Céline Devaux

Clotilde Lepers

Emmanuelle Porcher
email: porcher@mnhn.fr

SEX UNCOVERED SPECIAL ISSUE: CONSTRAINTS IMPOSED BY POLLINATOR BEHAVIOUR ON THE ECOLOGY AND EVOLUTION OF PLANT MATING SYSTEMS

Keywords: Pollinator foraging behaviour, Floral traits, Selfing rates, Plasticity, Inbreeding depression, Plant-pollinator interactions, Mutualistic networks

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INTRODUCTION

Flowering plants are stimulating models for studying the evolutionary biology of reproductive systems, owing to their wide diversity of mating systems [START_REF] Barrett | Mating strategies in flowering plants: the outcrossing-selfing paradigm and beyond[END_REF][START_REF] Charlesworth | Evolution of plant breeding systems[END_REF].

Typical topics of interest comprise the evolution of selfing rates [START_REF] Goodwillie | The evolutionary enigma of mixed mating systems in plants: Occurrence, theoretical explanations, and empirical evidence[END_REF], including self-incompatibility [START_REF] Goldberg | Species selection maintains self-incompatibility[END_REF], the evolution of separate sexes [START_REF] Spigler | Gynodioecy to dioecy: are we there yet?[END_REF] and sex chromosomes [START_REF] Charlesworth | Plant sex chromosome evolution[END_REF], and the maintenance of sexual reproduction [START_REF] Silvertown | The evolutionary maintenance of sexual reproduction: Evidence from the ecological distribution of asexual reproduction in clonal plants[END_REF]. The reproduction of the vast majority of Angiosperm species is unique in its reliance on animals as pollen vectors (~90%, [START_REF] Ollerton | How many flowering plants are pollinated by animals?[END_REF], yet the study of plant mating system evolution has long remained uncoupled from pollination ecology, focusing primarily on genetic drivers. As mentioned by [START_REF] Charlesworth | Evolution of plant breeding systems[END_REF], the failure to include ecological mechanisms into the evolution of plant mating may be due to their diversity: "Models of mating system evolution have emphasised genetic effects, even though (…) ecological circumstances, such as pollinator abundance or plant density, must often be important. Their complexity and variety, however, creates difficulties in developing any general theories".

The gap between the study of plant mating systems and pollination ecology has shrunk over the past decades, with many studies focusing mostly on animal-pollinated plants (reviewed e.g. in [START_REF] Harder | Pollen dispersal and mating patterns in animalpollinated plants[END_REF], 2006;[START_REF] Goodwillie | The evolutionary enigma of mixed mating systems in plants: Occurrence, theoretical explanations, and empirical evidence[END_REF][START_REF] Mitchell | Ecology and evolution of plant-pollinator interactions[END_REF][START_REF] Eckert | Plant mating systems in a changing world[END_REF]Karron et al., 2012;[START_REF] Thomann | Flowering plants under global pollinator decline[END_REF] but also on wind-pollinated plants [START_REF] Friedman | Wind of change: new insights on the ecology and evolution of pollination and mating in wind-pollinated plants[END_REF]. This rich literature has revealed general patterns and processes out of the complexity mentioned by [START_REF] Charlesworth | Evolution of plant breeding systems[END_REF]. One such pattern is the increase in selfing rates under pollen limitation and its long-term evolutionary consequences [START_REF] Wright | Evolutionary consequences of self-fertilization in plants[END_REF]. This intuitive expectation can now be challenged as pollinator abundance decline and reduced pollination service become a worldwide reality [START_REF] Potts | Global pollinator declines: trends, impacts and drivers[END_REF][START_REF] Gonzalez-Varo | Combined effects of global change pressures on animal-mediated pollination[END_REF]. Several papers discuss pollinator shortage as a cause of 4 outcross pollen limitation (see glossary) and increased immediate ecological selfing rates, which may determine future evolutionary changes in plant mating systems [START_REF] Eckert | Plant mating systems in a changing world[END_REF][START_REF] Thomann | Flowering plants under global pollinator decline[END_REF]. The latter prediction is supported by rapid evolution of the ability to self-fertilize observed in Mimulus guttatus in the absence of pollinators [START_REF] Bobdyl Roels | Rapid evolution caused by pollinator loss in Mimulus guttatus[END_REF].

Pollinator foraging behaviour also emerges as an important factor influencing plant selfing rates and their evolution. The predicted impact of foraging behaviour on plant mating systems is however less clear than that of pollinator abundance because selection on pollinator vs. plant traits do not always act in the same direction. In plants, selection favours floral traits that influence pollen transfer to promote reception of conspecific and compatible pollen, increase the quantity and quality of seeds produced (including the ratio of selfed to outcrossed seeds) and the amount of pollen exported to conspecifics. In pollinators, selection favours traits that maximize the rate of energy gain through foraging behaviour (optimal foraging theory, [START_REF] Pyke | Optimal foraging theory: a critical-review[END_REF], which may lead to non-optimal pollen transfer for plants.

Hence, although plants and pollinators are involved in true mutualistic interactions with reciprocal benefits, conflicts of interest are widespread [START_REF] Bronstein | The exploitation of mutualisms[END_REF][START_REF] Dufay | Conflicts between plants and pollinators that reproduce within inflorescences: evolutionary variations on a theme[END_REF]De Jong & Klinkhamer, 2005, p. 229). Constraints imposed by pollinators on plants, as well as constraints imposed by plants on pollinators, may induce plastic and evolutionary responses, such that the two partners are engaged in a permanent Red Queen-like coevolutionary race. The coevolution of plant and pollinator traits has been a major topic of research since Darwin, but constraints imposed by pollinator foraging behaviour on the ecology and evolution of plant mating systems are seldom integrated into experimental and theoretical studies. For example, most models of the evolution of plant selfing rates assume that these rates can evolve freely between zero and one. Another limit of studies connecting mating systems and pollination ecology is that they are often restricted to pairs of plant-pollinator species. Recent developments in ecological network theory have revealed that the community context, multi-species interactions, and the position of a species in a plantpollinator network can be key to understand the influence of pollinators on plant mating systems [START_REF] Vanbergen | Grazing alters insect visitation networks and plant mating systems[END_REF].

Here, we review how the interplay between pollinator behaviour and plant floral traits influences the immediate, ecological plant selfing rates (hereafter "ecological selfing rates"), the evolution of selfing rates, and their distribution in plant-pollinator networks (summarized in Fig. 1). We are interested in self-compatible plants, mostly with perfect flowers, that are pollinated by insects or birds [START_REF] Buchmann | The forgotten pollinators[END_REF], particularly bees and hummingbirds for which we have more data. In the first section, we show that the ecological selfing rates of about one half of flowering plant species is controlled partly by pollinator abundance and behaviour, which should therefore be included in theoretical investigation of plant mating system evolution. We argue, as do Karron et al. (2012), that the reciprocal effects of pollinator behaviour on floral traits are much better documented than their consequences for plant self-fertilization. Because we focus on pollinator behaviour, we intentionally exclude pollinator abundance, pollen limitation and their influence on the selection of floral traits, which were presented extensively elsewhere [START_REF] Elzinga | Time after time: flowering phenology and biotic interactions[END_REF][START_REF] Eckert | Plant mating systems in a changing world[END_REF][START_REF] Schiestl | Pollinator-mediated evolution of floral signals[END_REF][START_REF] Thomann | Flowering plants under global pollinator decline[END_REF]. One should keep in mind that these two components strongly determine ecological selfing rates and their evolution.

The second part of this review examines how theoretical studies of the evolution of plant selfing rates include pollinator behaviour and model the plant traits that can alleviate the constraints it might impose. We show that mechanistic models combining pollinator behaviour and the genetic consequences of selfing improve on pure ecological or pure genetic models by providing quantitative predictions of evolutionarily and ecologically stable plant 6 mating strategies. We propose a method to account for pollination ecology in models of the evolution of selfing rates, and provide experimental research avenues to help clarify the role of plant-pollinator interactions in the distribution of plant selfing rates. The last section shows that community-level processes can influence the ecology and evolution of plant mating systems, and outline how to use current knowledge on competing vs. facilitative interactions among plant species and pollinator species for a better understanding of the distribution and evolution of plant selfing rates.

THE INTERPLAY BETWEEN POLLINATOR BEHAVIOUR AND FLORAL TRAITS DETERMINES ECOLOGICAL PLANT SELFING RATES

The selfing rate or self-fertilization rate s is the fraction of selfed embryos produced by an individual plant. This fraction depends primarily on the rate of self-pollination, the relative amounts of self vs. outcross pollen transferred by pollinators or through non-pollinator means (e.g. stigma dragging). The self-pollination rate can be further modified by pre and postfertilization selection (see glossary), which is beyond the scope of this review. Only two categories of plant species have complete control over their selfing rate, although pollinators may still influence their seed set: (1) obligately outcrossing species (s = 0), such as selfincompatible or dioecious species, representing ca. 50% of species [START_REF] Igic | The distribution of plant mating systems: Study bias against obligately outcrossing species[END_REF] and (2) completely selfing species (s = 1) relying on prior autonomous selfing (see glossary), such as species producing closed flowers only, which are however extremely rare [START_REF] Goodwillie | The evolutionary enigma of mixed mating systems in plants: Occurrence, theoretical explanations, and empirical evidence[END_REF][START_REF] Culley | The cleistogamous breeding system: a review of its frequency, evolution, and ecology in angiosperms[END_REF].

