Eco-evolutionary dynamics of prior selfing rate promotes the coexistence without niche partitioning under reproductive interference

When the two or more plants species share the same pollinators, pollinator-mediated reproductive interference make coexistence difficult. Recent studies suggested prior autonomous selfing mitigate reproductive interference, could enabling coexistence without pollination niche partitioning (pre-emptive selfing hypothesis). However, there are no studies to test whether evolution of prior selfing promote the coexistence, considering eco-evolutionary dynamics of population size, selfing rate and inbreeding depression. To examine conditions that the evolution of prior selfing promote coexistence under mutual reproductive interference especially in the point of view for pollinator availability and dynamics of inbreeding depression, we constructed individual-based model in which two plant species compete against each other in the form of mutual reproductive interference and can evolve prior autonomous selfing rate. We expected that purging of deleterious mutations could cause evolutionary rescue because inferior species could rescue population density through the evolution of prior selfing if the strength of inbreeding depression decreases with an increase of population’s selfing rate. Our simulation demonstrated that the evolution of prior selfing could promote the coexistence while reproductive interference caused competitive exclusion without evolution. We found that lower pollinator availability tended to prefer rapid evolutionary shift to higher prior selfing rate, it neutralizes the negative effect of reproductive interference, and population dynamics exhibit neutral random walk in both species. When the strength of inbreeding depression decreased with an increase in population’s selfing rate, moderate pollinator availability resulted in long-term coexistence in which relative-abundance-dependent selection on the prior selfing rate rescue population density of inferior species intermittently. Synthesis. We showed that the evolution of prior selfing could increase population growth rate of inferior species and consequently enable the long-term coexistence with evolutionary rescue. This is the new mechanisms explaining co-evolutionary coexistence of closely related plant species without niche partitioning and consistent with recent studies reported that closely related mixed-mating species are sympatrically growing even under the mutual reproductive interference.

reproductive interference make coexistence difficult. Recent studies suggested prior 23 autonomous selfing mitigate reproductive interference, could enabling coexistence 24 without pollination niche partitioning (pre-emptive selfing hypothesis). However, there 25 are no studies to test whether evolution of prior selfing promote the coexistence, 26 considering eco-evolutionary dynamics of population size, selfing rate and inbreeding 27 depression.  Clarifying the conditions under which competing species can coexist is a traditional and 58 most fundamental subject in ecology (May, 1974;Chesson, 2000). Numerous empirical 59 and theoretical works have shown that niche partitioning between competing species is 60 required for their coexistence: i.e. the intraspecific competition should be larger than 61 interspecific competition (Chesson, 2000;Silvertown, 2004). Closely related species,   Recent studies further hypothesize that "prior" rather than "delayed"

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The pre-emptive selfing hypothesis should be tested in the context of eco-109 evolutionary dynamics of population size, selfing rate and inbreeding depression.   Community structure, pollination, seed production and germination processes 143 We develop an individual-based model of competition between two annual flowering 144 plant species (species with discrete generation) within a site whose carrying capacity is respectively. In this formulation, we assume that outcross pollen proportionally with the whole parameter range of 0 ≤ ≤ 1 (Table 1). In each simulation run, the 224 initial numbers of individuals for both species are equal as K/2. The initial autonomous 225 selfing rates for individuals were generated randomly with normal distribution whose 226 mean and standard deviation are rintial (1/2) and sdintial (1/6) for both species. Each run 227 continues for 2,000 generations or until either species goes extinct. coexistence with neutral dynamics (Fig. 1). 255 We compared difference in long-term stability between coexistences with 256 neutral dynamics and evolutionary rescue. We selected a typical parameter set for each 257 coexistence type: P = 0.4, α = 0.5, β = 0.9 for that with evolutionary rescue (ER set) and

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Eco-evolutionary dynamics with fixed inbreeding depression 274 We found that lower pollinator availability preferred the evolution of higher selfing rate 275 in both species, often promoting their coexistence with neutral dynamics (Fig. 2).

