There are now a number of well-studied cases in which hybridization between closely related sympatric species has increased, sometimes resulting in the replacement of species pairs by hybrid swarms. Many of these cases have been linked to anthropogenic environmental change, but the mechanisms leading from environmental change to species collapse, and the long-term effects of hybridization on species pairs, remain poorly understood. We used an individual-based stochastic simulation model to explore the conditions under which disturbances that weaken premating barriers to reproduction patterns between sympatric species might lead to increased hybridization and to species collapse. Disturbances often resulted in bouts of hybridization, but in many cases strong reproductive isolation spontaneously reemerged. This was sometimes true even after hybrid swarms had replaced parental species. The reemergence of species pairs was most likely when disturbances were of short duration. Counterintuitively, incipient species pairs were more likely to reemerge after strong but temporary disturbances than after weaker disturbances of the same duration. Even temporary bouts of hybridization often led to substantial homogenization of species pairs. This suggests that ecosystem managers may be able to refill ecological niches, but in general will not be able to resurrect lost species after species collapse.
Increased hybridization between sympatric species following environmental disturbances has been observed in a wide range of plant and animal taxa. As early as 1935, Wiegand observed that species in several genera of the family Rosaceae appeared to hybridize readily in areas that had been disturbed by frequent fires, clearing, or grazing (Wiegand 1935). Increased hybridization between green treefrogs (Hyla cinerea) and barking treefrogs (Hyla gratiosa) has occurred where vegetation has been removed from the areas surrounding shared breeding ponds (Mecham 1960; Lamb and Avise 1986). Many examples come from the fresh water fishes. Todd and Stedman (1989) found that the number of hybrids between lake herring (Coregonus artedii) and bloaters (Coregonus hoyi) in Lakes Michigan and Huron appears to have increased with fishing pressure and with increased predation by invasive sea lampreys (Petromyzon marinus). In Lake Victoria, hybridization between cichlid species Pundamilia pundamilia and P. nyererie is common in areas of high turbidity (Seehausen et al. 1997), and these areas may be increasing as a result of human activities (Verschuren et al. 2002). Perhaps the most well-studied case of species collapse due to hybridization is that of the benthic and limnetic stickleback species pair (Gasterosteus aculeatus species complex) in Enos Lake, British Columbia, Canada (Kraak et al. 2001; Gow et al. 2006; Taylor et al. 2006; Behm et al. 2010). The collapse of this species pair was temporally coincidental with the introduction of American signal crayfish (Pacifasticus lenisculus) to the lake (Foster et al. 2003). Crayfish are thought to have changed lake ecology by removing macrophytes and altering water clarity (Taylor et al. 2006; Behm et al. 2010).
It is often not known whether an increase in the number of hybrids in a given system is due to a change in hybrid fitness or to a change in hybridization rate, but it has been suggested that disturbances can sometimes increase hybridization rate by reducing the ability of individuals to select conspecific mates. For example, Wiegand (1935) hypothesized that habitat disturbance might induce irregularities in flowering time, thereby reducing allochrony between sympatric species and increasing the heterospecific pollination rate. Similarly, increased water turbidity might have reduced the ability of cichlids to identify conspecifics (Seehausen et al. 1997; van der Sluijs et al. 2008a). For treefrogs and sticklebacks, removal of vegetation may have homogenized the mating sites used by different species and caused an increase in heterospecific mating opportunities (Mecham 1960; Lamb and Avise 1986; Taylor et al. 2006). If the weakening of premating barriers to reproduction is severe, species pairs might be vulnerable to collapse into hybrid swarms. Alternatively, species pairs might be protected from collapse if they can rapidly evolve increased choosiness in mate selection when the transduction of mating signals is reduced or when heterospecific mating opportunities increase. For both practical and ethical reasons, hypotheses linking species collapse to a reduced ability to select conspecific mates have not been tested in the field, and few theoretical studies of this mechanism exist (but see Epifanio and Philipp 2000). Interestingly, after species collapse some hybrids show assortative mating behavior when introduced to undisturbed habitats, leading some researchers to suggest that species pairs might reemerge if predisturbance environments could be restored (Mecham 1960; van der Sluijs et al. 2008a). This also remains untested.
