These species supposedly rely on large-bodied mammals ('megafauna', >40 kg) such as elephants, primates and tapirs for their seed dispersal [START_REF] Rogers | Western gorilla diet: A synthesis from six sites[END_REF][START_REF] Guimarães | Seed dispersal anachronisms: rethinking the fruits extinct megafauna ate[END_REF]. This is in line with the idea that megafauna had a central role in the dispersal of early angiosperm seeds [START_REF] Eriksson | Seed size, fruit size, and dispersal systems in Angiosperms from the Early Cretaceous to the Late Tertiary[END_REF][START_REF] Tiffney | Vertebrate dispersal of seed plants through time[END_REF], facilitating Early Cenozoic dispersal of fleshy-fruited plants via the boreotropical route in Laurasia [START_REF] Morley | Interplate dispersal paths for megathermal angiosperms[END_REF][START_REF] Couvreur | Early evolutionary history of the flowering plant family Annonaceae: steady diversification and boreotropical geodispersal[END_REF]. Indeed, palms likely also possessed megafaunal fruits during their Late Cretaceous/Early Cenozoic dispersals across Africa, Asia and South America [START_REF] Baker | Global biogeography and diversification of palms sheds light on the evolution of tropical lineages. I. Historical biogeography[END_REF][START_REF] Onstein | To adapt or go extinct? The fate of megafaunal palm fruits under past global change[END_REF]. Furthermore, Asian elephants (Elephas maximus) and their ancestors were proposed as important seed dispersers of several of the megafaunal-fruited Artocarpus (Moraceae) species in South-East Asia [START_REF] Williams | Out of Borneo: biogeography, phylogeny and divergence date estimates of Artocarpus (Moraceae)[END_REF]. Many megafaunal seed dispersers, such as South American proboscideans, xenarthrans, and Notoungulata, went extinct in the Late Quaternary [START_REF] Barnosky | Assessing the causes of Late Pleistocene extinctions on the continents[END_REF], and present-day plants with megafaunal fruits therefore suffer from dispersal limitation, small geographical ranges, and, possibly, extinction [START_REF] Guimarães | Seed dispersal anachronisms: rethinking the fruits extinct megafauna ate[END_REF][START_REF] Pires | Pleistocene megafaunal extinctions and the functional loss of long-distance seed-dispersal services[END_REF][START_REF] Onstein | To adapt or go extinct? The fate of megafaunal palm fruits under past global change[END_REF].

Generally, our results suggest that large fruits (minimum c. 3 cm long) growing on short stipes and often dull-coloured (e.g. brown or orange) may have contributed to Cenozoic long-distance dispersal (Figure 1c, f, h and Figure 4a,e,g). These large fruits are found, for example, in extant Uvaria, Monoon or Trigynaea species, or in the Central American species in tribe Miliuseae (especially in the genera Sapranthus and Tridimeris). These fruits are associated with dispersal by relatively large mammals (e.g. primates as suggested for Uvaria, [START_REF] Zhou | Out-of-Africa' dispersal of tropical floras during the Miocene climatic optimum: evidence from Uvaria (Annonaceae)[END_REF] and likely contributed to the overland dispersal of Annonaceae throughout the Cenozoic, for example via vegetation corridors from Africa to Asia during the Neogene (Figure 3), which coincided with the 'out-of-Africa' dispersal of primates [START_REF] Zhou | Out-of-Africa' dispersal of tropical floras during the Miocene climatic optimum: evidence from Uvaria (Annonaceae)[END_REF][START_REF] Thomas | The historical origins of palaeotropical intercontinental disjunctions in the pantropical flowering plant family Annonaceae[END_REF]. Only few extant, frugivorous bird species, such as cassowaries (Casuarius), have gape widths large enough to swallow these fruits.