In the remaining half of animal-pollinated plant species, selfing rates are invariably influenced by pollinators, via the quantities of both outcross and self-pollen transferred among and within flowers (Figs. 1 and2). Outcross pollen deposition on plant stigmas is always fully constrained by pollinators. In contrast, self-pollen deposition on stigmas depends only partially, but sometimes strongly, on pollinators as it includes: (1) facilitated selfpollination, the transfer of self-pollen within flowers caused by pollinator visits, (2) geitonogamous self-pollination caused by pollinator visits among flowers on a plant, and (3) autonomous, i.e. without the help of pollinators, prior, competing and delayed self-pollination within flowers (Fig. 2 and definitions of the glossary). Note that the amount of self-pollen deposited "autonomously" by a plant on stigmas may still be influenced by previous outcross pollen limitation, as is sometimes the case with delayed autonomous selfing (e.g. [START_REF] Ruan | Style curvature and its adaptive significance in the Malvaceae[END_REF]. Besides, even if the amount of autonomous self-pollen is under the plant control, the rate of self-pollination depends on pollinators via the amounts of self and outcross pollen they deposit on stigmas.

In the following, we examine how pollinator behavioural traits interact with plant traits to constrain patterns of outcross and self-pollen deposition and thereby the ecological selfing rates of plants. We review how pollinators can respond plastically to variation in floral traits to optimize their energy gains, and which floral traits can vary plastically or genetically to modify pollinator behaviour and control plant selfing rates. We consider one self-compatible plant species specialized (see glossary) on one pollinator species or functional group [START_REF] Fenster | Pollination syndromes and floral specialization[END_REF], as is frequently done in studies of the relationship between pollinators and plant mating systems. Pollinator choice among multiple plant species (preference and constancy, see glossary), competition among plant species for shared pollinators, and their impacts on plant selfing rates are discussed only in the last section.

Pollinator traits influencing outcross and self-pollen transfer

Self-pollination rates are influenced by (1) the number of pollinator visits to individual plants and flowers, (2) the efficiency of pollen transfer from stamens to pollinators and from pollinators to stigmas, within and among flowers, and (3) the composition of pollen loads on pollinators, particularly the fraction of self vs. outcross pollen. All these components 8 ultimately depend on pollinator abundance, morphological and phenological matching of plants and pollinators, and pollinator foraging behaviour among and within plants. We focus on pollinator behaviour (Fig. 1) and do not address pollinator abundance, phenology or morphology (see e.g. [START_REF] Waser | Interspecific pollen transfer and competition between co-occurring plant species[END_REF][START_REF] Harder | Pollen dispersal and mating patterns in animalpollinated plants[END_REF] for details on pollen placement on pollinators; or O 'Neil, 1997;[START_REF] Elzinga | Time after time: flowering phenology and biotic interactions[END_REF]Bartomeus et al., 2011 for phenology).

Pollinator grooming behaviour influences pollen transfer efficiency within and among plants; its intensity and timing greatly determine patterns of pollen deposition of outcross and self-pollen throughout a foraging bout (see glossary). Grooming generally causes pollen to be deposited on fewer flowers (e.g. [START_REF] Harder | The mating consequences of sexual segregation within inflorescences of flowering plants[END_REF][START_REF] Castellanos | Pollen transfer by hummingbirds and bumblebees, and the divergence of pollination modes in Penstemon[END_REF], hence reduces pollen carryover, with contrasting impacts of within-vs. between-plant grooming. Betweenplant grooming reduces pollen dispersal among plants [START_REF] Holmquist | Influence of pollinator grooming on pollen-mediated gene dispersal in Mimulus ringens (Phrymaceae)[END_REF] and is likely to increase outcross pollen limitation. Within-plant, between-flower grooming reduces pollen carryover within plants and should increase geitonogamous selfing rates [START_REF] Matsuki | Pollination efficiencies of flowervisiting insects as determined by direct genetic analysis of pollen origin[END_REF]. The scant available data suggest that most grooming occurs between plants (see e.g. [START_REF] Harder | Behavioral responses by bumble bees to variation in pollen availability[END_REF][START_REF] Mitchell | The influence of Mimulus ringens floral display size on pollinator visitation patterns[END_REF][START_REF] Johnson | Pollen fates and the limits on male reproductive success in an orchid population[END_REF], but the pattern may vary among pollinator species and depend on pollen availability, as shown by a higher probability of grooming between flowers with increasing pollen availability [START_REF] Harder | Behavioral responses by bumble bees to variation in pollen availability[END_REF]. More intensive and more frequent grooming is observed for pollen-collecting visitors (e.g. bees) than for nectar-collecting visitors (e.g. birds or moths; [START_REF] Thomson | Pollen transport and deposition by bumble bees in Erythronium: influences of floral nectar and bee grooming[END_REF][START_REF] Castellanos | Pollen transfer by hummingbirds and bumblebees, and the divergence of pollination modes in Penstemon[END_REF]. As a result, nectar-feeding species tend to transfer pollen more efficiently than do pollen-feeding species [START_REF] Conner | The effect of wild radish floral morphology on pollination efficiency by four taxa of pollinators[END_REF][START_REF] Sahli | Visitation, effectiveness, and efficiency of 15 genera of visitors to wild radish, Raphanus raphanismum (Brassicaceae)[END_REF]; but see [START_REF] King | Why flower visitation is a poor proxy for pollination: measuring single-visit pollen deposition, with implications for pollination networks and conservation[END_REF]. More generally, the extent of pollen carryover is negatively related to geitonogamous selfing rates [START_REF] Geber | The relationship of plant size to self-pollination in Mertensia ciliata[END_REF]Robertson, 1992a;[START_REF] Morris | Systematic increase in pollen carryover and its consequences for geitonogamy in plant populations[END_REF]: pollinators that deposit most of their outcross pollen on the first few flowers transfer mostly self-pollen on the subsequent flowers of the plant. Grooming can partially cause the negative relationship between pollen carryover and geitonogamy [START_REF] Rademaker | Pollen dynamics of bumblebee visitation on Echium vulgare[END_REF][START_REF] Matsuki | Pollination efficiencies of flowervisiting insects as determined by direct genetic analysis of pollen origin[END_REF], but pollen carryover is also strongly governed by interactions between pollinator morphology and floral design [START_REF] Harder | Pollen dispersal and mating patterns in animalpollinated plants[END_REF].

The number of flowers a pollinator probes successively on a plant increases geitonogamous self-pollination [START_REF] Rademaker | Selfing rates in natural populations of Echium vulgare: a combined empirical and model approach[END_REF][START_REF] Karron | Pollinator visitation patterns strongly influence among-flower variation in selfing rate[END_REF]. Pollinators tend to probe more flowers on plants with larger floral displays (see glossary), but rarely probe more than a dozen flowers per plant, so that the fraction of flowers probed per plant is often a decreasing function of display size (reviewed in [START_REF] Snow | The ecology of geitonogamous pollination[END_REF][START_REF] Ohashi | Behavioural responses of pollinators to variation in floral display size and their influences on the evolution of floral traits[END_REF][START_REF] Harder | Beyond floricentrism: The pollination function of inflorescences[END_REF]. Multiple reasons can explain why pollinators leave plants before visiting all open flowers on a plant (reviewed in [START_REF] Snow | The ecology of geitonogamous pollination[END_REF]; the most general one involves the maximization of energy gains (optimal foraging). For pollinators, which have limited shortterm memory, visiting only a fraction of available flowers reduces the risk of visiting a given flower twice [START_REF] Ohashi | How long to stay on, and how often to visit a flowering plant? A model for foraging strategy when floral displays vary in size[END_REF][START_REF] Bronstein | The exploitation of mutualisms[END_REF], 2002). Similarly, pollinators leave a plant earlier when they encounter empty, rewardless flowers (e.g. Bailey et al., 2007 and references therein). Self-pollination also depends on the order in which flowers of a plant are visited by pollinators. As the first few flowers visited by pollinators contribute the most to outcross pollen transfer, outcross pollination is expected to be larger when independent pollinators visit flowers randomly on a plant than when all pollinators visit flowers in the same order (Devaux et al., unpublished manuscript, for a model).

