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Journal of Animal Ecology 2016, 85, 638–647 doi: 10.1111/1365-2656.12490 Stable coexistence of ecologically identical species: conspecific aggregation via reproductive interference Lasse Ruokolainen* and Ilkka Hanski Department of Biosciences, University of Helsinki, Viikinkaari 1, PO.Box 65, FIN-00014 Helsinki, Finland Summary 1. Stable coexistence of ecologically identical species is not possible according to the established ecological theory. Many coexistence mechanisms have been proposed, but they all involve some form of ecological differentiation among the competing species. 2. The aggregation model of coexistence would predict coexistence of identical species if there would be a mechanism that generates spatially aggregated distributions that are not completely correlated among the species. Our aim is to demonstrate that continued dispersal, triggered by reproductive interference between ecologically identical species, is such a mechanism. This study has been motivated by species using ephemeral patchy resources, such as decomposing fruits, fungal sporophores, carrion, and dung. 3. We analyse an individual-based model with sexual reproduction, in which the progeny develops in ephemeral resource patches and the new generation disperses to a new set of patches. We assume spatially restricted dispersal, that patches differ in detectability, and that unmated females continue dispersal. 4. In the model, reproductive interference (males spend some time searching for and/or attempting to mate with heterospecific females) reduces the mating rate of females, especially in the less common species, which leads to increased dispersal and reduces spatial correlation in species’ distributions. 5. For a wide range of parameter values, coexisting species show a systematic difference in their relative abundances due to two opposing forces: (1) uncommon species have reduced growth rate (Allee effect), which decreases abundance; (2) an abundance difference between the species reduces interspecific spatial correlation, which in turn reduces interspecific competition and allows the rarer species to persist at low density. 6. Our results demonstrate a new mechanism for coexistence that is not based on ecological differentiation between species. Key-words: aggregation model, competition, dispersal, mate search, patchy habitat Introduction Under which conditions two or more species competing for limiting resources are able to coexist in the same community is a fundamental question in population and community ecology (Hutchinson 1959; May 1973). A classic result supported by a wealth of theory (Chesson 2000) and empirical work (e.g. Gause 1934; Silvertown 2004) maintains that stable coexistence is possible only if species differ sufficiently in their ecology (Chesson 2000). The most obvious ecological differences that facilitate coexistence include niche differences in resource use. However, *Correspondence author: E-mail: [email protected] there are also other mechanisms that may allow coexistence, such as temporal niche shifts (species using the same resource at different times), differences in species’ functional responses to a common limiting factor, and dissimilar responses to environmental fluctuations (Chesson 2000). Many coexistence mechanisms that assume ecological differences among species are only manifested in spatially structured communities (Amarasekare 2003). For instance, coexistence can be mediated via competition–colonization trade-off (e.g. Lehman & Tilman 1997), spatial heterogeneity in competitive hierarchy (e.g. Mouquet & Loreau 2003) and differences in species’ dispersal patterns (Amarasekare 2009; Bode, Bode & Armsworth 2011). The hallmark of stable coexistence is that species have positive expected growth rate when rare. Stable © 2016 The Authors. Journal of Animal Ecology © 2016 British Ecological Society Spatial coexistence of identical species coexistence should be distinguished from transient, albeit possibly long-lasting, coexistence of identical species, whose relative abundances exhibit a random walk until only one species remains (Hubbell 2001). In general, coexistence among competitors requires that intraspecific competition is stronger than interspecific competition (Chesson 2000). In spatially structured populations, this can happen if the spatial distributions of the species are not completely correlated. In the 1980s, several researchers realized that small-scale spatial aggregation of individuals influences the outcome of competition (Atkinson & Shorrocks 1981; Hanski 1981, 1983; Shorrocks et al. 1984; Ives & May 1985; Ives 1988). Intraspecific spatial aggregation increases the strength of intraspecific competition, because more individuals experience high level of competition in high-density areas than low level of competition in low-density areas. If the spatial distributions of competing species are not completely correlated, the level of intraspecific competition may thereby become greater than the level of interspecific competition. This amplification of intraspecific competition has to occur at the scale of regional populations over the full generational cycle for the effect on coexistence to be realized, and the aggregation of individuals should not be proportional to their density in the landscape (Chesson 2012). Some authors went as far as claiming that the ‘aggregation model’ could explain the coexistence of competitors without any ecological differences between species (Atkinson & Shorrocks 1981; Shorrocks et al. 1984; Silvertown & Law 