We also find strong support that moniliform fruits (long strings of bead-like fruitlets, found in e.g. extant Dasymaschalon, Desmos and Monanthotaxis, [START_REF] Wang | A plastid DNA phylogeny of Dasymaschalon (Annonaceae) and allied genera: Evidence for generic non-monophyly and the parallel evolutionary loss of inner petals[END_REF]Guo et al., 2017b, Figure 1a, Figure 4j), dehiscent fruits (e.g. found in extant Xylopia and Cymbopetalum, Figure 1j, Figure 4i), and (relatively) small seeds (Figure 4c) are traits associated with long-distance dispersal. Both moniliform and dehiscent fruits have been shown to be particularly attractive to birds [START_REF] Gautier-Hion | Fruit characters as a basis of fruit choice and seed dispersal in a tropical forest vertebrate community[END_REF][START_REF] Lomáscolo | Signal convergence in fruits: a result of selection by frugivores[END_REF]Guo et al., 2017b), although Xylopia has been observed to be fed on by both birds and primates [START_REF] Johnson | A revision of Xylopia L. (Annonaceae): the species of tropical Africa[END_REF]. These vertebrate dispersers facilitate germination in these species by removing the aril, the sarcotesta, or both (i.e. structures that inhibit germination) [START_REF] Stull | Plastid and seed morphology data support a revised infrageneric classification and an African origin of the pantropical genus Xylopia (Annonaceae)[END_REF]. The disjunct tropical African/Asian distributions of Dasymaschalon and suggests that dispersal may have occurred via the Afro-Asian land bridge in the Neogene (Figure 3). During this time, frugivorous songbirds (Passeri) showed waves of expansion from Australia through Asia to the rest of the globe [START_REF] Moyle | Tectonic collision and uplift of Wallacea triggered the global songbird radiation[END_REF], possibly facilitating these plant dispersals. Similar bird-dispersed traits may have assisted longdistance dispersal in other tropical families, such as the fleshy berries of Melastomataceae (Renner, 2004b), and the dehiscent fruits of Meliaceae [START_REF] Koenen | Recently evolved diversity and convergent radiations of rainforest mahoganies (Meliaceae) shed new light on the origins of rainforest hyperdiversity[END_REF]. Furthermore, seasonally migratory frugivorous birds, or large-bodied and strong-flying fruit pigeons (Ptilinopus) and frugivorous hornbills (Penelopides) [START_REF] Holbrook | Implications of long-distance movements of frugivorous rain forest hornbills[END_REF][START_REF] Kissling | The global distribution of frugivory in birds[END_REF] may have assisted historical 'island hopping' of Annonaceae and other tropical plants lineages across Asia, Oceania and the Pacific (e.g. in Cinnamomum, Lauraceae, [START_REF] Huang | Origins and evolution of cinnamon and camphor: A phylogenetic and historical biogeographical analysis of the Cinnamomum group (Lauraceae)[END_REF]. Against our expectation, we found that cauliflorous fruits (sometimes associated with bat-dispersal, Table 1), may hinder long-distance dispersal (Figure 4h). Possibly, by growing in the understorey, these fruits may be dispersal limited due to the sedentary behaviour of understory frugivores [START_REF] Givnish | Ecology of plant speciation[END_REF][START_REF] Onstein | Frugivory-related traits promote speciation of tropical palms[END_REF].

Although some of the long-distance dispersal traits identified in this study (e.g. few, large fruits) have been recognized as specialized dispersal syndromes associated with specialized frugivores (i.e. large-bodied animals, highly dependent on fruits, efficient dispersers, feeding on few plant species) [START_REF] Howe | Specialized and generalized dispersal systems: where does 'the paradigm' stand?[END_REF], some traits (e.g. small seeds, dehiscent fruits) may instead reflect a more generalized, opportunistic dispersal strategy [START_REF] Howe | Specialized and generalized dispersal systems: where does 'the paradigm' stand?[END_REF]. It is therefore expected that a mix of specialized and generalized dispersal agents have been important for the dispersal of vertebrate-dispersed plants (incl. Annonaceae) across continents. Phylogeny, biogeography and traits: some of the limitations in this study Our sampling of Annonaceae (234 / 2400) is sparse and raises the question whether these taxa are sufficiently representative of their distribution and traits to make a meaningful inference. Most (but not all, e.g. Anaxagorea, Xylopia) genera occupy a single area, and most traits show phylogenetic signal (e.g. fruit length, dehiscence, syncarpy and moniliform fruits, Table S7), indicating that most biogeographical and trait transitions happened relatively early during Annonaceae evolution, i.e. throughout the Paleogene (66-23 Ma) and Neogene (c. 23-2.6 Ma), and our sampling (97% of genera were sampled) would be able to capture these events. Undoubtedly, we underestimated the real number of long-distance dispersal events and functional trait transitions, especially during more recent times. Biogeographical studies that target Annonaceae sampling within genera (e.g. [START_REF] Zhou | Out-of-Africa' dispersal of tropical floras during the Miocene climatic optimum: evidence from Uvaria (Annonaceae)[END_REF]Guo et al., 2017b;[START_REF] Pirie | Parallel diversifications of Cremastosperma and Mosannona (Annonaceae), tropical rainforest trees tracking Neogene upheaval of South America[END_REF] therefore provide a more comprehensive understanding of Annonaceae dispersal at finer temporal and spatial scales. Importantly, phylogenetically labile traits (e.g. exocarp traits, Table S7, Figure S3) which did not appear significant in the Annonaceae-wide analysis, could provide valuable insights into trait-related long-distance dispersal within genera. Unfortunately, functional trait data for most Annonaceae taxa is currently lacking.