All above characteristics of pollinators affect the transfer of outcross and self-pollen among flowers, but not within-flower facilitated selfing (see glossary), which remains little studied. Facilitated selfing has been demonstrated unambiguously in a small number of species(e.g. [START_REF] Anderson | Facilitated selfing offers reproductive assurance: A mutualism between a hemipteran and carnivorous plant[END_REF][START_REF] Duncan | High self-pollen transfer and low fruit set in buzz-pollinated Dianella revoluta (Phormiaceae)[END_REF][START_REF] Johnson | Pollen fates and the limits on male reproductive success in an orchid population[END_REF][START_REF] Owen | Facilitated autogamy and costs of selfing in the perennial herb Bulbine bulbosa (Asphodelaceae)[END_REF][START_REF] Vaughton | Does selfing provide reproductive assurance in the perennial herb Bulbine vagans (Asphodelaceae)?[END_REF], but its broader contribution to total selfing rates in natural populations is currently unknown (see Box 1 for a method). It is unclear whether facilitated 10 selfing is primarily controlled by flower characteristics, such as spatial (herkogamy) or temporal (dichogamy) separation of anthers and stigmas (Lloyd & Webb, 1986;Webb & Lloyd, 1986;[START_REF] Brunet | Effects of floral morphology and display on outcrossing in Blue Columbine, Aquilegia caerulea (Ranunculaceae)[END_REF] or if it can be influenced by pollinator behaviour. Buzzpollination by native bees causes high rates of facilitated self-pollination in the partially selfincompatible Dianella revoluta [START_REF] Duncan | High self-pollen transfer and low fruit set in buzz-pollinated Dianella revoluta (Phormiaceae)[END_REF]. Furthermore, reduced time spent at individual flowers by hawkmoths has been associated with decreased seed production in selfcompatible Petunia lines [START_REF] Brandenburg | Hawkmoth pollinators decrease seed set of a low-nectar Petunia axillaris line through reduced probing time[END_REF]), but we do not know whether any of the effect can be attributed to facilitated selfing. From available experimental studies, we can nevertheless argue that increased numbers of flowers probed per plant or increased probing time per flower should contribute to increased facilitated selfing at the plant level.

Floral traits influencing self-pollination rates via pollinator behaviour

Floral traits affecting self-pollination can be divided into three broad categories: (1) traits related to autonomous selfing [START_REF] Lloyd | Self-fertilization and cross-fertilization in plants. 1. Functional dimensions[END_REF], (2) traits modifying mechanically pollinator-mediated outcross and self-pollen transfer, without altering pollinator behaviour (e.g. floral design, pollen size and stickiness, and within and among flowers temporal separation of male and female functions; Webb & Lloyd, 1986;[START_REF] Lloyd | Self-fertilization and cross-fertilization in plants. 1. Functional dimensions[END_REF] and (3) traits modifying pollinator behaviour directly. We focus on the latter floral traits, which typically influence two types of foraging behaviours: (3.1) patterns of flower visitation among plants (attraction, preference and constancy, see glossary), which are mostly discussed in the last section and (3.2) patterns of flower visitation within plants (number and sequence of flowers visited, as well as probing time).

Floral display (see glossary) may be the most studied plant trait influencing pollinator behaviour. Plants with larger floral displays attract more pollinators, thereby receiving more outcross and geitonogamous pollen [START_REF] Snow | The ecology of geitonogamous pollination[END_REF][START_REF] Rademaker | Selfing rates in natural populations of Echium vulgare: a combined empirical and model approach[END_REF][START_REF] Karron | The influence of floral display size on selfing rates in Mimulus ringens[END_REF][START_REF] Williams | Effects of floral display size and biparental inbreeding on outcrossing rates in Delphinium barbeyi (Ranunculaceae)[END_REF]. Floral display can be modified plastically, for example via flower wilting when pollinators are abundant (Harder & Johnson, 2005), or flower abortion inducing pollinators to leave the plant [START_REF] Ito | Reduction of geitonogamy: Flower abscission for departure of pollinators[END_REF]; both mechanisms reduce the risk of geitonogamous selfing. Floral display can also be modified via evolutionary changes in the total flower production, in the distribution of open flowers among days (individual phenology) or in the longevity of flowers [START_REF] Elzinga | Time after time: flowering phenology and biotic interactions[END_REF][START_REF] Devaux | Selection on variance in flowering time within and among individuals[END_REF]. How these changes in floral display modify selfing rates depends on the rates and patterns of flower visitation by pollinators but the general trend is again an increase in plant selfing rates with larger floral displays.

Many other floral traits are also cues for pollinator attraction and influence visitation rates and outcross pollen receipt. These include flower size, reward production, floral shape, colour, and scent [START_REF] Cozzolino | Specificity in pollination and consequences for postmating reproductive isolation in deceptive Mediterranean orchids[END_REF], or more anecdotal characteristics, such as colourful leaves [START_REF] Keasar | The signaling function of an extrafloral display: what selects for signal development?[END_REF], sterile anthers (staminodes, [START_REF] Sandvik | Quantitative importance of staminodes for female reproductive success in Parnassia palustris under contrasting environmental conditions[END_REF] or sterile flowers (e.g. Centaurea cyanus, [START_REF] Garcia-Jacas | Generic delimitation and phylogeny of the subtribe Centaureinae (Asteraceae): A combined nuclear and chloroplast DNA analysis[END_REF]. Nectar production and its replenishment dynamics have received particular attention, because they are critically related to geitonogamy. For example, bumblebees experiencing unrewarding (nectarless) plants probe more flowers on subsequent rewarding plants, such that the geitonogamous selfing rates of rewarding plants increased with the frequency of unrewarding plants in the population [START_REF] Ferdy | Geitonogamy in rewarding and unrewarding inflorescences: modelling pollen transfer on actual foraging sequences[END_REF]. Conversely, maintaining nectarless flowers within an otherwise nectar-producing inflorescence may encourage pollinators to leave a plant early, thereby reducing geitonogamy [START_REF] Hirabayashi | Significance of nectar distribution for bumblebee behaviour within inflorescences, with reference to inflorescence architecture and display size[END_REF]Bailey et al., 2007 and references therein;[START_REF] Whitehead | Pollination: the price of attraction[END_REF]. Pollinator behaviour within a plant, hence geitonogamy, can also be modified by floral complexity (more flowers visited in plants with simpler flowers, [START_REF] Ohashi | Consequences of floral complexity for bumblebee-mediated geitonogamous self-pollination in Salvia nipponica Miq. (Labiatae)[END_REF] or inflorescence architecture (e.g. lower selfing in racemes vs. umbels, [START_REF] Harder | Beyond floricentrism: The pollination function of inflorescences[END_REF][START_REF] Jordan | Manipulation of bee behavior by inflorescence architecture and its consequences for plant mating[END_REF] or in more tightly twisted inflorescences, [START_REF] Iwata | Inflorescence architecture affects pollinator behaviour and mating success in Spiranthes sinensis (Orchidaceae)[END_REF]. 12 Again, floral traits influencing facilitated self-pollination are poorly known, apart from structural features preventing self-pollination, such as anther caps [START_REF] Peter | Anther cap retention prevents self-pollination by elaterid beetles in the South African orchid Eulophia foliosa[END_REF] and spatial separation of sexes. In contrast, the production of complex floral design or shape can induce higher probing time [START_REF] Ohashi | Consequences of floral complexity for bumblebee-mediated geitonogamous self-pollination in Salvia nipponica Miq. (Labiatae)[END_REF], which can translate into higher seed set [START_REF] Brandenburg | Hawkmoth pollinators decrease seed set of a low-nectar Petunia axillaris line through reduced probing time[END_REF], potentially because of higher facilitated selfing.

There is ample and long-standing evidence that plant selfing rates are constrained by pollinator morphology and foraging behaviour [START_REF] Harder | Pollen dispersal and mating patterns in animalpollinated plants[END_REF], which may favour plant traits that can alleviate constraints imposed by pollinators. Evolution of plant traits under pollinator-mediated selection has been extensively studied [START_REF] Elzinga | Time after time: flowering phenology and biotic interactions[END_REF] for plant phenology ;[START_REF] Schiestl | Pollinator-mediated evolution of floral signals[END_REF] for floral signals), but with surprisingly little emphasis on plant mating systems, except in verbal models [START_REF] Eckert | Plant mating systems in a changing world[END_REF][START_REF] Thomann | Flowering plants under global pollinator decline[END_REF]. In the next section, we review the few theoretical studies that include pollinator behaviour in models of the evolution of plant mating systems. We argue that combining pollination ecology and the genetics of inbreeding depression is necessary to describe accurately and to understand plant mating system evolution. We conclude by pointing out experimental data needed to extend theoretical work on the evolution of plant mating system under pollinator constraints.

THE ROLE OF POLLINATORS IN THE EVOLUTION OF PLANT SELFING RATES

We clarify how the interplay between plants and pollinators determines plant fitness components, besides selfing rates, and review how models of the evolution of selfing rates implicitly or explicitly integrate plant-pollinator interactions.