1987), but as pointed out by Chesson (1991), the more or less independent spatial distributions of competing species require some mechanism – identical species would converge to identical spatial distributions and aggregation would not therefore alter the balance between intraspecific and interspecific competition. Notice, however, that interspecific differences among the species that reduce spatial covariance in their distributions may have nothing to do with resource use, and hence stably coexisting species can be identical in their resource requirements – as long as there is some mechanism that prevents the convergence of their spatial distributions. Notice also that spatially aggregated distributions of individuals that are not related to local resource abundance are not generally adaptive – it would typically pay for individuals in highdensity patches to move to low-density patches – but in reality there are constraints preventing individuals from reaching the ideal free distribution (e.g. Jackson, Humphries & Ruxton 2004; Abrams & Ruokolainen 2011). In theory, conspecific aggregation may allow ecologically identical species to coexist only if individuals respond dissimilarly, in one way or another, to conspecifics and heterospecifics, without compromising the premise that they are, in every respect, identical. This is what Chesson (1991) referred to by some ‘social factors’ being needed for stable coexistence of identical species in the aggregation model. One such mechanism was 639 described by Zhang, Lin & Hanski (2004). They assumed that species reproduce in discrete resource patches, such as fig wasps in figs, and that mating occurs after eclosion but before dispersal. In this situation, if only one or a few females of a particular species have laid eggs in a resource patch, the mating in the next generation occurs entirely (if there is only one ovipositing female), or largely, among siblings (with several ovipositing females), and it would pay for the female to produce a female-biased sex ratio among her offspring to reduce competition among the brothers for mates (local mate competition). If females are able to adjust sex ratio at the time-scale of a few generations, an uncommon species would have a more female-biased sex ratio than a common species, which would increase the growth rate of the former and lead to stable coexistence; each species tends to increase when rare (Zhang, Lin & Hanski 2004). Here, we describe another and more general mechanism that may lead to stable coexistence of ecologically identical species. This mechanism relies on individual mating behaviour, resulting in reproductive interference between species. We start from the observation that two general reasons for movements in sexually reproducing species are searching for mates and foraging for resources. Consider a species breeding on a patchy resource, such as drosophilids breeding in decaying fruits (Sevenster & van Alphen 1996) and carrion and dung-inhabiting flies and beetles (Hanski 1980, 1987a; Ives 1991), in which newly eclosed individuals disperse before mating (unlike in fig wasps). Assume that dispersing individuals are attracted by olfactory cues to a new set of resource patches, in which they mate and reproduce. The resource patches differ in terms of how detectable (attractive) they are, due to various environmental factors. Crucially, we then assume that, following a period of dispersal and mating in the resource patches, females that remain unmated continue dispersal, while mated females settle down and start reproducing. Thus, we assume that individual movement decisions are affected by mating, which has been documented for many species (Bellamy & Byrne 2001; Fauvergue, Lo Genco & Lo Pinto 2008). In the present study, we show that this mechanism, prolonged dispersal until mated, combined with some level of interspecific courting or mating attempts, may reduce correlation in the spatial distributions of the competing species sufficiently to allow ecologically identical species to stably coexist in the same metacommunity. Importantly, both components are required for coexistence; reproductive interference alone is not sufficient, and continued dispersal needs to be engaged in response to high abundance of heterospecifics. In addition, we show that under a range of conditions coexisting species show, unexpectedly, persistent differences in their relative abundances across the region. Systematic abundance differences between species have previously been demonstrated only for models with demographic differences between the species. © 2016 The Authors. Journal of Animal Ecology © 2016 British Ecological Society, Journal of Animal Ecology, 85, 638–647 640 L. Ruokolainen & I. Hanski Model We assume an individual-based model, in which species with discrete generations breed in discrete, ephemeral resource patches that last for one generation only. Once the life cycle in a particular generation has been completed, the old resource patches disappear and new ones become available. The model is motivated by insects such as drosophilids, blowflies and dung beetles and flies, which lay their eggs in decomposing fruits, carcasses and dung pats. Comparable dynamics occur in other species using other types of resources with spatially aggregated distribution of individuals, for which our model can be considered as a rough approximation. Assume a set of n patches in each generation, randomly located within a unit square area. Each patch is characterized by its spatial location (coordinates xi, yi) and ‘attractiveness’ (detectability) Ai. Attractiveness