Besides the sampling, we acknowledge uncertainty with respect to divergence times and biogeographic reconstruction, in part due to lack of suitable internal calibrations and informative priors, and the models used to infer ancestral areas and traits remain very simplistic [START_REF] Ree | A likelihood framework for inferring the evolution of geographic range on phylogenetic trees[END_REF][START_REF] Pagel | Bayesian analysis of correlated evolution of discrete characters by reversible jump Markov Chain Monte Carlo[END_REF][START_REF] Drummond | BEAST: bayesian evolutionary analysis by sampling trees[END_REF][START_REF] Ree | Maximum likelihood inference of geographic range evolution by dispersal, local extinction, and cladogenesis[END_REF][START_REF] Matzke | Probabilistic historical biogeography: new models for founder-event speciation, imperfect detection, and fossils allow improved accuracy and modeltesting[END_REF]. For example, among-lineage and through-time rate heterogeneity [START_REF] Couvreur | Early evolutionary history of the flowering plant family Annonaceae: steady diversification and boreotropical geodispersal[END_REF]Massoni et al., 2015b) was not taken into account, and analyses could be improved by including fossils directly in the inference, especially to account for, or estimate, extinction. Our phylogenetic reconstructions show that lineages of major Annonaceae clades are inferred to be slightly older than those obtained in previous studies [START_REF] Su | Evolutionary divergence times in the Annonaceae: evidence of a late Miocene origin of Pseuduvariain Sundaland with subsequent diversification in New Guinea[END_REF][START_REF] Couvreur | Early evolutionary history of the flowering plant family Annonaceae: steady diversification and boreotropical geodispersal[END_REF]but see, Massoni et al., 2015b), although 95% HPDs overlap, and phylogenetic relationships are similar to previous results (Chatrou et al., 2012;Guo et al., 2017a). The reason for these older ages is likely our use of uniform (as compared to lognormal) distributions for the calibration priors [START_REF] Sauquet | Testing the impact of calibration on molecular divergence times using a fossil-rich group: The case of Nothofagus (Fagales)[END_REF]. Furthermore, our biogeographical inference (Figure 3) is consistent with previous biogeographical reconstructions in Annonaceae (for a detailed discussion on historical biogeography in Annonaceae, see [START_REF] Doyle | Phylogeny, molecular and fossil dating, and biogeographic history of Annonaceae and Myristicaceae (Magnoliales)[END_REF][START_REF] Couvreur | Early evolutionary history of the flowering plant family Annonaceae: steady diversification and boreotropical geodispersal[END_REF][START_REF] Zhou | Out-of-Africa' dispersal of tropical floras during the Miocene climatic optimum: evidence from Uvaria (Annonaceae)[END_REF][START_REF] Thomas | The historical origins of palaeotropical intercontinental disjunctions in the pantropical flowering plant family Annonaceae[END_REF], but we obtained some differences between the DEC+J and DEC biogeographical scenarios (Figures 3 andS2), with moderate consequences for traitassociated long-distance dispersal (i.e. inconsistencies for seed size, seed number and fruit colour). Nevertheless, even though the Annonaceae fossil record is poorly understood, our results are consistent with fossil woods from the Paleocene-Eocene of England [START_REF] Crawley | Angiosperm woods from British Lower Cretaceous and Palaeogene deposits[END_REF] and Oregon [START_REF] Wheeler | Woods of the Middle Eocene Nut Beds flora, Clarno Formation, Oregon, USA[END_REF], supporting the Laurasian boreotropical dispersal route.

We cannot discard the possibility that historical dispersal happened by modes other than frugivores, as it has previously been argued that long-distance dispersal shows little correlation with fruit trait syndromes [START_REF] Thomas | The historical origins of palaeotropical intercontinental disjunctions in the pantropical flowering plant family Annonaceae[END_REF]. Indeed, long-distance dispersal could have happened by rare rafting events on vegetation floats, diaspores in the mud adhering to the feet of birds, or extreme meteorological events. Furthermore, some fruits may be able to float and remain viable for a longer time in salt water (e.g. in invasive mangroveassociated Annona species on Fiji), and may thus have been dispersed by sea currents (Renner, 2004a). Nevertheless, if long-distance dispersal would have been independent from frugivory-related traits, we would expect a random distribution of traits across dispersal events, whereas we detected a significant association between Annonaceae long-distance dispersal and ten out of fifteen frugivory-related traits (Figure 4). Furthermore, our simulation study indicates that this is unlikely driven by neutral / random evolution of these traits on the Annonaceae phylogenetic tree (Figures S4 andS5).

Last, we lack a mechanistic model linking traits and dispersal rates. Although we have taken a trait-based approach to infer the potential frugivores important for long-distance dispersal (Figure 2), actual, present-day dispersers remain unknown for most plant species (incl. Annonaceae) and data availability tends to be localized. Further confidence and precision could therefore be gained in future work addressing these specific limitations.

Conclusion

Since Humboldt's travels (e.g. 1889), an important finding in the field of historical biogeography has been that long-distance dispersal (vs. vicariance) may have been the rule rather than the exception to explain the pantropical distribution of many plant families (e.g. Myristicaceae, [START_REF] Doyle | Phylogeny, molecular and fossil dating, and biogeographic history of Annonaceae and Myristicaceae (Magnoliales)[END_REF]Melastomataceae, Renner, 2004b;Monimiaceae, Renner et al., 2010;Arecaceae, Baker & Couvreur, 2013;Moraceae, Williams et al., 2017). Nevertheless, it has remained puzzling by which mechanism these long-distance dispersal events have occurred [START_REF] Van Steenis | The land-bridge theory in botany with particular reference to tropical plants[END_REF][START_REF] Thorne | Major disjunctions in the geographic ranges of seed plants[END_REF][START_REF] Morley | Interplate dispersal paths for megathermal angiosperms[END_REF]. This study contributes to our understanding of the plant traits (such as fruit size, type and colour) and dispersal agents that may have facilitated past intercontinental long-distance dispersal of Annonaceae across the tropical realms. These frugivory-related traits are not unique for this family, and similar traits may thus explain the disjunct distributions of tropical plants more generally. Positively correlated with frugivore body size, so that large fruits rely on large-bodied frugivores for their dispersal.