Constraints imposed by pollinators on plant fitness components and the evolution of plant selfing rates

The fitness of a plant is determined by the number of outcrossed and selfed seeds it produces and the number of pollen grains it successfully exports to other plants (male outcrossed siring success), weighted by the relative offspring fitnesses. Hence the fitness of animal-pollinated plants depends critically on pollinators, also via resource allocation to attraction traits, and on inbreeding depression (see glossary, [START_REF] Lloyd | Some reproductive factors affecting the selection of self-fertilization[END_REF][START_REF] Lande | The evolution of self-fertilization and inbreeding depression in plants. 1. Genetic models[END_REF][START_REF] Charlesworth | The genetics of inbreeding depression[END_REF] Two major phenomena involving pollinators and influencing plant fitness components are often included in studies of the evolution of plant selfing rates without explicit modelling of pollinators (reviewed in [START_REF] Goodwillie | The evolutionary enigma of mixed mating systems in plants: Occurrence, theoretical explanations, and empirical evidence[END_REF]: pollen limitation and pollen discounting (see glossary). Pollen limitation is a key component favouring the evolution of higher selfing rates [START_REF] Cheptou | Allee effect and self-fertilization in hermaphrodites: Reproductive assurance in demographically stable populations[END_REF]Porcher & Lande, 2005b) and depends greatly on pollinator abundance [START_REF] Ashman | Pollen limitation of plant reproduction: ecological and evolutionary causes and consequences[END_REF][START_REF] Eckert | Plant mating systems in a changing world[END_REF][START_REF] Thomann | Flowering plants under global pollinator decline[END_REF]. Several authors have proposed that stronger outcross pollen limitation can mimic declines in pollinator density and hamper the evolution of complete outcrossing [START_REF] Sakai | Why be completely outcrossing? Evolutionarily stable outcrossing strategies in an environment where outcross-pollen availability is unpredictable[END_REF][START_REF] Masuda | An ESS model for the mixed production of cleistogamous and chasmogamous flowers in a facultative cleistogamous plant[END_REF]Morgan & Wilson, 2005). Pollen discounting, a negative relationship between selfing rate and pollen export, can be caused by pollinators transferring large amounts of self-pollen among multiple flowers of plants, which are therefore lost for outcrossing (Karron & Mitchell, 2012), and hinders the evolution of high selfing rates [START_REF] Goodwillie | The evolutionary enigma of mixed mating systems in plants: Occurrence, theoretical explanations, and empirical evidence[END_REF].

More generally, correlations or functional relationships among fitness components are important drivers of the evolution of plant mating systems. Several models show that the maintenance of mixed mating can result from relationships between male fertility, female self fertility and female outcross fertility (including pollen discounting, [START_REF] Johnston | Correlations among fertility components can maintain mixed mating in plants[END_REF], between viability and selfing rate [START_REF] Jordan | Functional pleiotropy and mating system evolution in plants: frequency-independent mating[END_REF], or between selfing and a cost of interaction with pollinators (Lepers et al., unpublished manuscript). Correlations among plant fitness components are partly governed by pollinators (see below), particularly by their foraging behaviour within plants in response to floral traits (e.g. floral display, [START_REF] Best | Pollinator foraging on foxglove (Digitalis purpurea): a test of a new model[END_REF]). Yet, models that use these correlations without integrating pollinators explicitly are useful to address the effects of pollinators on selfing rates and have helped understand the qualitative role of pollination in the evolution of plant mating. Assuming a positive correlation between the number of selfed and outcrossed ovules is relevant for many animal-pollinated species in which more pollinator visits increase both geitonogamous selfpollination and the number of outcrossed seeds (Johnston et al., 2009 and references therein).

Similarly, a negative correlation between reward production and selfing rate (as in Lepers et al., unpublished manuscript), or between the production of costly open (vs. closed) flowers and selfing rate (as in [START_REF] Masuda | An ESS model for the mixed production of cleistogamous and chasmogamous flowers in a facultative cleistogamous plant[END_REF]data in Oakley et al., 2007) can be used to understand the evolution of selfing syndromes (see glossary; reviewed by [START_REF] Sicard | The selfing syndrome: a model for studying the genetic and evolutionary basis of morphological adaptation in plants[END_REF].

Further progress towards more reliable, quantitative predictions of equilibrium mating systems requires mechanistic models of the constraints that pollinator behaviour imposes on plant selfing rates, which are still few. Morgan et al. (2005) used optimal foraging theory to model evolution of selfing by assuming a decreasing rate of geitonogamous selfing with increasing plant density, which was justified because pollinators are more likely to switch between plants when flight distances are smaller [START_REF] Cresswell | Spatial heterogeneity, pollinator behaviour and pollinator-mediated gene flow: Bumblebee movements in variously aggregated rows of oil-seed rape[END_REF][START_REF] Mustajarvi | Consequences of plant population size and density for plant-pollinator interactions and plant performance[END_REF].

Another approach has included the demography of plant and pollinator populations, highlighting the possibility of demographic extinction of pollinator and plant populations during the transition to higher selfing rates (Lepers et al., unpublished manuscript), due to reduced production of rewards for pollinators. The most comprehensive mechanistic models tackle the evolution of floral traits influencing pollinator behaviour, and therefore plant selfing rates. For example, models that jointly describe the evolution of daily floral display and pollinator foraging behaviour show that pollinators can generate stable intermediate geitonogamous selfing rates [START_REF] De | The consequences of pollination biology for selection of mass or extended blooming[END_REF][START_REF] Masuda | An ESS model for the mixed production of cleistogamous and chasmogamous flowers in a facultative cleistogamous plant[END_REF]Devaux et al., unpublished manuscript). Similarly, models of the evolution of nectar content have analysed how the production of rewardless flowers can decrease the geitonogamous selfing rate of individual plants [START_REF] Bailey | Empty flowers as a pollination-enhancement strategy[END_REF] and conversely how pollinator learning can increase the geitonogamous selfing rates of rewarding plants that co-occur with non-rewarding plants [START_REF] Ferdy | Geitonogamy in rewarding and unrewarding inflorescences: modelling pollen transfer on actual foraging sequences[END_REF].

Models combining pollinator foraging and the evolution of floral traits are promising tools to study the ecological drivers of plant mating system evolution, but they can still be improved. The number of flowers probed, hence the geitonogamous selfing rate of selfcompatible hermaphrodite species, critically depends on pollinator foraging behaviour, but the latter is simplified in existing models: pollinators are assumed to visit all flowers on a plant [START_REF] De | The consequences of pollination biology for selection of mass or extended blooming[END_REF], the number of pollinator visits per plant is assumed proportional to floral display [START_REF] Masuda | An ESS model for the mixed production of cleistogamous and chasmogamous flowers in a facultative cleistogamous plant[END_REF][START_REF] Masuda | Evolution of floral dimorphism in a cleistogamous annual, Impatiens noli-tangere L. occurring under different environmental conditions[END_REF], the probability to leave a plant is assumed unrelated to floral display (Devaux et al., unpublished manuscript), and pollinators are assumed to leave a plant immediately after visiting a rewardless flower [START_REF] Bailey | Empty flowers as a pollination-enhancement strategy[END_REF]; these assumptions are at odds with empirical observations (Robertson, 1992b;[START_REF] Duan | Reproductive ecology of the Qinghai-Tibet Plateau endemic Gentiana straminea (Gentianaceae), a hermaphrodite perennial characterized by herkogamy and dichogamy[END_REF][START_REF] Ishii | The size of individual Delphinium flowers and the opportunity for geitonogamous pollination[END_REF]. Such assumptions are unavoidable, and highlight the difficulty of including realistic but sufficiently general models of pollination ecology in models of the evolution of plant selfing rates (but see [START_REF] Ferdy | Geitonogamy in rewarding and unrewarding inflorescences: modelling pollen transfer on actual foraging sequences[END_REF] for a model incorporating pollinator learning).

The interplay between pollinators and the dynamics of purging inbreeding depression determines the evolution of plant selfing rates

Inbreeding depression (see glossary and Box 2), the relative fitness of selfed vs. outcrossed offspring, is a central evolutionary force that has received much attention in the population genetics approach to studying plant mating system evolution (reviewed in [START_REF] Charlesworth | The genetics of inbreeding depression[END_REF]. The joint evolution of inbreeding depression and plant mating systems, i.e. the purging of deleterious mutations with increasing selfing rates, has been extensively studied both experimentally [START_REF] Husband | Evolution of the magnitude and timing of inbreeding depression in plants[END_REF] and theoretically, but has rarely been included in ecological models of plant mating system evolution. Allowing for an evolving rather than constant inbreeding depression in models of pollination ecology can nevertheless greatly alter the outcomes of models of the evolution of selfing. First, conditions favouring the maintenance of outcrossing are much more restricted in the presence of evolving rather than constant inbreeding depression (Porcher & Lande, 2005a;[START_REF] Rathcke | Competition and facilitation among plants for pollination[END_REF]. Second, purging creates a strong positive feedback on the evolution of selfing: an increase in the population selfing rate decreases inbreeding depression (Fig. 3), thereby strongly favouring the further evolution of increased selfing. This can destabilize equilibria that appear evolutionarily stable in models where inbreeding depression does not depend on the selfing rate. [START_REF] Porcher | The genetic consequences of fluctuating inbreeding depression and the evolution of plant selfing rates[END_REF] demonstrated that incorporating a genetic model for inbreeding depression and the possibility of purging destabilizes intermediate selfing rates that would otherwise be maintained by temporal variation in inbreeding depression [START_REF] Cheptou | The cost of fluctuating inbreeding depression[END_REF].