Ai influences the likelihood that dispersing individuals are drawn to the patch (below), and it depends on exposure and other features of microtopography as well as on the current environmental conditions, such as the direction and strength of wind, which influence the diffusion of olfactory cues used by dispersing individuals to locate the resource patches. We assume that all patches have the same carrying capacity K, which influences population regulation (below). This assumption reduces stochasticity in the simulations, but does not have a qualitative effect on the results. Patch attractiveness A is assumed to be log-normally distributed, A ~ exp[N(lA, rA)], with parameters lA and rA setting the mean and the standard deviation respectively. Each generation begins by mated females of each species reproducing in the patch in which they are located following dispersal, with a per-capita fecundity b. Hence, the total number of offspring produced per female in species j in patch i is N0 ij = bNij. Each offspring has equal probability of being a male or a female. The offspring compete for the resources in the patch, such that the pooled number of fully developed individuals in patch i is restricted, on average, to the carrying capacity. That is, if ΣjN0 ij > Ki, the probability of individual survival is given by Psurv = Ki / ΣjN0 ij. If ΣjN0 ij ≤ Ki, all individuals survive, Psurv = 1. Following the development of the offspring in patch i, all of them, comprising the next generation, disperse to a set of n newly appeared resource patches with different coordinates and attractiveness values. The probability of an individual arriving at patch k (Pik disp ) depends on the distance between patch k and the natal patch i (dik) as well as the attractiveness of patch k (Ak), such that: expðddik ÞAk s: m¼1 expðddim ÞAm Pik disp ¼ Pn eqn 1 The numerator gives the dispersal propensity to patch k, which is scaled by the summed propensity over all patches, assuring that RPik disp ¼ 1. Here, s is a constant probability of surviving the episode of dispersal and d is the scale of dispersal (average dispersal distance is given by 1/d in the exponential dispersal kernel). Following dispersal, individuals search for mates, which takes place randomly within each resource patch. Thereby, a female of species j encounters a male of either species with probability Pjenc , defined as: Pjenc ¼ 1 expðEC EH Þ; eqn 2a where the exponential term gives the expected proportion of females that do not encounter any males, and EC and EH indicate conspecific and heterospecific encounter propensities: EC ¼ aC MC 1 þ hðaC FC þ aH FH Þ eqn 2b EH ¼ aH MH : 1 þ hðaH FC þ aC FH Þ eqn 2c Individuals of conspecific and heterospecific males (MC and MH) are encountered with rates aC and aH, respectively, and each encounter is associated with a ‘handling’ time h. Thus, mate search time by males is reduced by the handling time associated with encounters with both conspecific (FC) and heterospecific (FH) female individuals. The parameters aC and aH reflect a combination of male and female traits involved in the search process. If there are no differences between the species in this respect, aC = aH. Otherwise we assume that there are some chemical or morphological cues that help individuals in species recognition and hence aC > aH. Note that Eqn. (2) imposes an Allee effect – population growth is reduced at low density – the strength of which depends on the parameters h and aC. The Allee effect arises when many females fail to mate due to strong interspecific mating interference. When only one species is present, strong saturation of males (due to high h and/or aC) can lead to perpetuating mating failure (Allee effect), especially when local carrying capacities are low. In Eqn. (2b,c), heterospecific females reduce mating rate because males waste time in searching and courting them, unless aH = 0. Similarly, heterospecific males reduce mating rate by reducing the number of females that are available for mating at any point in time (i.e. not courted by a heterospecific male). In Eqn. (2b,c), the encounter propensity between conspecific males and females is reduced by the handling time of individual encounters. Thus, the availability of conspecific males depends on the abundance of both conspecific and heterospecific females. The actual encounter probability also needs to take into consideration not only the reduced availability of males but also the fact that females are occupied in male–female encounters. This is taken into account here in Eqn. (2a), which gives the probability that a female encounters any male. To obtain © 2016 The Authors. Journal of Animal Ecology © 2016 British Ecological Society, Journal of Animal Ecology, 85, 638–647 Spatial coexistence of identical species the probability that a female encounters and consecutively mates with a conspecific male, Eqn. (2a) is modified by multiplying Penc with the probability that an encountered male is conspecific: Pjmate ¼ Pjenc EC ; EC þ EH eqn 3 where the probability of encounter with a conspecific male is given by the proportion EC/(EC + EH), which takes into account the availability of different males to the females. In the special case of h = 0, female encounter probability becomes Penc = 1 – exp(–aCMC – aHMH), where the exponential term decreases much faster with increasing male abundances than when h > 0. This means that Penc approaches 1 when h goes to zero. In turn, female mating probability approaches Pmate = aCMC/(aCMC + aHMH). Reproductive interference still operates, as the presence of