We modified the ecological speciation model introduced by Dieckmann and Doebeli (1999) and developed by the same and other authors (Doebeli and Dieckmann 2000, 2003; Bolnick and Doebeli 2003; Bolnick 2004, 2006) to investigate species collapse through hybridization when the ability of individuals to identify and select conspecific mates is reduced. Our model explicitly tracks individual genotypes in a simulated population where genotype governs the resource use and mating behavior of each individual. Reproductive isolation between species pairs is maintained by strong assortative mating. By reducing the strength of assortative mating displayed by individuals of each genotype, we simulated environmental disturbances that reduced the ability of individuals to identify or select conspecific mates. We simulated disturbances that began rapidly as well as disturbances that increased slowly over many generations, and we simulated disturbances that resulted in permanent environmental change as well as temporary disturbances that lasted for one or for multiple generations. We used these simulations to answer three questions: (1) Can a weakening of premating barriers to reproduction lead to the collapse of a species pair through hybridization? (2) How do the magnitude, rate, and duration of environmental change affect the probability of species collapse? and (3) Under what conditions can species reemerge after collapse through hybridization?
To investigate the hybridization and collapse of ecological species, we first needed a model of the speciation process to establish the initial conditions for an ecological species pair. A number of recent studies have used quantitative genetic approaches to model speciation processes (e.g., Polechova and Barton 2005; Doebeli et al. 2007; Ispolatov and Doebeli 2009). Quantitative genetic approaches assume that individual phenotypes are governed by an infinite number of loci at which alleles have infinitesimal effects (Bulmer 1980). However, the effect sizes of alleles at loci governing mate choice are known to affect the probability of speciation (Gavrilets and Vose 2005, Gavrilets and Vose 2009; Gavrilets et al. 2007) and are likely also to affect the probabilities of species collapse and reemergence. In general, adaptive speciation is expected to occur most readily when allele effect sizes are intermediate or large (Gavrilets and Vose 2005, 2009; Doebeli et al. 2007; Gavrilets et al. 2007). Moreover, there is evidence from nature that mate preference in incipient species pairs is, at least in some cases, governed by small numbers of loci with large effects (Henry et al. 2002; Haesler and Seehausen 2005; van der Sluijs et al. 2010). To capture the possible effects of noninfinitesimal alleles, we constructed a genetically explicit model in which the phenotypes that govern an individual's resource use and mate choice are each controlled by a finite number of loci. Speciation in our model does not depend on initial variability at the loci that govern mate selection, nor does it depend on unrealistically high mutation rates. Thus, our model overcomes some important objections that have faced past models of ecological speciation (Gavrilets 2005; Polechova and Barton 2005).
We present the full mathematical apparatus of our model in Appendix S1, and we summarize the model here. We describe the genetic architecture and model dynamics, explain the process we used to obtain simulated species pairs, and explain how we tested the response of species pairs to environmental disturbance. We have made no attempt to parameterize the model to fit any particular system in nature. For illustrative purposes, we have described the model in terms of a hypothetical fish species pair, but the model could equally apply to other animal or plant taxa.
Our model tracks individuals with explicit genotypes in a diploid population that undergoes discrete generations in a single spatial patch. Each individual is characterized by sex and by three genetically determined phenotypes: an ecological phenotype, a marker phenotype, and an assortative mating phenotype. Each phenotype is governed by three additive and diallelic loci. Alleles at each ecological or each marker locus have the same size of effect but may be either positive or negative. By convention, we scale the range of possible ecological and marker phenotypes from −1 to +1. Alleles at each assortative mating locus may be either neutral or positive, and we scale the range of possible assortative mating phenotypes from 0 to +1.
An individual's ecological phenotype determines the type of resources that the individual uses. For example, ecological loci might govern preferred foraging habitat. Individuals with negative ecological phenotypes might prefer benthic habitats and thus consume primarily benthic resources, whereas individuals with positive ecological phenotypes might prefer limnetic habitats and thus consume primarily limnetic resources (Fig. 1). The marker phenotype is used by females to assess potential mates. For example, mate selection might be based in part on body color, and negative alleles might confer dark body color whereas positive alleles might confer light body color. The assortative mating phenotype determines whether and how strongly a female prefers to mate with males carrying marker phenotypes similar to her own. A female with an assortative mating phenotype near +1 is likely to reject a suitor with a marker phenotype even slightly different from her own, whereas a female with an assortative mating phenotype of 0 will mate at random. Our model follows a number of recent models of assortative mating and adaptive speciation by not including the potential for disassortative mating (e.g., van Doorn et al. 2004; Burger and Schneider 2006; Burger et al. 2006; Otto et al. 2008; Pennings et al. 2008). Our results are qualitatively unchanged if we include disassortative mating in the model (see Appendix S2).