(van der [START_REF] Van Der Pijl | Principles of dispersal in higher plants[END_REF][START_REF] Jordano | Fruits and frugivory. Seeds: the ecology of regeneration in plant communities 2[END_REF][START_REF] Herrera | Seed dispersal by vertebrates. Plant-animal interactions: an evolutionary approach[END_REF][START_REF] Onstein | Frugivory-related traits promote speciation of tropical palms[END_REF][START_REF] Onstein | To adapt or go extinct? The fate of megafaunal palm fruits under past global change[END_REF] 2 Fruit(let) number Number of monocarps / fruits attached to fruit stalk.

Allometric constraint and / or increase of dispersal probability. Trade-off between fruit size and number. [START_REF] Howe | Specialized and generalized dispersal systems: where does 'the paradigm' stand?[END_REF] 3 Seed length (cm) Length of single seed.

Positively correlated with frugivore body size, so that large seeds rely on large-bodied frugivores for their dispersal.

(van der [START_REF] Van Der Pijl | Principles of dispersal in higher plants[END_REF][START_REF] Jordano | Fruits and frugivory. Seeds: the ecology of regeneration in plant communities 2[END_REF][START_REF] Herrera | Seed dispersal by vertebrates. Plant-animal interactions: an evolutionary approach[END_REF][START_REF] Onstein | Frugivory-related traits promote speciation of tropical palms[END_REF]Onstein et al., Plant height is positively related to dispersal distance. [START_REF] Thomson | Seed dispersal distance is more strongly correlated with plant height than with seed mass[END_REF] 561 562 563

Figure 1 :

 1 Figure 1: Diversity of vertebrate-dispersed Annonaceae fruit types. Illustration of frugivory-related traits: (a) moniliform fruits, Monanthotaxis sp; (b) conspicuous fruit display, Malmea manausensis; (c) large apocarpous fruits on short stipes, Uvaria muricata; (d) large (pseudo-)syncarpous fruit with several seeds, Duguetia confinis; (e) large syncarpous fruit, Monodora myristica; (f) large apocarpous fruits on short stipes, Uvaria klainei; (g) dehiscent fruits, Xylopia Africana; (h) large apocarpous fruits on short stipes with several seeds, Uvaria klainei. Photos were taken from World Annonaceae (http://annonaceae.myspecies.info/); photo credit: L.W. Chatrou (a), T.L.P. Couvreur (b, c, eh), J. van der Maesen (d).

Figure 2 :

 2 Figure 2: Ordination illustrating the frugivory-related trait syndromes in Annonaceae.Principal component analysis (PCA) of the 10 functional traits which were significantly associated with long-distance dispersal in Annonaceae. Grey dots indicate the position of the species in the ordination (n = 133 species without any missing trait data). The animal silhouettes (toucan, bat, and elephant) illustrate our expectation with respect to fruit traits and primary seed dispersers, i.e. bird, bat or (large) mammal fruit traits (see introduction). The ordination shows that traits are correlated and explain distinct variation in trait space, potentially related to bird, bat or mammal trait 'syndromes'. The amount of total variation explained by principal components PC1 and PC2 is indicated at the axes.

Figure 3 :

 3 Figure 3: Annonaceae biogeographical inference. The biogeographical reconstruction under the DEC+J model (dispersal = 0.0008, extinction = 0, jump-dispersal = 0.0166) on the Annonaceae maximum clade credibility (MCC) tree visualizes the 24 long-distance dispersal events (dashed branches). The pie-charts indicate the most probable ancestral area(s) (Africa, Asia, Pacific, North America, South America, Madagascar). The long-distance dispersal routes (Laurasian geodispersal, Afro-Asian land bridge, South America-Africa stepping stones and Pacific island hopping) are shown for the respective time periods. The subfamilies are indicated at the tips.

Figure 4 :

 4 Figure 4: Frugivory-related traits associated with intercontinental long-distance dispersal in Annonaceae. The average value of a trait (continuous traits, a-e) or the probability of the presence of a trait (binary traits, f-j) is indicated for long-distance dispersal events and dispersal routes as compared to Annonaceae lineages not involved in long-distance dispersal, based on ancestral state reconstructions and biogeographical inference from the DEC+J model. The traits associated with dispersal routes (represented by colours other than grey) significantly deviating from Annonaceae not involved in long-distance dispersal (grey) are inferred with linear models (continuous, a-e) or generalized linear models (binary traits, fj). The red asterix indicates effects significantly supported by both the DEC and DEC+J models, a green asterix if only supported by DEC+J and a black asterix if only supported by DEC. Box-and-whiskers indicate average, 95% distribution and outliers of trait values. LDD = long-distance dispersal.

Table 1 : Fifteen frugivory-related traits measured for Annonaceae species (n = 228) and their hypothesized functionality with respect to frugivory.

 1

	Trait	Description	Functionality	References
	1 Fruit length (cm)	Length of monocarp or fruit.