heterospecifics reduces mating probability via the aHMH term, and this reduction becomes more prominent with increasing asymmetry in species abundances, which leads to a strong tendency for a rare species to continue dispersing. The final, and crucial, assumption of the model is the possibility of multiple episodes of dispersal within each generation. Following the initial round of dispersal from natal patches to the new ones, females that have not become mated during the discrete time interval considered in Eqn. (2) perform another round of dispersal among the new patches. Increasing the number of possible dispersal episodes above two had little qualitative effect on the results, and hence we report results for two dispersal episodes only. We assume that males continue dispersal with probability 1 – Pmate, and thus more males disperse from a patch from which a large fraction of conspecific females dispersed because they remained unmated. In other words, males tend to follow the dispersal behaviour of females. Importantly, we assume that environmental conditions change between each episode of dispersal, such that the Ai values are redrawn anew from the same distribution as for the first episode of dispersal. We also vary the variance of Ai (rA) to make sure our conclusions are not sensitive to this assumption. In model analysis, we assume that there are two species with identical demographic parameters b and s. We start by considering the case where the species do not differ in terms of resource use and competitive ability, but they do differ in some trait that affects their dispersal behaviour as reflected by the values of patch attractiveness A. That is, the species are not ecologically identical. We denote the between-species correlation in the patch attractiveness values by qA, which defines how similarly the species respond to variation in patch attractiveness (Ruokolainen & Fowler 2008; Ruokolainen 2013). We calculate the attractiveness of patch i for species j at time t as 3 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 ð1 q u þ x Þq j;t t A A 6 7 Aij ðtÞ ¼ exp4rA qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi þ lA 5; 1 1 þ ð1 qA ÞqA 641 2 eqn 4 where φt and xj,t are standard normal random deviates. φt is common to the two species, while xj,t are species specific. Equation (4) generates a series of attractiveness values for each patch and each species, such that the patch-specific attractiveness values are correlated between species, given by the correlation coefficient qA. Simulations are initiated by placing 10 individuals of each species in each resource patch with probability 05. The dynamics are simulated for 2000 time steps, of which the first 1000 steps are discarded as a transient. Results interspecific differences in foraging behaviour We start by considering situations where resource patches attract different species in a dissimilar manner, when there is only one dispersal episode. We thus assume that while the species do not differ in their resource use and competitive abilities, they differ in some trait that affects their dispersal behaviour. When the correlation in the patch attractiveness values is low, the species coexist at similar regional abundances due to spatially segregated distributions (Fig. 1a,b). Increasing the value of qA from zero does not affect coexistence until it is abruptly lost at an intermediate value of qA (Fig. 1a). At higher values of qA, the spatial distributions of the two species tend to converge, which leads to competitive exclusion of one of the species (Fig. 1a,b). This result demonstrates that reproductive interference alone does not facilitate species coexistence. ecologically identical species Here, we assume that qA = 1, in other words the two species respond identically to the environment (have the same patch attractiveness values) and are hence identical in every respect. This means that the species identity of an individual does not affect its probability of local survival nor dispersal to a given patch from another patch. Under these assumptions, coexistence is possible only if there is sufficient segregation in the spatial distributions of the species. The main result from the analyses below is that coexistence is possible if males are attracted by and/or search for heterospecific females at least to some extent (aH > 0) and some time is thereby wasted (Fig. 2). When there are no interactions between the adults of the two species (aH = 0), or when individuals do not differentiate between conspecifics and heterospecifics (aC = aH), coexistence is not possible and one of the species goes extinct (Fig. 2a). However, as noted above, if coexistence is observed, it arises due to the effect of continued dispersal. © 2016 The Authors. Journal of Animal Ecology © 2016 British Ecological Society, Journal of Animal Ecology, 85, 638–647 642 L. Ruokolainen & I. Hanski Fig. 1. Differences in patch attractiveness as experienced by different species allow coexistence of otherwise similar competitors. (a) The effect of the correlation in patch attractiveness between two species (qA) on their long-term regional abundances. The y-axis shows the mean population size across patches averaged across time. (b) Sample time series for qA = 02 (above) and for qA = 06 (below). The yaxis shows the mean population size across patches. The colour indicates the rank order of species in each simulation: red = more abundant species, blue = less abundant species. Parameters: n = 20, K = 200, lA = 3, rA = 1, b = 10, d = 1, s = 1, h = 005, aC = 1 and aH = 02. Only one dispersal episode was