Our objective was to study species pairs in which reproductive isolation is initially maintained by strong assortative mating. In the extreme case of panmixia, assortative mating is not expected to evolve in a population that initially mates at random if the fitness of the phenotype under assortment is independent of frequency (de Cara et al. 2008). Therefore, we allowed the marker phenotype to have a fitness effect that depends on its genetic background at the ecological loci. Essentially, this situation will arise whenever females select mates according to traits with fitness effects that are not strictly independent of their ecological background. For example, consider the case in which females choose mates according to body color. Light conditions may vary between foraging habitats, and different body colors will be more or less conspicuous under different light conditions (Gray et al. 2008; Seehausen et al. 2008b; Fig. 1). If conspicuousness affects an individual's ability to avoid predation, the survival rate of an individual with a particular marker phenotype will depend on that individual's preferred foraging habitat. The interaction between marker and ecological phenotypes causes linkage disequilibria to arise between marker and ecological loci, and allows the marker phenotype to act as a surrogate for the ecological phenotype under frequency-dependent selection. Coadaptation between genes is expected to create selection for reduced recombination (Nei 1967; Feldman 1972; Karlin and McGregor 1974), and in nature marker loci sometimes appear in linkage complexes with ecological loci (Streelman et al. 2003; Albertson et al. 2005; T. B. Malek et al. unpubl. ms.). Therefore, we allowed each marker locus in our model to be linked to a single ecological locus, with a recombination rate ρ between them. Ribiero and Cachita (2009) found that a similar architecture allows the evolution of reproductive isolation between sympatric populations in an analytical model.
In each generation, the model population undergoes viability selection followed by mating. Viability selection is independent of sex and is divided into two steps. First, individuals undergo a round of frequency-independent selection in which fitness is determined by the relationship between an individual's marker and ecological phenotypes. Fitness is highest when the phenotypes have the same sign, and lowest when the phenotypes have opposite signs. Individuals then undergo a round of frequency-dependent selection resulting from competition for resources. Because the ecological phenotype determines the resources an individual can use, individuals compete most strongly with other individuals having similar ecological phenotypes. The probability that an individual with a particular ecological phenotype survives frequency-dependent selection depends on the density of resources available to that individual and on the competition that individual experiences from all other individuals in the population.
Mating in our model is by female choice. Each female that survives viability selection is approached at random by potential mates from the pool of surviving males, and mates with or rejects each male with a probability that depends on her assortative mating phenotype and the difference between their marker phenotypes. Thus, assortative mating by females imposes sexual selection on male marker phenotype. Dieckmann and Doebeli's (1999) parameter s scales the strength of assortative mating behavior associated with each assortative mating genotype. The behavioral effect of each assortative mating allele is greatest when s is small. Each female can mate only once, whereas males may mate once, more than once, or not at all. A female that rejects a potential mate may die without reproducing before her next mating opportunity. Thus, assortatively mating females incur a cost of choosiness. The offspring of each successful mating receive one allele from each parent at each ecological, marker, and assortative mating locus. Ecological and assortative mating alleles segregate independently. Each marker allele is drawn from the same chromosome as the linked ecological allele with probability (1 –ρ) and from the opposite chromosome with probability ρ. Each allele in each offspring mutates to the opposite allele with probability μ. Individual offspring are assigned to be either male or female with equal probability. Offspring proceed to frequency-independent selection to begin the next generation.
OBTAINING SIMULATED SPECIES PAIRS
Under appropriate parameter values, frequency-dependent viability selection acting on the ecological phenotype is disruptive in a randomly mating population in our model. Linkage disequilibria between the ecological and marker loci allow the marker phenotype to act as a surrogate for the ecological phenotype. Females that mate assortatively by marker phenotype have offspring with more extreme ecological phenotypes, and these offspring are favored by disruptive selection. Thus, disruptive selection favors assortatively mating females, and allows assortative mating alleles to invade the randomly mating population. Under some conditions, strong reproductive isolation can evolve between subpopulations (see Appendix S1). This process is similar to those that drive the evolution of reproductive isolation in other well-known models of ecological speciation in sympatry (Otto et al. 2008; Pennings et al. 2008; Ribeiro and Caticha 2009).