The joint evolutionary dynamics of inbreeding depression and plant mating system are often overlooked in ecologically-oriented models because their analysis requires complex genetic models over and above the complexity of ecological processes. A method based on an approximation for the purging of inbreeding depression (e.g. [START_REF] Lande | High inbreeding depression, selective interference among loci, and the threshold selfing rate for purging recessive lethal mutations[END_REF] provides a powerful way around this complexity (Box 2), on the condition that genomic mutation rates to deleterious alleles causing inbreeding depression remains moderate (Box 2, [START_REF] Porcher | Evaluating a simple approximation to modeling the joint evolution of self-fertilization and inbreeding depression[END_REF]. This approximation has been used in some ecological models to study the joint role of ecological and genetic constraints in plant mating system evolution [START_REF] Johnston | Evolution of intermediate selfing rates in plants: pollination ecology versus deleterious mutations[END_REF]Devaux et al., unpublished manuscript;Lepers et al., unpublished manuscript). These models show that ecological and genetic mechanisms interact strongly to determine evolutionary outcomes.

For example, Devaux et al. (unpublished manuscript) identified two types of equilibrium selfing rates when modelling the evolution of floral display and geitonogamous selfing under pollinator constraints: (1) ecological equilibria constrained by pollinator behaviour only, which exist regardless of inbreeding depression, and (2) evolutionarily stable equilibria maintained by a trade-off between pollinator attraction and avoidance of geitonogamous selfing, and governed by evolving inbreeding depression. This model also suggests that a baseline rate of unavoidable geitonogamous selfing constrained by pollinators can trigger purging of inbreeding depression and create conditions favouring evolution of increased autonomous selfing. In view of this interaction between ecological and genetic mechanisms, we encourage modellers interested in the ecological drivers of plant mating system evolution to account for evolving inbreeding depression, which can be easily done using approximation methods (Box 2).

Experimental limits to theoretical models

No model has yet analysed the joint evolution of plant selfing rates and pollinator characteristics: the morphologies and foraging behaviours of pollinators are generally assumed to be constant (but plastic) functions of floral signals. Univariate pollinator-mediated selection on multiple floral traits and their genetic architecture are well documented [START_REF] Kingsolver | The strength of phenotypic selection in natural populations[END_REF][START_REF] Geber | Inheritance and natural selection on functional traits[END_REF][START_REF] Ashman | Genetic constraints on floral evolution: a review and evaluation of patterns[END_REF][START_REF] Karron | Outcrossing rates of individual Mimulus ringens genets are correlated with anther-stigma separation[END_REF][START_REF] Galliot | Genetics of flower size and nectar volume in Petunia pollination syndromes[END_REF]. Several papers have shown that floral traits could adapt rapidly [START_REF] Ashman | Pollen limitation of plant reproduction: ecological and evolutionary causes and consequences[END_REF][START_REF] Thomann | Flowering plants under global pollinator decline[END_REF], and a recent review has suggested that plants could adapt more rapidly to pollinator-mediated selection than pollinators do to floral traits, which can explain why we frequently observe pollination syndromes and floral convergence in plants (Schiestl & Johnson, 2013 and references therein). Thus, the rarity of coevolutionary models could reflect the lack of data on traits and behaviour of pollinators, and their adaptive potential, although a few models of coevolution of plant and pollinator traits do exist [START_REF] Kiester | Models of coevolution and speciation in plants and their pollinators[END_REF][START_REF] Zhang | Adaptive divergence in Darwin's race: How coevolution can generate trait diversity in a pollination system[END_REF], but do not address the evolution of plant mating.

Modelling the joint evolution of plant mating and pollinator traits would require the following experimental steps: (1) for plants, estimation of facilitated self-pollination and elucidation of pollinator characteristics and behaviour involved (see Box 1 for a method); (2) for plants again, estimation of the multivariate selection induced by pollinators on several floral traits simultaneously, as both direct and indirect (correlated) selection is responsible for the observed phenotypic distribution of floral traits; (3) for pollinators, accurate description of the genetic architecture (number of and correlation among genes) and the selection gradients on morphological and behavioural traits imposed by plants or their competitors; and ( 4) estimation of the adaptive potential of both floral and pollinator traits.

THE RECIPROCAL CONTRIBUTION OF PLANT-POLLINATOR NETWORKS TO PLANT SELFING

RATES

The interactions between plants and pollinators determine immediate ecological selfpollination rates, as well as the evolution of plant selfing rates. Most studies, both experimental and theoretical, address this topic by focusing on pairs of interacting species, whereas plants and their pollinators are part of complex interaction networks [START_REF] Bascompte | The nested assembly of plantanimal mutualistic networks[END_REF][START_REF] Strauss | Ecological and evolutionary consequences of multispecies plant-animal interactions[END_REF][START_REF] Pocock | The robustness and restoration of a network of ecological networks[END_REF], which should influence plant mating systems and their evolution. The combination of estimates from independent populations scattered across the globe indicates a U-shaped distribution of plant selfing rates, with a strong bias towards highly outcrossing species and numerous species with intermediate selfing rates [START_REF] Goodwillie | The evolutionary enigma of mixed mating systems in plants: Occurrence, theoretical explanations, and empirical evidence[END_REF][START_REF] Igic | The distribution of plant mating systems: Study bias against obligately outcrossing species[END_REF]. Whether this distribution is representative of local plant communities is debatable, nevertheless it is likely that selfing rates exhibit interspecific variation within communities. In the following we argue that (1) in a network, the distribution of selfing rates of plant species that are not completely outcrossing or completely selfing can be explained partly by the multispecies interactions operating at an ecological time scale (Fig. 1), and (2) conversely, on longer time scales, the evolution of plant mating systems, particularly the transition to higher selfing, can constrain the architecture of plant-pollinator networks.

The influence of the architecture of mutualistic networks on plant ecological selfing rates and their evolution

Here, we review the scarce available data and make predictions for the expected impact of multispecies interactions on plant mating. We also point out the data needed to test these predictions and better understand community-level effects on plant selfing rates.

Plant-pollinator networks are shaped by pollinator optimal foraging and morphological or phenological matching between partners (e.g. [START_REF] Junker | Specialization on traits as basis for the niche-breadth of flower visitors and as structuring mechanism of ecological networks[END_REF]. Within a given network, plants differ in the identity of their pollinators, which is a primary mechanism leading to differences in selfing rates in a plant community: different pollinator species have different foraging behaviour and pollen transfer efficiencies and therefore contribute to variation in selfing rates [START_REF] Morinaga | Consequences of differences in flowering date on seed production in Heloniopsis orientalis (Liliaceae)[END_REF][START_REF] Brunet | Impact of insect pollinator group and floral display size on outcrossing rate[END_REF][START_REF] Matsuki | Pollination efficiencies of flowervisiting insects as determined by direct genetic analysis of pollen origin[END_REF]but see Eckert, 2002). Mutualistic interaction networks are also characterized by their nestedness (see glossary), which implies asymmetric relationships between plant and pollinator species: specialist plant (respectively pollinator) species interact (more often) with generalist pollinator (respectively plant) species [START_REF] Bascompte | The nested assembly of plantanimal mutualistic networks[END_REF][START_REF] Thébault | Stability of ecological communities and the architecture of mutualistic and trophic networks[END_REF].

This architecture determines the level of interferences among specialist plant species because of shared (generalist) pollinators, and among specialist pollinator species because of shared (generalist) plant species. The combination of all interference components determines the number of pollinator visits per plant and the quantity of heterospecific, outcross and self-20 pollen deposited per pollinator visit, hence immediate ecological selfing rates [START_REF] Wilcock | Pollination failure in plants: why it happens and when it matters[END_REF][START_REF] Vanbergen | Grazing alters insect visitation networks and plant mating systems[END_REF].