assumed. Fig. 2. Examples of typical model outcomes: (a) only one of two identical species survives (aH = aC = 1), (b) species coexist with similar long-term regional abundances (aH = 02) and (c) species coexist with a persistent asymmetry in regional population sizes (aH = 06). Red and blue indicate species with higher and lower long-term abundance respectively. The value on the left axis (grey line) gives the mean number of mated females in each species, while the value on the right axis gives the degree of spatial correlation between the species. Constant parameters: n = 20, K = 200, lA = 3, rA = 1, qA = 1, b = 10, d = 1, s = 1, aC = 1, h = 01, and the number of dispersal episodes = 2. Courting heterospecific females leads to a reduction in the mating rate of especially the locally less common species, and as unmated females continue dispersal, spatial correlation in the abundances of the two species (i.e. the correlation between abundances across patches) is reduced and the likelihood of coexistence is increased. In the long run, the two species may be regionally equally common (Fig. 2b), but when the reproductive interference is strong, a persistent abundance difference between the two species can emerge (Fig. 2c). The asymmetry is due to two opposing forces. First, the rarer the less common species is, the smaller interspecific spatial correlation is and hence the weaker interspecific competition is. Second, the common species reduces the mating success of the rare species, while the rare species has no comparable effect on the common species. Coexistence is not possible when aH is either very small or very large, approaching aC (Fig. 3). When aH is small, there is not enough reproductive interference to repel a species away from the patches where the other species is numerically dominant and hence the spatial distributions of the two species converge. On the other hand, if aH is close to aC, female mating probability critically depends on the relative abundances of conspecific and heterospecific males. In this case, a reduction in male abundance reduces mating rate, which further reduces abundance and quickly leads to extinction (Fig. 2a). Moreover, coexistence is not possible when mating rate becomes saturated by large handling time (Fig. 3). When h is large, females of the less common species have low probability of mating after the first episode of dispersal; they continue dispersal, but mating rate is low also after the second episode of dispersal because of large h. The less common species then suffers a low growth rate, which is not sufficiently compensated for by reduced correlation in the spatial distributions of the species. The species coexist at similar long-term densities when aH is intermediate and h © 2016 The Authors. Journal of Animal Ecology © 2016 British Ecological Society, Journal of Animal Ecology, 85, 638–647 Spatial coexistence of identical species is small (Fig. 3), such that the species affect each other’s mating success over a broad range of abundances. Finally, we reiterate that in the model coexistence and competitive exclusion depend on density-dependent mating success and associated prolonged dispersal. If this component of the model is eliminated by assuming, e.g., a constant mating probability independent of male density, say Pmate = 05, species’ relative abundances exhibit a random walk until only one species remains, which may take Fig. 3. (a) Heterospecific mate search rate (aH) and handling time (h) interact in affecting coexistence of identical species. Here, aH is varied, while keeping aC constant (aC = 1). The colour scale indicates the relative abundance of the less abundant species. Constant parameters: n = 20, K = 200, lA = 3, rA = 1, qA = 1, b = 10, d = 1 and s = 1, and the number of dispersal episodes = 2. 643 a long time in a large population. In contrast, when mating success is density dependent, extinction, when it occurs, happens rapidly. sensitivity to parameter values The structure of the landscape does not have major qualitative effects on the results, beyond that stochastic extinction of the regionally rarer species is more likely from small landscapes (small number of resource patches, n) with small local carrying capacity (Fig. 4a). Increasing the size of the landscape reduces the role of demographic stochasticity and makes it more likely that there is a systematic difference in the abundances of the two species (Fig. 4b). Individual fecundity (b) has no qualitative effect on the results, although naturally with very low fecundity no species will persist (not shown). In the above analyses, we assumed that there is no cost to dispersal (s = 1). For a wide range of parameter values, assuming a dispersal cost does not have a qualitative effect on the results, but when survival during dispersal becomes low, coexistence becomes impossible due to an Allee effect in the rare species with high overall dispersal rate (Fig. 4c). We have also assumed that the species are identical, including symmetric interspecific mating interference. If this is not the case, for instance, because one species is more strongly attracted to heterospecifics than the other, asymmetry in regional abundances increases and eventually, when asymmetry in mating interference is strong, one species goes extinct (Fig. 4d). Coexistence is not possible if variation in patch attractiveness (rA) is very large (Fig. 5), in which case most individuals are attracted to a small number of resource Fig. 4. Sensitivity of simulation results to model parameters. (a) Local carrying capacity (K), (b) landscape