Acknowledgements

Miun, Jeisin Jumian, Tawadong Tangah and Aloysius Laim for assistance in the field. We acknowledge the Sabah Biodiversity Centre (SaBC) for access permits. We also thank Jürg Schönenberger and University of Vienna for hosting the PROTEUS database. Lorenzo Ottaviani, Véronique Normand and Florinde Vessies are acknowledged for their contributions to the trait data. This research was funded by a Swiss National Science Foundation Early Postdoc.Mobility grant (P2ZHP3_161991) to R.E.O. and an Agence Nationale de la Recherche grant (ANR-12-JVS7-0015-01, MAGNIPHY) to H.S. The University of Amsterdam provided support through the Faculty Research Cluster 'Global Ecology' and a starting grant to W.D.K. R.E.O. further acknowledges the support of the German Centre for Integrative Biodiversity Research (iDiv) Halle-Jena-Leipzig funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) -FZT 118.


Hye-Yun Jung

Kyeong-Hwa Lee

Development of group creativity in mathematical modeling

Keywords: Mathematical modeling, group creativity, interaction, creative synergy

Introduction

In many previous studies, mathematical modeling is considered an instrument to develop mathematical creativity, in rather individual contexts (e.g., Palsdottir & Sriraman, 2017, p. 49). However, there is a growing consensus that group creativity is important for the 21 st century [START_REF] Woodman | Toward a theory of organizational creativity[END_REF]. This study aims to explore interaction supporting the development of group creativity during mathematical modeling activities and the impact of group creativity on the mathematical modeling process.

Theoretical Background and Methods

Mathematical modeling is a cyclic and recursive process that requires understanding a real situation and creating a model (Jung et al., 2018, p. 155). Figure 1 illustrates key stages in this iterative modeling process. Vorhölter (2017, p. 345) discuss a perspective of group based modeling activities that potentially can support the development of group creativity. Group creativity has been considered a function of individual behavior, the interaction of the individuals involved, and the creative synergy of the interaction within the group (Woodman et al., 1993, pp. 302-304). Jung and Lee (2018, p. 373) made a distinction between three types of interaction when investigating group creativity, namely: mutually complementary-, conflict based-, and metacognitive-interaction. This study aims to investigate the following two questions: (1) What types of interaction can be observed during modelling activities that support the development of group creativity? (2) What impact on the modelling process can be observed in the interactions? Six 11 th grade students and a teacher participated in this research. Based on our previous study suggesting that 3 to 4 members were appropriate, the students were divided into two groups. The researchers and the teacher worked together to design the task, and how to implement based on the question: "What are your own strategies to prevent or cope with blackouts?". All the lessons were videotaped, audio-recorded and transcribed. Field-notes were made during the lesson observations. Students' worksheets were collected. The unit of analysis was the observed types of interaction at each stages of the mathematical modeling process.

Result and Discussion

The three types of interaction supporting the development of group creativity and its creative synergy were observed in the activity and found to impact the development of their group creativity. Both mutually complementary-and conflict based-interaction were observed in both groups, but metacognitive-interaction was observed only in Group A. First, mutually complementary interaction was observed at the real world inquiry and the factor finding stages. Although each group member shared their various thoughts, meaningful information for deriving mathematical model was made by the accumulation of all those thoughts through mutual complementary interaction. The creative synergy and effect of the interaction was the expansion of factors that could affect real world phenomena related to blackouts. Second, conflict based interaction was observed at the simplification stage. Because of the diversity of thoughts and their inconsistency, conflicts had occurred among group members. This interaction resulted in rich evidence, as the creative synergy, for key factors to consider and clarification and validation of the criteria to evaluate the selected key factors. Third, metacognitive interaction was observed at the mathematical model derivation stage. Each group reflected on the modeling process and their initial mathematical model. As a result, the students could have an elaborated mathematical model with reasonable justification. In this study we extended the scope of the effectiveness of mathematical modeling to develop creativity education from the individual context to the group context. Previous studies stressed the necessity of practical studies on interaction as a process of supporting the development of group creativity (Sawyer, 2012, pp. 243-244). This study provides the first steps in this direction.

Figure 1 :

 1 Figure 1: Mathematical modeling process chart (Jung et al., 2018, p. 155)


Heiner Klock
email: hklock@uni-koblenz.de

Hans-Stefan Siller
email: hans-stefan.siller@mathematik.uni-wuerzburg.de

Measuring an aspect of adaptive intervention competence in mathematical modelling processes

Keywords: Diagnosis, intervention, adaptive behaviour, linear regression

To provide appropriate support during modelling processes is challenging for teachers. Especially modelling tasks based on a holistic approach offer a multitude of solutions that the teacher has to deal with. Several authors therefore emphasize the importance of a precise diagnosis in the intervention process. Adaptive interventions are a suitable support for students whereas a previous diagnosis should be the basis. A process model is presented that describes an idealized intervention adapted to students' modelling processes. In this model, a diagnostic and an intervention-related part can be distinguished. We investigate the question whether adaptive intervention competence can be described through a one-or two-dimensional model and whether a cause and effect relationship between a correct diagnosis and the selection of an adaptive intervention can be determined. The results indicate that the meaning of a previous diagnosis can be confirmed empirically in this sample.