In pollinator-sharing plant species, the rate of heterospecific vs. conspecific outcross pollen transfer is governed by the floral constancy of pollinators [START_REF] Ashman | Toward a predictive understanding of the fitness costs of heterospecific pollen receipt and its importance in co-flowering communities[END_REF] and see glossary). Within-bout floral constancy of individual pollinators is likely to maintain high outcrossing rates by increasing the relative amount of conspecific vs. heterospecific pollen deposited on stigmas. We are unaware of any experimental study of this relationship between floral constancy and selfing rates, but floral constancy is influenced by the structure of both plant and pollinator communities, which should contribute to variation in the selfing rate of a given plant species among communities. Similarities in floral traits among plant species of a community tend to lower floral constancy: [START_REF] Jager | Do pollinators influence the assembly of flower colours within plant communities?[END_REF] observed higher probabilities of pollinators switching between co-occurring Oxalis species of similar colour. Conversely, [START_REF] Gegear | The effect of variation among floral traits on the flower constancy of pollinators[END_REF], 2005) predicted and verified experimentally that the diversity of plant species in a community increases floral constancy, particularly when plant species differ in multiple floral traits. Interference among pollinators in a community can also alter floral constancy, and thus the amount of outcross pollination. For example, experimental removal of an abundant pollinator caused weaker interspecific competition for food resources among the remaining pollinator species, which decreased their floral constancy, thus plant seed set, in natural populations of Delphinium barbeyi [START_REF] Brosi | Single pollinator species losses reduce floral fidelity and plant reproductive function[END_REF]; the consequences on selfing rates were however not examined.

In addition to heterospecific pollen transfer, interference among (specialist) plant species sharing pollinators also impacts pollinator visitation rates, with two contrasting patterns: (1) decreased visitation rates (competition), caused by a combination of higher density of competitor plants and higher pollinator preference for competitor plants [START_REF] Rathcke | Competition and facilitation among plants for pollination[END_REF][START_REF] Vamosi | Pollination decays in biodiversity hotspots[END_REF][START_REF] Flanagan | Effects of multiple competitors for pollination on bumblebee foraging patterns and Mimulus ringens reproductive success[END_REF], and (2) increased visitation rates (facilitation), resulting from more effective attraction cues, maintenance of larger populations of pollinators [START_REF] Sargent | Plant-pollinator interactions and the assembly of plant communities[END_REF][START_REF] Liao | The presence of co-flowering species facilitates reproductive success of Pedicularis monbeigiana (Orobanchaceae) through variation in bumble-bee foraging behaviour[END_REF], or availability of complementary resources for pollinators [START_REF] Ghazoul | Floral diversity and the facilitation of pollination[END_REF]. Competitive and facilitative interactions influence selfing rates because they control the amount of outcross pollen deposited on stigmas [START_REF] Vamosi | Pollination decays in biodiversity hotspots[END_REF][START_REF] Alonso | Is reproduction of endemic plant species particularly pollen limited in biodiversity hotspots?[END_REF]. Which of these predominates among plant species likely depends on phylogenetic distances among species (facilitation is more likely among closely related species, [START_REF] Moeller | Facilitative interactions among plants via shared pollinators[END_REF][START_REF] Schuett | Phylogenetic community context influences pollen delivery to Allium cernuum[END_REF][START_REF] Sargent | Effect of local community phylogenetic structure on pollen limitation in an obligately insectpollinated plant[END_REF] and the overlapping of population flowering phenologies within [START_REF] Fründ | Linne's floral clock is slow without pollinators: flower closure and plant-pollinator interaction webs[END_REF] and among days [START_REF] Motten | Pollination ecology of the spring wildflower community of a temperate deciduous forest[END_REF][START_REF] Devaux | Displacement of flowering phenologies among plant species by competition for generalist pollinators[END_REF][START_REF] Runquist | Community phenology and its consequences for plant-pollinator interactions and pollen limitation in a vernal pool plant[END_REF].

Predicting how heterospecific pollen transfer and competition for pollinator visitation jointly impact plant mating is straightforward: both mechanisms cause conspecific outcross pollen limitation, which should be associated with increased selfing. Only a couple of studies have demonstrated increased (ecological) selfing rates due to competition for pollinators: in Mimulus ringens [START_REF] Bell | Interspecific competition for pollination lowers seed production and outcrossing in Mimulus ringens[END_REF] and Laguncularia racemosa [START_REF] Landry | Pollinator-mediated competition between two co-flowering Neotropical mangrove species, Avicennia germinans (Avicenniaceae) and Laguncularia racemosa (Combretaceae)[END_REF]. At broader time scales, highly selfing populations of Arenaria uniflora are thought to have evolved to avoid competition with A. glabra [START_REF] Fishman | Pollinator-mediated competition, reproductive character displacement, and the evolution of selfing in Arenaria uniflora (Caryophyllaceae)[END_REF]. In contrast, the effect of pollinator sharing on selfing rates in plant species with facilitative interactions is less intuitive, because heterospecific pollen transfer and increased pollinator visitation rates should compensate one another. In Clarkia communities characterized by facilitative interactions, increased autonomous selfing is selected for under low plant species diversity [START_REF] Moeller | Ecological context of the evolution of self-pollination in Clarkia xantiana: Population size, plant communities, and reproductive assurance[END_REF], which suggests weak outcross pollen limitation and limited impacts of heterospecific pollen transfer in highly diverse plant communities. The negative effects of heterospecific pollen transfer can be avoided by increased floral constancy of pollinators [START_REF] Gegear | Flower constancy in bumblebees: a test of the trait variability hypothesis[END_REF], separate pollen placement on pollinator bodies [START_REF] Waser | Interspecific pollen transfer and competition between co-occurring plant species[END_REF]22 Huang & Shi, 2013 and references therein) or higher tolerance to heterospecific pollen transfer [START_REF] Ashman | Toward a predictive understanding of the fitness costs of heterospecific pollen receipt and its importance in co-flowering communities[END_REF].

Finally, we may predict lower selfing rates on average for generalist than for specialist plant species for two reasons. First, generalist plant species should receive more independent visits by pollinators, which should deposit larger amounts of outcross pollen. In a nested network, a significant fraction of this outcross pollen may however be heterospecific, because generalist plant species are visited by specialist as well as generalist pollinators. [START_REF] Fang | A directed network analysis of heterospecific pollen transfer in a biodiverse community[END_REF] for example observed higher rates of heterospecific pollen transfer in generalist vs. specialist plants. Heterospecific pollen transfers may explain why the general negative relationship between pollinator diversity and outcross pollen limitation remains weak [START_REF] Davila | Ecosystem services of pollinator diversity: a review of the relationship with pollen limitation of plant reproduction[END_REF]. Second, interference among pollinators can alter pollinator behaviour within plants, thereby influencing selfing rates via geitonogamous pollen transfer. Optimal foraging selects for pollinators that leave plants before interacting with competitors and predators.

Hence, generalist plant species could exhibit lower geitonogamous selfing rates because interference among multiple pollinator species is likely to reduce the number of flowers each pollinator probes on a plant. One experimental study provides indirect support for this phenomenon: [START_REF] Greenleaf | Wild bees enhance honey bees' pollination of hybrid sunflower[END_REF] showed that in sunflower (Helianthus annuus) fields containing male-fertile and male-sterile individuals, honey bees that interacted with wild bees on male-sterile plants flowers were more likely to switch to a male-fertile plant than when they interacted with a conspecific, thereby enhancing pollen transfer among individuals.

Further investigation is needed to confirm or rule out the prediction of larger outcrossing rates in generalist vs. specialist plant species, for which at present there is little direct experimental evidence.

There is thus mounting evidence that the architecture of plant-pollinator networks can contribute to plant selfing rates and their evolution (Fig. 1). Experimental data are however needed to explore the relationship between selfing rates and network architecture, particularly plant specialization to pollinators (see glossary), and broaden our understanding of the underlying mechanisms. Particularly, quantified plant-pollinator networks are crucial for an accurate assessment of plant specialization [START_REF] Ings | Review: Ecological networks -beyond food webs[END_REF]. Note however that most networks are based on visitation data, which may not be representative of actual pollen transfer networks [START_REF] Alarcón | Congruence between visitation and pollen-transport networks in a California plant-pollinator community[END_REF][START_REF] King | Why flower visitation is a poor proxy for pollination: measuring single-visit pollen deposition, with implications for pollination networks and conservation[END_REF]. We also need reliable estimates of selfing rates, based on genetic markers for plant species of the same network [START_REF] David | Reliable selfing rate estimates from imperfect population genetic data[END_REF], to document the community-level distribution of plant selfing rates, now only available in different ecological contexts [START_REF] Goodwillie | The evolutionary enigma of mixed mating systems in plants: Occurrence, theoretical explanations, and empirical evidence[END_REF]. As a first step, selfing rates could be regressed on specialization (number of visiting pollinator species) across all plant species of a given plant-pollinator network at a given time. Alternatively, analyses could focus on a single or a few plant species and make use of the documented spatial or temporal variation in mutualistic networks. For example, [START_REF] Vanbergen | Grazing alters insect visitation networks and plant mating systems[END_REF] estimated the selfing rate of Cirsium palustre and characterized plant-pollinator networks across a gradient of grazing intensity. They observed higher selfing rates, associated with less densely connected networks, in ungrazed vs. intensively grazed habitats. However, for a given grazing intensity, selfing rates were positively related to network connectance. No general conclusion can be drawn from this single study with conflicting patterns, but the work of [START_REF] Vanbergen | Grazing alters insect visitation networks and plant mating systems[END_REF] does confirm that the architecture of plant-pollinator networks impacts plant selfing rates.