size (n), (c) dispersal survival (s) and (d) asymmetry in mating interference between the species. Notice that increasing asymmetry in heterospecific search rates first leads to asymmetric abundances of the two species, but eventually leads to the exclusion of one of the species. Here, the heterospecific mating rate against species 1 is constant aH1 = 05, while that against species 2 (aH2) is varied. Constant parameters: n = 20, K = 200, rA = 1, qA = 1, b = 10, h = = 01, aC = 1, aH = 02, d = 1, s = 1, and the number of dispersal episodes = 2. Red and blue stand for the more abundant and less abundant species respectively. © 2016 The Authors. Journal of Animal Ecology © 2016 British Ecological Society, Journal of Animal Ecology, 85, 638–647 644 L. Ruokolainen & I. Hanski Fig. 5. Spatial variation in patch attractiveness and average dispersal distance interact in affecting species coexistence. The colour scale indicates the relative abundance of the less abundant species. Constant parameters: n = 20, K = 200, qA = 1, b = 10, h = 01, aC = 1, aH = 025, s = 1, and the number of dispersal episodes = 2. patches. On the other hand, variation in patch attractiveness interacts with the spatial scale of dispersal (d), such that more localized dispersal promotes coexistence, and in the extreme case, coexistence is possible even when there is no spatial variation in patch attractiveness (Fig. 5). With long dispersal distances, rA has to be greater than a threshold value for coexistence, below which the spatial distributions convergence. In the example in Fig. 5, asymmetric coexistence is possible only for intermediate values of rA. Discussion The present results demonstrate that coexistence of ecologically identical species is possible in the aggregation model, if individuals can continue dispersing in response to individual abundances. Here, we assume that this arises due to reproductive interference, meaning here that males court for and/or attempt to mate with heterospecific females. Reproductive interference reduces the mating probability, and if unmated females continue dispersal and patch attractiveness values change in time, the spatial distributions of the competing species become, to some extent, uncorrelated, which facilitates coexistence. Our model also makes the unexpected prediction that stably coexisting identical species may exhibit a persistent difference in their regional abundances, which has been previously associated with ecological differentiation between species. Abundance differences arise in the model due to the opposing effects of an Allee effect in reproduction and a dynamic relationship between species abundances and spatial covariance. Below, we discuss the mechanisms underlying these results in greater detail and consider these results in the light of previous theory and empirical data. Stable coexistence in our model is based on three assumptions. First, we assume that there is variation in the detectability of the resource patches by dispersing individuals, which promotes spatially aggregated distributions. This assumption is expected to be widely applicable; this is the main explanation for spatially aggregated distributions in, e.g., carrion flies (Hanski 1987a; Ives 1988, 1991), fruit flies (Sevenster & van Alphen 1996; Takahashi 2006), fungivorous flies (Hanski 1987b) and dung beetles (Hanski & Cambefort 1991). Conspecific aggregation can also arise due to aggregation pheromones (Takahashi 2006), as in some fruit flies (e.g. Hedlund et al. 1996), but in this case, there are interspecific differences in longrange pheromones. Alternatively, spatial variation in detectability is not necessary for coexistence if dispersal is strongly localized (Fig. 5). In this case, local abundances become, to some extent, uncoupled from abundances at the landscape level, and hence different species can numerically dominate in different resource patches. Secondly, we assume that the movement behaviour of females is affected by their mating status, which has been observed in experimental studies (e.g. Fauvergue, Lo Genco & Lo Pinto 2008; Wenninger, Stelinski & Hall 2009). Male dispersal was assumed to reflect the mating success and mating-status related dispersal of females. Thirdly, we assume that the detectability of resource patches varies in time, which makes it more likely that individuals dispersing from patches with low conspecific, but high heterospecific, density end up in patches with low density of heterospecifics. Such variation is likely whenever detectability depends on the prevailing weather conditions, which may change rapidly. For example, carrion flies use olfactory cues to locate carcasses (Hammack et al. 1987), and olfactory cues also play an important role in the foraging behaviour of fruit flies (Gaudry, Nagel & Wilson 2012). It is reasonable to assume that environmental conditions, such as moisture, temperature, exposure to sunlight, and the strength and direction of wind, will all affect the quality and quantity of the substances emitted from the resource patches and how the odours diffuse into the environment. We assume, for simplicity, that there is no spatio-temporal autocorrelation in patch attractiveness. Our model predicts coexistence of identical species, but also that identical species can exhibit a persistent difference in their regional abundances, which arises under a broad range of conditions. This is counter-intuitive, as the general expectation is that the relative abundances of ecologically identical species undergo a random walk until all but one species are extinct (e.g. Hubbell 