Introduction

When using modelling tasks according to a holistic approach, group work is an effective instructional strategy [START_REF] Clohessy | Examining the role of group work as an effective instructional strategy when teaching problem solving[END_REF]. In less structured and independently carried out working processes, adaptive teacher interventions provide appropriate help for students. When difficulties arise in group work, teacher interventions should ensure progress without giving too many content-related hints on the solution. Frequently, a spontaneous reaction is necessary and there is little time available. Adaptive interventions should create a balance between direct instruction and students' independent work [START_REF] Leiss | Adaptive Lehrerinterventionen beim mathematischen Modellierenempirische Befunde einer vergleichenden Labor-und Unterrichtsstudie[END_REF]. However, intervening adaptively is therefore a challenging activity for teachers [START_REF] Blum | Mathematical modelling: Can it be taught and learnt[END_REF].

For this reason, a modelling seminar was developed and integrated into university teacher training. The overall intention is to facilitate pre-service teachers' adaptive intervention competence and evaluate their development through the seminar. By a teacher intervention, we generally mean a verbal intrusion into the students' solution process (cf. [START_REF] Leiss | Hilf mir es selbst zu tun[END_REF]. We present the construct of adaptive intervention competence which is measured using a quantitative test instrument. In this article, the data of the seminar are used to examine the dimensionality of the construct and to investigate the cause and effect relationship between diagnostic and intervention-related aspects. [START_REF] Leiss | Hilf mir es selbst zu tun[END_REF] has developed a general model for teacher interventions (see Figure 1) in which he differentiates between three aspects: the basic knowledge, the area and the characteristics of an intervention [START_REF] Tropper | Teachers' temporary support and worked-out examples as elements of scaffolding in mathematical modeling[END_REF]. A diagnosis of the situation (trigger of the intervention, previous interventions, knowledge required to solve the task, students' competence level, time available) and a diagnosis of difficulties (type of difficulty, area and cause of the difficulty, assignment in a theoretical modelhere: the modelling cycle) is necessary to create a basic knowledge which is crucial for the selection of an adequate intervention. The area of intervention describes to which aspect the intervention refers to. Organizational interventions concern the design of the learning environment ("Watch the time!"). Affective interventions influence students' emotional aspects extrinsically ("You can do this!"). Strategic interventions are help on a meta-level ("What is still missing?" (Blum & Borromeo Ferri, 2009, p. 52)). Content-related interventions are related to concrete contents of the task ("A car consumes 7 litres per kilometre."). The area is the central feature of an intervention [START_REF] Leiss | Hilf mir es selbst zu tun[END_REF]. In particular, strategic interventions are considered to have high potential to support students to overcome difficulties in the modelling process [START_REF] Link | Problemlöseprozesse selbstständigkeitsorientiert begleiten[END_REF][START_REF] Stender | The use of heuristic strategies in modelling activities[END_REF].

Adaptive interventions

Interventions can be classified by different characteristics like the intention of the intervention (statement, question, request), its duration and the addressee (single student, group, whole class) [START_REF] Leiss | Hilf mir es selbst zu tun[END_REF]. The aspects basic knowledge, area and characteristics of an intervention describe a general and idealized intervention. Based on that, [START_REF] Tropper | Teachers' temporary support and worked-out examples as elements of scaffolding in mathematical modeling[END_REF] defined the notion of adaptive teacher interventions which are based on a diagnosis of the situation and can be described as an independence-preserving form of support, adapted in form and content to students' learning process, in order to enable them to overcome a (potential) barrier in the process and to continue the process as independently as possible. (2015, p. 1226) Four essential characteristics of adaptive interventions can be identified from this and further definitions (see [START_REF] Leiss | Hilf mir es selbst zu tun[END_REF][START_REF] Stender | The use of heuristic strategies in modelling activities[END_REF]. In our work adaptive interventions:

 are based on a diagnosis.  are adapted in form and content to students' learning process.  provide minimal help.  preserve independence.

These four aspects are crucial for supporting students in mathematical modelling processes. They are the basis for assessing interventions in terms of adaptivity.