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Conditions for the coexistence with neutral dynamics was more limited by higher 277 inbreeding depression (Fig. 2). The coexistences with neutral dynamics were always 278 realized when the two species evolved the prior selfing rate close to 1.0, which 279 neutralized their mutual reproductive interference (Fig. 1). During the coexistence, of I and P are large, the eco-evolutionary dynamics tended to be terminated by 285 competitive exclusion (Fig. 2). Especially when both of I and P are large, competitive 286 exclusion by outcrosser always terminated the eco-evolutionary dynamics (Fig. 2). The 287 coexistence with evolutionary rescue rarely occurred when the inbreeding depression 288 was fixed and independent of the population's selfing rate (Fig. 2).  The coexistence with evolutionary rescue continued until the 10,000-th generation if the 306 fluctuations of the relative abundances ( , ) and the prior selfing rates ( , ) have once 307 started, while the coexistence with neutral dynamics never coexisted before reaching the 308 10,000-th generation (Fig. 4).

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Dependence of simulation consequences on ch and rinitial 311 In the simulations with ER sets, we found that coexistence with evolutionary rescue 312 nearly always occurred with high initial population's selfing rate (rinitial ≥ 0.75) and 313 presence of mutual reproductive interference (ch > 0.0). When the initial population's 314 selfing rate was low (rinitial ≤ 0.25), the both types of coexistence rarely or very 315 infrequently occurred in both the ER and ND sets (Fig. 5). Moreover, no competitive 316 exclusion by outcrosser was found when the initial population's selfing rate was high 317 (rintial ≥ 0.75). Meanwhile, the strength of reproductive interference (ch) seems unlikely 318 to largely influence the coexistence with neutral dynamics with the ND parameter 319 setting. However, the coexistence of evolutionary rescue never occurred without mutual 320 reproductive interference (ch = 0.0) with the ER set.

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Simulation consequences with fixed prior selfing rate and fixed population size 323 We found that coexistence for 2,000 generations very rarely occurred when the prior 324 selfing rates were fixed in the two species for the both parameter settings except when 325 both species had the same and very high prior selfing rates (Fig. 6). Winners were 326 always the species having higher prior selfing rates with the ND parameter set whereas 327 winners were usually the species having the lower and higher prior selfing rates in the 328 below and above areas of the line of r2 = -r1 + 0.6, respectively, with the ER set ( Fig.   329  6). In the simulations with the fixed abundance of two species, the evolutionary shift to 330 the higher prior selfing rate was favored only when the relative abundance of focal 331 species was lower than 1/2 with the ER parameter set (Fig. 7). Meanwhile, under the 332 ND set, very high prior selfing rate was always favored independent on their abundance 333 (Fig. 7). often occurred and stably continued for very long-term (Figs. 3, 4). 345 Firstly, we discuss the processes enabling the coexistence with evolutionary 346 rescue in our model (Fig. 1). At the early generations, the stochastic process makes  The coexistence with neutral dynamics was often found in conditions with 391 lower pollinator availability and weak fixed or moderately variable inbreeding 392 depression (Figs. 2, 3). In such conditions, the higher prior selfing rate evolves very 393 quickly to be almost completely 1.0 in both species (Fig. 1), which should be free from 394 the negative effect of reproductive interference from competitor. Both species exhibit 395 population dynamics of neutral random walk (Hubbell, 2001;Chave, 2004) and coexist, 396 so that stochastic events will stop this type of coexistence at some point in time (Fig. 4).

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In our model, this type of coexistence was usually found in the parameter conditions exclusion occurred more slowly comparing to the exclusion by outcrosser (Fig. 1). The 417 difference was likely due to that reproductive interference no more reduced seed 418 production in highly selfing species.

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In both types of coexistence, co-evolutionary shifts to extremely high prior 420 selfing rate (over 0.9) was necessary in both competing species (Fig. 1)

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The coexistences found in these study systems could be explained by prior-selfing 439 mediated evolutionary rescue, which are predicted by our model. To test this possibility, 440 monitoring of eco-evolutionary dynamics of these competing species in the fields will 441 be required. Although the complete test will require much time and effort, to examine 442 the relationships among population's selfing rate, inbreeding depression and relative 443 abundance in the field should improve our understanding of co-evolutionary 444 coexistence mechanisms without pollination niche partitioning as the first step.

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In conclusion, our model successfully showed that the evolution of prior