Because our goal was to study the effects of disturbance on species pairs, we restricted our simulations to parameter values that favored the evolution of reproductive isolation (Bolnick and Doebeli 2003; Bolnick 2004) (see Appendix S1). We initialized our model with populations in which all ecological and marker loci were polymorphic and all individuals mated at random. We iterated the model for 500 generations while disallowing mutation at assortative mating loci to eliminate transient states resulting from the initialization. Thereafter, we allowed mutation at all loci. We defined “speciation” as the evolution of distinct phenotypic modes on the marker trait axis separated for at least 10 consecutive generations by at least one discrete marker phenotype with a density of less than 1% of the most dense discrete marker phenotype in the smaller of the two modes. This is similar to but more stringent than the test for phenotypic bimodality used by Bolnick (2004). We conducted 40 unique simulations, and in 35 cases speciation occurred within 2000 (mean 1351, first decile 902, ninth decile 1835) generations. After speciation, an average of 0.11% of females accepted mates with phenotypes different from their own (including mutants and hybrids), and 0.04% of matings were between members of different phenotypic modes. We call the phenotypic modes “incipient species” to indicate that reproductive isolation between the modes was strong but incomplete.
The model described above allows us to simulate species pairs that have evolved in strict sympatry, where populations are initially panmictic. In nature, panmixia may be rare, and ecological speciation may often occur when gene flow within populations is limited by extrinsic factors such as space (Fitzpatrick et al. 2009). In such cases, strong assortative mating can evolve and ecological speciation can occur even when the phenotype under assortment is not under frequency-dependent selection (Gavrilets et al. 2007). Thus, while speciation in sympatry may require coadaptation or linkage between marker and ecological loci, speciation in parapatry may be possible under a more general set of genetic architectures. To investigate the extreme case in which the marker and ecological loci are unlinked and selectively independent, we began with the incipient species pairs obtained above, permanently removed the viability effect of the marker phenotype, and set the recombination rate between marker and ecological loci to 0.5. We then iterated the model for 100 generations to eliminate residual effects of linkage and viability selection. We refer to incipient species pairs obtained from the original simulated speciation process as the “linked case,” and to species pairs after this modification as the “unlinked case.” Incipient species with unlinked and selectively independent marker and ecological loci can also be generated by explicitly spatial models (e.g., Doebeli and Dieckmann 2003; Gavrilets and Vose 2005; Gavrilets et al. 2007; Sadedin et al. 2009; Thibert-Plante and Hendry 2009), but our approach allows us to derive each unlinked case simply and directly from a linked case and so facilitates comparison between the cases.
TESTING THE RESPONSE OF SPECIES PAIRS TO DISTURBANCE
We selected 10 of our 40 simulations for further study. Each selected simulation had resulted in exactly two incipient species, and the incipient species pairs had marker phenotypes fixed at opposite extremes (i.e., +1 and −1). By employing these criteria, we ensured that we were exploring disturbances to qualitatively similar systems. We used the selected species pairs to study the linked case, and we modified the same species pairs as described above to obtain 10 incipient species pairs for the unlinked case.
We were interested in the resistance and resilience of incipient species pairs to disturbances that reduced the ability of individuals to identify and discriminate against heterospecific mates. Thus, we modeled disturbances that increased the parameter s, and therefore increased the probability that a female with any assortative mating genotype would accept a heterospecific mate. To compare the effects of weak and strong disturbances on incipient species pairs, we tested each of our simulated incipient species pairs 25 times against each of 20 simulated disturbances with strengths ranging from Δs= 0 (no disturbance) to Δs= 0.95 (strong disturbance). We modeled rapid-onset and slow-onset disturbances by allowing s to change either instantly or at a constant rate over 20, 50, 100, 500, 750, or 1000 generations. We tested each species pair 10 times against disturbances with each of these onset rates and at each of 11 disturbance strengths ranging from Δs= 0 to Δs= 0.50 (i.e., 770 simulated disturbances per species pair). To investigate the potential for species recovery if disturbances could be corrected, we modeled cases in which disturbances were permanent or in which disturbances were removed after 1, 100, 200, 300, 400, 500, 1000, or 2000 generations. We tested each species pair 10 times against disturbances of each duration and with each of 20 strengths ranging from Δs= 0 to Δs= 0.95 (i.e., 1800 simulated disturbances per species pair). We performed additional simulations to ensure the accuracy of our results in parts of parameter space where outcomes were highly variable.