Adaptive intervention competence in mathematical modelling processes

Due to the high demands on adaptive interventions in mathematical modelling processes, a process model was developed using the work of [START_REF] Leiss | Hilf mir es selbst zu tun[END_REF]. The model describes an idealized intervention supporting groups of students in mathematical modelling processes (see Figure 2). The Steps 1 and 2 form the diagnostic part of the model and thus the diagnostic competence. An accurate diagnosis is essential for the selection of an adaptive intervention [START_REF] Blum | Mathematical modelling: Can it be taught and learnt[END_REF][START_REF] Leiss | Hilf mir es selbst zu tun[END_REF]. If difficulties arise in the solution process, they have to be diagnosed. It is useful to identify the modelling phase first (Step 1 in Figure 2) in which the students are currently working [START_REF] Borromeo Ferri | Mathematical modelling in teacher educationexperiences from a modelling seminar[END_REF]. Based on knowledge about typical difficulties in the individual modelling phases, initial indications for the cause of the difficulty can be obtained. Several studies indicate potential difficulties in single modelling phases (e.g., [START_REF] Galbraith | A framework for identifying student blockages during transitions in the modelling process[END_REF]. With the help of this knowledge a focused diagnosis is possible (Step 2 in Figure 2). [START_REF] Link | Problemlöseprozesse selbstständigkeitsorientiert begleiten[END_REF]. However, depending on the situation and its framework conditions, organisational, affective or content-related interventions may be suitable. In Steps 1 to 3but especially in Step 3 the knowledge about the situation (see Figure 2; [START_REF] Leiss | Hilf mir es selbst zu tun[END_REF] influences decision making. This knowledge is ideally acquired before the intervention process due to its crucial meaning for the selection of an adaptive intervention. At this point, it may be suitable not to intervene prematurely. This provides students with the opportunity to overcome the difficulty by themselves [START_REF] Leiss | Hilf mir es selbst zu tun[END_REF]. The adaptivity is appraised before implementationa priorion the basis of the four characteristic aspects mentioned above. Finally, an evaluation must be carried out after implementationa posteriori. It has to be determined whether the intended behaviour has occurred, whether the difficulty has been overcome and whether students are working independently. The adaptivity of an intervention can finally be determined afterwards. Even if it matches all aspects of an adaptive intervention, a priori, it needs not be successful [START_REF] Stender | Wirkungsvolle Lehrerinterventionsformen bei komplexen Modellierungsaufgaben[END_REF][START_REF] Vorhölter | Teacher behaviour in modelling classes[END_REF], a posteriori. The intervention is assessed by the teacher before and after implementation. Therefore, we distinguish between a priori and a posteriori intervention competence. If necessary, the teacher has to go through the intervention process again.

The process model describes cognitive and action-related aspects of an intervention. The ability to perform this process appropriately is what we call adaptive intervention competence in mathematical modelling processes.

Hypotheses

In this article, we investigate the dimensionality of the measured construct and whether the diagnostic competence (Steps 1 and 2) and the a priori intervention competence (Step 3) show an empirical interrelation. Since various authors emphasize the importance of an accurate diagnosis for the adaptivity of an intervention [START_REF] Blum | Mathematical modelling: Can it be taught and learnt[END_REF][START_REF] Leiss | Hilf mir es selbst zu tun[END_REF], our hypotheses are:

(H1)
The cognitive part of adaptive intervention competence can be described by a twodimensional model (diagnostic and a priori intervention competence).

(H2) There is a cause and effect relationship between diagnostic and a priori intervention competence (Klock & Siller, 2019).

Method

Pre-service teachers were surveyed with the help of a quantitative test instrument in a pre-postdesign before and after attending a teacher training seminar on mathematical modelling. We use this data to answer the mentioned research questions. Since the evaluation of the seminar is not part of this article, we refer to another publication for a description of its contents (Klock & Siller, 2019).

Sample

The data were collected in the winter term 2017/2018 and in the summer term 2018. The preservice teachers are all trained for teaching professions at secondary schools. The sample description is given in Table 1. The genders are distributed almost evenly, the students are on average 23 years old and are in their sixth to seventh term of study. In order to generate a sufficient sample size for the analysis of dimensionality, the method of virtual persons according to [START_REF] Hartig | Schätzung von Veränderungen mit "plausible values[END_REF] was applied. In this approach pre-and post-test data of the same persons (n=156) are used in a simple logistic Rasch model. The advantage of this approach is that items' difficulty parameters are estimated using the same model in pre-and posttest. However, potential dependencies between the measured values of the same person are not considered.

Instrument

Piloting the test in another sample (n=66), four of ten task vignettes were eliminated based on statistical quality criteria. The test instrument [START_REF] Klock | Lehrerkompetenzen zum mathematischen Modellieren -Test zur Erfassung von Aspekten professioneller Kompetenz zum Lehren mathematischen Modellierens[END_REF][START_REF] Klock | Aspekte professioneller Kompetenz zum Lehren mathematischer Modellierung bei (angehenden) Lehrkräften -Erfassung und Evaluation[END_REF] consists finally of six text vignettes, each showing a modelling task and a typical students' conversation while solving the task. The scale "diagnosis" consists of three multiplechoice items per text vignette (18 items) with four possible answers each. The scale "intervention" consists of complex multiple-choice items with four items per text vignette (24 items; see The test construction is based on the presented process model (see Figure 2). The diagnostic part is operationalized by the scale "diagnosis". The scale measures the ability to identify the modelling phase, the difficulty in the modelling process and to select a support goal. A priori intervention competence is operationalized by the scale "intervention". The statements have to be assessed with regard to the last three of the four aspects of adaptivity mentioned above and aspects of the situation shown by the text vignette. The items were evaluated based on expert ratings assigning scores dichotomously (0 and 1 raw points).