2001; Chave 2004). While systematic abundance differences are interpreted to reflect differences in species’ demographic parameters, there is little doubt that the dynamics of most ecological communities are influenced by a combination of niche-related and neutral processes (Chesson 2000; Leibold & McPeek 2006; Ruokolainen et al. 2009). In the present model, there is no need for niche or other © 2016 The Authors. Journal of Animal Ecology © 2016 British Ecological Society, Journal of Animal Ecology, 85, 638–647 Spatial coexistence of identical species biological differences among the species. Instead, the asymmetry in regional abundances is maintained by two opposing forces: an Allee effect in reproduction (and the cost of dispersal) tends to decrease the relative abundance of the less common species. In turn, when the species has become rare, interspecific spatial covariance becomes small, which reduces interspecific competition and protects the rare species from global extinction. Increased dispersal with decreasing local abundance in our model is somewhat reminiscent of the competition–colonization trade-off (Lehman & Tilman 1997), where an inferior competitor with higher dispersal rate can colonize patches not occupied by the superior competitor. Here, there are no interspecific differences in species’ competitive abilities nor in their dispersal capacities, but nonetheless the less common species persists because it disperses more, triggered by reproductive interference from the common species. Coexistence of many seemingly similar species is well documented for insect communities breeding in discrete ephemeral resources, such as carrion, dung and decomposing fruits, in which resource competition is often fierce (Beaver 1977; Ives 1991; Sevenster & van Alphen 1996; Zhang, Lin & Hanski 2004). Moreover, coexistence of similar species on these resources as inferred from observational studies has been supported by experiments (Hanski 1987c; Kouki & Hanski 1995). Studies on fruit-feeding drosophilids (Atkinson & Shorrocks 1981) and carrion flies (Hanski 1981) originally stimulated the aggregation model of coexistence, which predicts that species using the same resource may coexist if they have, to some extent, independently aggregated spatial distributions, amplifying the level of intraspecific over the level of interspecific competition (Sevenster 1996; Chesson 2000; Hartley & Shorrocks 2002). The key biological question in this context is which mechanisms may reduce spatial correlation in the distributions of competing species. The most likely mechanisms include differences in species’ foraging and movement behaviours (see, e.g. Shorrocks et al. 1984; Ives & May 1985; Chesson 1991). Coexistence of otherwise identical species is possible if they have sufficiently dissimilar probabilities of detecting resource patches (Fig. 1). For instance, patch attractiveness may depend on temperature, and the activity of different species may be dissimilarly affected by temperature; or the species may be attracted to specific metabolites produced by bacteria in the resource patches (Ives 1991). These mechanisms are analogous to coexistence via temporal niche differentiation in non-spatial models; competitors that respond dissimilarly to environmental fluctuations can coexist (Chesson 2000). A different mechanism was described by M’Gonigle et al. (2012), who showed that sexual selection in a heterogeneous landscape, combined with a cost associated with female mate search, can promote coexistence of ecologically equivalent species by generating persistent single-species spatial clusters. This mechanism requires the presence of fixed envi- 645 ronmental heterogeneity, which ‘freezes’ the spatial patterns (M’Gonigle et al. 2012), without which species’ relative abundances would drift and ultimately only one species would remain. Another mechanism related to sexual reproduction was described by Zhang, Lin & Hanski (2004), who showed that sex-ratio adjustment due to local mate competition may provide the necessary rare species advantage that may lead to stable coexistence (see Introduction). Here, we have described another coexistence mechanism for sexually reproducing species, which does not require any differences in the biology of the species, no fixed spatial variation in resource distribution, nor any sex-ratio adjustment. Instead, this mechanism relies on interspecific reproductive interference (Gr€ oning & Hochkirch 2008) combined with mating-status dependent movement behaviour (Bellamy & Byrne 2001; Fauvergue, Lo Genco & Lo Pinto 2008). Coexistence arises when unmated females move away from high density of heterospecifics to increase their chances of mating. Combined with spatiotemporal variation in patch attractiveness or highly localized dispersal, such movement behaviour generates a rare species advantage – positive growth rate when the species is rare (a general criterion for invasibility) – due to reduced spatial covariance between the competing species. This is an example of mechanisms leading to growth-density covariance (Chesson 2000; Amarasekare 2003): the average per-capita growth rate of an invading species is elevated due to reproduction in areas with low interspecific competition. In our case, the rare species experiences reduced interspecific competition because individuals frequently redisperse following a change in the attractiveness of the resource patches, and hence these individuals disperse to resource patches independently of the distribution of the common species among the patches. Frequency-dependent reproductive