Finally, studies of pollinator floral constancy are still rare: existing data deal with the specialization of pollinator species only, whereas floral constancy is defined at the individual level. Floral constancy and specialization can overlap (a pollinator species specialized on a single plant species can only be constant), but remain distinct features of pollinator behaviour (a generalist pollinator can be or not constant within a foraging bout, see glossary). Hence, we believe that pollinator specialization is informative to study the dynamics of plant-pollinator networks, but not to understand realized pollination patterns at the network level. Estimates of floral constancy should ideally quantify the probability of pollinator switching, and go beyond binomial classifications (in/fidelity, as in [START_REF] Brosi | Single pollinator species losses reduce floral fidelity and plant reproductive function[END_REF].

The influence of plant mating systems on plant-pollinator network architecture

Evolutionary changes in selfing rates, particularly autonomous selfing, may in the short-term involve minor modifications of floral traits (e.g. herkogamy, Webb & Lloyd, 1986), and have little consequence for pollinator visitation rates and patterns. In the long term however, they can induce more conspicuous changes and dramatically reduce pollinator visits, e.g. via a decrease in floral size, nectar and scent production, or pollen/ovule ratio [START_REF] Sicard | The selfing syndrome: a model for studying the genetic and evolutionary basis of morphological adaptation in plants[END_REF], which could eventually alter the architecture of plant-pollinator networks. Few studies so far have examined how plant mating systems shape plant-pollinator networks, with the exception of [START_REF] Ollerton | Geographical variation in diversity and specificity of pollination systems[END_REF] and [START_REF] Davila | Ecosystem services of pollinator diversity: a review of the relationship with pollen limitation of plant reproduction[END_REF], who found no difference in plant specialization between self-compatible and self-incompatible species (a qualitative approach).

Yet, comparing self-compatible and self-incompatible species may not be appropriate to detect a relationship between plant specialization and selfing rate, because self-compatible species exhibit a wide range of selfing rates, from complete outcrossing to complete selfing [START_REF] Goodwillie | The evolutionary enigma of mixed mating systems in plants: Occurrence, theoretical explanations, and empirical evidence[END_REF].

We present here a preliminary analysis that corroborates our prediction that predominantly selfing species should be visited by fewer pollinator species than predominantly outcrossing species. For this analysis, we brought together data on plant mating system from the Biolflor database [START_REF] Klotz | Biolflor: Eine Datenbank zu biologisch-ökologischen Merkmalen der Gefäßpflanzen in Deutschland[END_REF] with three published networks providing qualitative or quantitative plant-pollinator interactions: a forest understory [START_REF] Robertson | Flowers and insects: lists of visitors to four hundred and fifty-three flowers[END_REF], a meadow [START_REF] Memmott | The structure of a plant-pollinator food web[END_REF] and the Norwood farm [START_REF] Pocock | The robustness and restoration of a network of ecological networks[END_REF] networks. The same tendency of fewer pollinator species on predominantly selfing plant species is observed across the three networks (Fig. 4), although differences among the mating system classes are not all significant. A higher diversity of pollinator species on outcrossing species can result from two non-exclusive phenomena: a lower visitation rate to highly selfing species, which is mechanically associated with fewer pollinator species via a sampling effect, and a higher "true" specialization of selfing plant species. This example emphasizes the need for quantified interaction networks, to separate the contributions to plant specialization due to overall pollinator (or plant) abundance vs. diversity of visiting pollinator species. Several authors (e.g. [START_REF] Blüthgen | Specialization, constraints, and conflicting interests in mutualistic networks[END_REF] have stressed the influence of plant or pollinator abundance on the measurement of specialization, but specialization is still frequently measured as a number of species, so that highly-selfing plant species receiving few visits may be mistaken for extremely specialist species. In the two quantified networks available here the number of pollinator species was always strongly and significantly correlated with the total number of visits on a plant (not shown). There was also a tendency, although not significant, for fewer visits to highly-selfing plant species vs. highlyoutcrossing plant species. When controlling for the effect of the number of visits a residual effect of mating system on the number of pollinator species remained, but only in the Norwood network for which predominantly outcrossing plant species were visited by a higher diversity of pollinators. This analysis has several shortcomings (crude classification of plant mating systems, single trait approach ignoring correlates of mating systems that may also influence plantpollinator interactions, species considered as independent samples, etc.), and does not provide a causal relationship between plant selfing rates and the plant-pollination networks. However, it offers new research directions, both theoretical and experimental, to understand the contribution of plant mating systems to the architecture of plant-pollinator networks. Selfing syndrome is a characteristic set of morphological and functional plant traits that enhance pollen transfer efficiency within flowers and/or decrease pollinator visitation. Selfing syndrome usually includes small flowers, thus reduced anther-stigma distance (herkogamy), reduced petal size, and reduced corolla width (following [START_REF] Sicard | The selfing syndrome: a model for studying the genetic and evolutionary basis of morphological adaptation in plants[END_REF]. Specialization has many definitions but is generally inversely related to the total number of species an individual, a population or a species interacts with. This number can be weighted by the frequency of interactions with each partner species.

BOX 1: A METHOD FOR ESTIMATING FACILITATED SELFING

Estimation of facilitated selfing is challenging because it requires devices to mark pollen or follow pollinator visits, while controlling for resource allocation, outcross pollen limitation and pollinator attraction. However, facilitated selfing could contribute significantly to observed selfing rates and their evolution. Indirect evidence of facilitated selfing is available, but only for plant species with specific floral types (Fig. 2 Roridula species for which facilitated selfing is performed by insects (hemipterans) that do not contribute to the other selfing components, performed by bees.

A simple, but adjustable, experiment to estimate all components of selfing

Estimating the three components of selfing or self-pollination (Fig. 2 needs to be small enough to keep track of the entire pollinator visitation sequence and large enough such that pollinators do not visit all open flowers, but generate variation in the number of flowers visited per plant; some flowers may have to be removed and some pollinators may have to be excluded from the experimental cage to avoid too long visitation sequences. 50 drivers of the evolution of the selfing rate, particularly ecological mechanisms, some of which are governed by pollinators and their behaviour (Porcher & Lande, 2005b;Devaux et al., unpublished manuscript;Lepers et al., unpublished manuscript). Singular strategies (selfing rates) correspond to fitness maxima or minima, which can be distinguished from the sign of the second partial derivative with respect to selfing rate at this strategy. Graphically, the singular strategy is evolutionarily stable (i.e. a maximum) if the constraint function is smaller (respectively larger) than inbreeding depression when the equilibrium selfing rate is increased (respectively decreased; Fig. 3).

The approximation ignores genotypic association among the loci controlling the selfing rates and those controlling inbreeding depression, and is therefore accurate only for moderate, but biologically realistic, genomic rates to deleterious mutations causing inbreeding depression (U < 0.2, [START_REF] Porcher | Evaluating a simple approximation to modeling the joint evolution of self-fertilization and inbreeding depression[END_REF]. For larger mutation rates, differential purging occurs between genotypes with different selfing rates, a phenomenon that is not accounted for in the approximation, which thus becomes inaccurate. Large U may be found in perennial plants (see [START_REF] Porcher | Evaluating a simple approximation to modeling the joint evolution of self-fertilization and inbreeding depression[END_REF] and may better account for the observed similar levels of inbreeding depression in completely outcrossing and mixed-mating populations [START_REF] Winn | Analysis of inbreeding depression in mixed-mating plants provides evidence for selective interference and stable mixed mating[END_REF].

  self-pollination induced by pollinator visits. Geitonogamous selfing (g, solid white lines; left panel of Fig. 2) corresponds to self-pollination among flowers induced by pollinators probing several open flowers on the same plant. Outcross pollination (o, solid black lines) refers to pollen deposited on a flower that originates from other plants in the population. Estimates obtained from the method proposed in Box 1 are given with upper-case letters next to three flowers (right panel of Fig. 2).

  of the glossary): Johnson et al. (2005) make use of the absence of autonomous selfing in Disa cooperi, Vaughton et al. (2008) of the absence of geitonogamous selfing in Bulbine vagans and Owen et al. (2007) of the absence of both in Bulbine bulbosa; on the other hand, Anderson et al. (2003) use

  in the glossary) requires a detailed description of single-pollinator visits to individual plants. The method requires N replicate caged plants with F individually-marked open perfect flowers. Identical numbers of flowers control for resource allocation if selfing (not self-pollination) rates are to be estimated. Each plant should be visited by a single pollinator carrying no pollen, which precludes outcross pollination and the visitation order of the pollinator should be recorded (some flowers can be visited several times, and some flowers may remain unvisited). The components of selfing and self-pollination can then be estimated by analysing the seed set of the N × F flowers or by counting pollen grains deposited within each flower stigmas, respectively. The simplest estimation method requires discarding all flowers visited more than once and counting pollen grains, not seeds, per flower to eliminate the delayed autonomous selfing component. Pollen loads provide information about (1) autonomous selfing for unvisited 48 flowers (2) autonomous and facilitated selfing jointly for flowers visited once as the first flower of the sequence, thus by a pollinator carrying no self-pollen, and (3) all three components of selfing for flowers visited once as the second flower of the sequence, by a pollinator carrying self-pollen from one previously visited flower (Fig. 2 of the glossary, right panel). More sophisticated methods could use seed sets from all F flowers but would need to control for delayed autonomous selfing (possibly via the number of visits per focal flower or per plant, depending on the underlying mechanisms) and for the quantity of geitonogamous self-pollen deposited on flowers as a function of their visitation rank. For practical reasons F

FIGURE LEGENDS Figure 1 .