Results

To evaluate the dimensionality of the construct, the simple logistic Rasch model (Rost, 1996, p. 115) was applied to compare two models (H1). The two models and the results of Rasch analysis are shown in Figure 3. The two models are compared with the help of the residual estimates (final deviance, AIC). The residuals are significantly smaller in the 2-dim. Model which indicates a better description of the data. In both models, all item-fit values are within the recommended interval (standardized weighted mean squares > 0.8 and < 1.2) by Bond and Fox (2013, p. 279), which points to a general fit of the Rasch model. The reliabilities are acceptable with regard to the EAPreliability. All indications point to a better fit of the two-dimensional model. We choose the 2-dim. model since it describes the data better and the reliabilities are acceptable.

The scales in the 2-dim. model correlate with high significance (r = .70). The diagnostic and intervention-related part can thus be empirically separated but also form the construct of adaptive intervention competence in mathematical modelling processes since they are highly correlated. (H1) can be confirmed in this sample. (H2) examines the relationship between these two dimensions. For this reason, a linear regression was performed using the post-test-scores (n=78). The weighted likelihood estimates of the Rasch model (WLE-scores) are used to calculate a linear regression between the scales "diagnosis" (independent variable) and "intervention" (dependent variable). Table 3 shows the results. The two scales "diagnosis" and "intervention" show a medium correlation (R = .45). There is a medium goodness-of-fit for the data (R 2 = .20) and a high test power (1- error = .99). The variable "diagnosis" predicts statistically significant the variable "intervention" (F(1, 73) = 18,701, p <.001).

Model

If the score of the scale "diagnosis" increases by one standard deviation, the score of the scale "intervention" increases on average by  = .45 standard deviations. According to that (H2) can also be confirmed in this sample.

R

Discussion and conclusion

Within the scope of our survey, cognitive performance dispositions of adaptive intervention competence were measured. With the help of text vignettes in some extent situational abilities are measured via the selection of a suitable but predetermined answer alternatives. The test does not operationalise the construct of adaptive intervention competence completely. Only the diagnostic and a priori intervention competence is measured. Action-related aspects are not considered in the test instrument. They can be evaluated by means of videos recorded during the seminar. The videos show pre-service teachers supporting groups of students working on a modelling task. However, it can be assumed that the cognitive skills measured are a prerequisite for an adequate diagnosis and intervention.

It was found that a cognitive aspect of adaptive intervention competence can be described by a twodimensional model consisting of diagnostic and intervention-related parts. There is a cause and effect relationship between these dimensions. The scale "diagnosis" predicts skills measured by the scale "intervention" significantly. This can be confirmed by similar results when pre-test scores are analysed. In these data, the effect of the scale "diagnosis" is smaller than in the post-test data. Since diagnostic and intervention competences are acquired in the seminar, the significance of diagnostic skills seems to increase at higher skill levels (Klock & Siller, 2019). The diagnosis plays an important role in the intervention process. However, these preliminary results have to be confirmed by further data.

Figure 1 :

 1 Figure 1: Process model for general teacher interventions (Leiss, 2007; translation by authors)

Figure 2 :

 2 Figure 2: Process model for adaptive interventions in mathematical modelling processes

  Step 3 describes the choice and realization of the intervention. Few studies examined the effectiveness of various interventions. Studies by Link (2011), Stender (2016) and Vorhölter, Grünewald, Krosanke, Beutel and Meyer (2013) indicate that strategic interventions are particularly suitable. Interventions that follow rules of good communication consist of several interventions at different strategic levels

Figure 3 :

 3 Figure 3: One-(left) and two-dimensional (right) model and results of Rasch analysis

Table 1 : Sample description

 1

	n	Gender	Age		Term
		male/female	M	SD	M	SD
	78	35/43	23.06	2.69	6.71	2.89

Table 2 : Item examples for the two scales "diagnosis" and "intervention" (Klock & Wess, 2018)

 2 Table 2). Critical questioning of results in the modelling process.  C. Independent construction of mental models for given problem situations.  D. Reliable translation of simplified real situations into mathematical models. 

	Scale	Number of items	Item examples
			To which phase of the solution process can the group of students mainly be assigned to?
			A. construct/understand		
		6	B. simplify/structure		
			C. mathematise		
			D. interpret		
			Diagnose students' difficulty working on the task in this situation. The students …
			A. … have difficulties in making assumptions.		
	Diagnosis	6	B. … draw the wrong conclusion from their mathematical result. C. … have difficulties in understanding the context.		 
			D. … use an unsuitable mathematical model.		
			Please indicate which support goal you would formulate for the group following this
			situation.
	A. Independent acquisition and evaluation of information. Please indicate which of the following interventions are suitable for an independence  preserving support of modelling skills in this situation. suitable unsuitable B. Intervention 6 A. "First of all, estimates how long a car is."   24 B. "First, consider only part of the problem, e.g. how many cars are  
			in traffic jams at all."
			C. "Exactly, calculate this value."		
			D. "Think about how you could get the missing data."		

Table 3 : Results of linear regression

 3

Acknowledgment

We thank the German Ministry for Education and Research for funding the project MoSAiK (Kauertz & Siller, 2016) support code 01JA1605in the framework of "Qualitätsoffensive Lehrerbildung".


Keywords: Voie ferrée, milieu périodique, méthode des éléments finis semi analytique, théorème de, Théorie Variationnelle des Rayons Complexes, milieux ouvert, PML, IRIS