interference is common especially among closely related species (Gr€ oning & Hochkirch 2008), and it can be as important as resource competition in affecting coexistence (Kishi, Nishida & Tsubaki 2009). We have modelled reproductive interference as time wasted in heterospecific mating attempts. This is supported by empirical findings, suggesting that the time females spend being courted by heterospecific males can reduce the mating success of females of the species in the local minority (Friberg, Leimar & Wiklund 2013). Other forms of reproductive interference include signal jamming and hybridization (Gr€ oning & Hochkirch 2008). In nature, reproductive interference is often asymmetric (e.g. Hochkirch, Gr€ oning & B€ ucker 2007) due to, e.g., differences in body size between the species. For instance, males may prefer to court larger heterospecific females as observed in groundhoppers (Hochkirch, Deppermann & Gr€ oning 2006). While we have assumed symmetric interference, increasingly asymmetric interspecific interference would increase the asymmetry in species’ regional abundances and eventually leads to the exclusion of one species (Fig. 4d). © 2016 The Authors. Journal of Animal Ecology © 2016 British Ecological Society, Journal of Animal Ecology, 85, 638–647 646 L. Ruokolainen & I. Hanski Observational and experimental studies have indicated that reproductive interference can lead to spatial segregation, sexual displacement and resource partitioning (Gr€ oning & Hochkirch 2008; Kishi & Tsubaki 2014). In line with these results, previous theoretical models have concluded that reproductive interference hampers coexistence (e.g. Kishi & Nakazawa 2013). This is due to a positive feedback between increasingly asymmetric relative abundances of the species and reduced fecundity of the less abundant species; it is disadvantageous to be the less abundant species (Kishi & Tsubaki 2014). In contrast, in our spatial model, reproductive interference promotes regional coexistence under a broad range of conditions. In this case, although reproductive interference leads to rare species disadvantage locally, this can be reversed to rare species advantage at the regional level. Landscapelevel coexistence can also arise for other reasons, whenever low conspecific density triggers prolonged dispersal. Recently, Nishida, Takakura & Iwao (2015) have reported that identical species with reproductive interference can coexist with highly segregated spatial distributions, which they call parapatric coexistence (see also Ribeiro & Spielman 1986). Their result is contingent on highly localized dispersal: adults emigrate from their natal patch to a randomly selected neighbouring patch or remain in the natal patch. We have shown that when dispersal is not localized, interference alone is not sufficient to allow regional coexistence, which in our model depends on the possibility of unmated females to continue dispersal. Nonetheless, in agreement with Nishida, Takakura & Iwao (2015), increasingly localized dispersal increases the possibility for symmetric coexistence also in our model. We call species identical even if there is a difference in the mate search parameter a for conspecifics and heterospecifics. If there is no such difference, the two species cannot coexist in this model (Fig. 3). Clearly, there must be some pre-zygotic or post-zygotic differences between two sexually reproducing species, otherwise they would merge into one species. Increasing aH reduces mating probability and thus increases the likelihood of continued dispersal of non-mated females, especially in the locally less abundant species. Increasing the search rate for heterospecifics (aH) decreases asymmetry in species’ abundances, while increasing the search rate for conspecifics (aC) has the opposite effect. One caveat to our results concerns the evolution of dispersal in the kinds of situations we have modelled. We assume that females perform only one episode of dispersal unless they fail to mate. Individuals might perform several episodes of dispersal, and individuals located in high-density patches might have elevated rate of dispersal to avoid resource competition. If mated females continue dispersal in response to crowding, the exclusion of all but one species becomes more likely when their sensitivity to crowding increases. This happens because in this case, the spatial distributions of different species converge and thereby the rare species advantage is lost. However, the fact that carrion and dung-inhabiting flies and beetles (Hanski 1987b) and drosophilids breeding in decomposing fruits (Shorrocks et al. 1984) exhibit highly aggregated spatial distributions suggests that there are severe constraints that prevent individuals from achieving anything even resembling the ideal free distribution. One factor that penalizes prolonged dispersal is strong priority effect: the progeny of the first individuals to oviposit have an advantage in scramble competition (Hanski 1987b,c). Furthermore, the presence of conspecifics may be used as a cue of favourable habitat, as has been documented for a wide variety of animals (Bowler & Benton 2005). 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Received 12 August 2015; accepted 4 January 2016 Handling Editor: Jean-Michel Gaillard Supporting Information Additional Supporting Information may be found in the online version of this article. Appendix S1. Programming code for simulating the model, implemented in R. © 2016 The Authors. Journal of Animal Ecology © 2016 British Ecological Society, Journal of Animal Ecology, 85, 638–647