 LEGENDS1 FIGURE LEGENDS

Figure 2 .

 2 Figure 2. Clarification (left panel) and one estimation method (right panel, see also Box 1) of

Figure 3 .

 3 Figure 3. Evolutionarily stable (closed circles) and unstable (open circles) selfing rates found

Figure 4 .

 4 Figure 4. Relationship between mating system and plant specialization in three plant-

Journal of Evolutionary Biology

ACKNOWLEDGEMENTS

We thank Colin Fontaine and Russell Lande for insightful discussions and suggestions, François Ory for drawings used in Fig. 1, as well as two anonymous reviewers who helped improved an earlier version of the manuscript. This work was supported by the Region Nord-Pas-de-Calais grant to C.L, by the French CNRS program PICS grant #5273 to E.P. and by a grant from the Balzan Foundation.

CONCLUDING REMARKS

The study of plant mating systems in plant-pollinator networks is still in its infancy, but there is already conclusive evidence that ecological plant selfing rates and their evolution are shaped by conflicts of interest between plants and their pollinators, and by interactions between pollinator behaviour and plant mating systems at the network level. The relative contribution of such ecological constraints vs. genetic drivers to the evolution of plant mating systems, as well as the role of temporal variation in plant-pollinator networks, remains largely unknown and should be explored both empirically and theoretically. Regardless of what drives the evolution of plant selfing rates, it is associated with changes in floral traits, as is the case in the selfing syndrome: the consequences of plant mating system evolution on the architecture of plant-pollinator networks is another topic that warrants further investigation.

GLOSSARY

Floral constancy (or fidelity) refers to the propensity for an individual pollinator to visit flowers of a single floral type (hence one or a few plant species) within a foraging bout. It can be measured by the number of transitions among floral types visited within a bout [START_REF] Waser | Flower constancy: definition, cause, and measurement[END_REF][START_REF] Chittka | Flower constancy, insect psychology, and plant evolution[END_REF]. Constancy is widespread across pollinator species and is explained, at least partially, by the limited short-term memory of pollinators for visual and olfactory cues and by their limited motor learning for handling flowers [START_REF] Chittka | Flower constancy, insect psychology, and plant evolution[END_REF].

Floral display is the total number of flowers that are open simultaneously on a plant on a given day. Note that floral display sometimes also includes floral size (e.g. [START_REF] Goodwillie | Correlated evolution of mating system and floral display traits in flowering plants and its implications for the distribution of mating system variation[END_REF], despite an existing trade-off between number and size of flowers [START_REF] Sargent | Phylogenetic evidence for a flower size and number trade-off[END_REF].

A foraging bout is the time a pollinator spends visiting flowers during a single sequence, between the moment it leaves its nest and the moment it returns to it.

Inbreeding depression is the relative decrease in fitness of selfed vs. outcrossed progeny, caused mostly by a combination of highly deleterious, nearly recessive alleles and mildly deleterious, nearly additive alleles. Recessive deleterious mutations are more likely to be eliminated by natural selection (purging) in inbred homozygotes, which creates a negative relationship between inbreeding depression and the population selfing rate [START_REF] Lande | The evolution of self-fertilization and inbreeding depression in plants. 1. Genetic models[END_REF]; see Box 2).

Nestedness characterizes networks with many specialist species and few extremely generalist species, as well as asymmetric specialization (specialist species tend to interact with generalist species).

Pollen carryover is the extent to which pollen collected on a flower is transported and deposited on stigmas of other flowers (of the same plant or different plants) during a foraging bout; it depends on both the pollen uptake rate and pollen deposition rate [START_REF] De | Geitonogamy: the neglected side of selfing[END_REF].

Pollen discounting is the reduction in outcrossed male siring success associated with an increase in selfing rate, due to decreased amounts of exported pollen [START_REF] Nagylaki | A model for the evolution of self-fertilization and vegetative reproduction[END_REF].

Pollen limitation is the reduction in plant reproductive success (fruit or seed set) due to inadequate quantity or quality in pollen receipt; it is usually tested for through supplementary pollination (see [START_REF] Knight | Pollen limitation of plant reproduction: Pattern and process[END_REF] for a review).

Pollinator preference is the propensity for an individual pollinator to visit a plant species disproportionately to the availability of resources this species provides [START_REF] Cock | Assessment of preference[END_REF]; it is usually measured as number of visits per plant relative to other plant species.

Self-pollination rate is the fraction of self-pollen vs. conspecific outcross pollen deposited on plant stigmas.

Selfing rate is the rate of self-fertilization, the fraction of selfed vs. outcrossed embryos produced by an individual plant. It is defined at fertilization (primary selfing rate) but usually measured at a later stage (in seeds, seedlings or even adults, secondary selfing rate). Primary and secondary selfing rates can differ from the self-pollination rate due to (1) selfincompatibility, which can be partial or cryptic (e.g. via differences in growth rates of selfed vs. outcrossed pollen tubes) and (2) post-fertilization selection processes, for example selective flower abscission, fruit abortion or inbreeding depression.

Selfing and outcrossing components of self-compatible animal-pollinated plants with perfect flowers (following [START_REF] Lloyd | Self-fertilization and cross-fertilization in plants. 2. The selection of selffertilization[END_REF]. Autonomous selfing (a, dotted white lines; left panel of Fig. 2) corresponds to autogamous (within-flower) self-pollination occurring without pollinator visits; it is divided into three modes depending on the timing of outcross-vs. selfpollination: prior, competing (simultaneous), and delayed autonomous selfing. Facilitated selfing (f, dashed white lines; left panel of Fig. 2) corresponds to autogamous (within-flower)

BOX 2: AN APPROXIMATION FOR EVOLUTIONARY EQUILIBRIA OF PLANT SELFING RATES: how to include the purging of inbreeding depression into ecological models of the evolution of selfing

The evolutionary dynamics of inbreeding depression greatly influence plant mating system evolution and should not be overlooked. The joint evolution of inbreeding depression and selfing rates can be modeled using detailed genetic models of inbreeding depression, which has rarely been done in ecological theoretical studies (but see Porcher & Lande, 2005a;[START_REF] Rathcke | Competition and facilitation among plants for pollination[END_REF][START_REF] Porcher | The genetic consequences of fluctuating inbreeding depression and the evolution of plant selfing rates[END_REF] because it requires complex models and long computation time.

Alternatively, an approximation assuming that plant selfing rates evolve by small mutational steps allows modeling the dynamics of purging without a full genetic model for inbreeding depression [START_REF] Lande | High inbreeding depression, selective interference among loci, and the threshold selfing rate for purging recessive lethal mutations[END_REF][START_REF] Johnston | Evolution of intermediate selfing rates in plants: pollination ecology versus deleterious mutations[END_REF]. This approximation amounts to letting the level of inbreeding depression vary with the selfing rate, and finding joint equilibria of the mating system and inbreeding depression, instead of assuming constant inbreeding depression (see [START_REF] Porcher | Evaluating a simple approximation to modeling the joint evolution of self-fertilization and inbreeding depression[END_REF] for more details). A numerical or analytical relationship between inbreeding depression and population selfing rate can be obtained from any genetic model (e.g. [START_REF] Kondrashov | Deleterious mutations as an evolutionary factor. 2. Facultative apomixis and selfing[END_REF][START_REF] Charlesworth | Inbreeding depression, genetic load, and the evolution of outcrossing rates in a multilocus system with no linkage[END_REF]. Analytical relationships are derived from polynomial regressions [START_REF] Johnston | Evolution of intermediate selfing rates in plants: pollination ecology versus deleterious mutations[END_REF]Lepers et al., unpublished manuscript) with relatively simple models of inbreeding depression (e.g. based on a single locus, [START_REF] Charlesworth | Inbreeding depression, genetic load, and the evolution of outcrossing rates in a multilocus system with no linkage[END_REF].

A change in the selfing rate modifies inbreeding depression, but also other components of plant fitness, via the automatic advantage of selfing [START_REF] Fisher | Average excess and average effect of a gene substitution[END_REF], reproductive assurance in pollen-limited environment, or pollen discounting. The approximation examines the indirect selection gradient on small changes in the selfing rate to find joint equilibria of the mating system and inbreeding, which occur at the intersection of the inbreeding depression function and a constraint function (Fig. 3). This constraint function summarizes all other