To investigate gene flow between the incipient species after disturbance, we defined a “homogenization index” equal to two times the probability that an allele drawn at random from any one of an infinite number of implicitly modeled neutral loci present in both species would be descended from an allele resident in the opposite species in the generation of disturbance. This homogenization index is similar to Wright's panmictic index PST (where PST= 1 –FST) (Wright 1951), but alleles are defined by their species of origin rather than by their identity. The homogenization index is 0 if there has been no gene flow between the incipient species, and increases to 1 as the species become fully mixed. The homogenization index captures gene flow, but because it assumes an infinite number of neutral loci, it does not capture the potential for selection or genetic drift to create novel variation between species. Thus, homogenization index is a useful measure of the potential for hybridization to reduce interspecific variation.
We identified an incipient species pair as “collapsed” if there was a single local maximum of population density on the marker trait axis (i.e., no more than one discrete marker phenotype was more dense than both of its immediate neighbors) for at least one generation at any time after the disturbance. We called the marker phenotype “effectively fixed” if there was a single local maximum of population density on the marker trait axis and at least 95% of all individuals in the population expressed that marker phenotype for 10 consecutive generations. We defined a system's “resistance” as the probability that an incipient species pair in the system avoided collapse after a disturbance of a given strength, and its “resilience” as the probability that incipient species reemerged after collapse. For each of our simulations we recorded the number of generations from disturbance until species collapse (if collapse occurred), the number of generations until effective fixation of the marker phenotype (if fixation occurred), the number of generations until incipient species reemerged (if they reemerged), and the homogenization index 2000 generations after the disturbance began.
When a permanent disturbance reduced the ability of females to identify and discriminate against heterospecific males, the rate of hybridization between incipient species increased. The homogenization index increased with the strength of disturbance (Fig. 2). If the disturbance was sufficiently strong, the incipient species pair collapsed into a hybrid swarm. The number of generations from disturbance to species collapse decreased with the increasing strength of disturbance (Fig. 2). On average, incipient species in the unlinked case collapsed faster than those in the linked case under the same strength of disturbance. However, variation in the time to species collapse was large, particularly when disturbances were weak. Thus, in any given pair of linked and unlinked case simulations, the unlinked case may or may not have collapsed faster than the linked case.
When the disturbance was permanent but weak, bouts of hybridization were often temporary, and reproductive isolation between incipient species often reemerged in the model population (Fig. 3). This was sometimes true even if the original incipient species pair had collapsed into a hybrid swarm (Fig. 4). Incipient species reemerged in both linked and unlinked cases, but species were more likely to reemerge in the linked case than in the unlinked case. The average time to species reemergence was 485 (first decile 165, ninth decile 938) generations in the linked case, and 136 (first decile 60, ninth decile 236) generations in the unlinked case.
Incipient species pairs are able to reemerge after disturbance because bouts of hybridization create selection for stronger assortative mating through a process of reinforcement. By reducing the ability of females to discriminate against heterospecific males, disturbances reduce the behavioral effect of each assortative mating allele and weaken assortative mating in the population. Females with the weakest assortative mating phenotypes are the most likely to hybridize, and thus hybrids tend to carry fewer assortative mating alleles than members of the parental species. If the increase in hybridization rate is small, a hybrid swarm does not develop. Females with extreme marker phenotypes remain common, and sexual selection against hybrid males remains strong. This selects for an increase in the frequency of assortative mating alleles in the population. When assortative mating becomes sufficiently strong, incipient species pairs reemerge. When a hybrid swarm does not develop after a disturbance, sexual selection can drive the reemergence of incipient species even when ecological selection is removed from the model. In such cases, linkage disequilibria between the marker and ecological loci are not required for species reemergence.
When an incipient species pair does collapse into a hybrid swarm after disturbance, the density of individuals with intermediate ecological phenotypes increases. This restores disruptive selection on the ecological phenotype. In this case, linkage disequilibria between the marker and ecological loci are required to translate frequency-dependent ecological selection into selection for increased assortative mating. In the linked case, these linkage disequilibria are maintained by coadaptation and linkage, and incipient species often reemerge. In the unlinked case, partial reproductive isolation between the most extreme marker phenotypes can maintain linkage disequilibria for some generations. In general however, populations in the unlinked case are less resilient to collapse than populations in the linked case. The average time to reemergence in the unlinked case was shorter simply because species pairs that failed to reemerge quickly usually failed to reemerge at all.
When the disturbance was permanent and strong, incipient species pairs collapsed into hybrid swarms and reproductively isolated subpopulations rarely reemerged (Fig. 3). Incipient species pairs in the linked case were more resistant to disturbance than incipient species pairs in the unlinked case. Disturbances caused hybridization by reducing the mean strength of assortative mating behavior in the population. Because incipient species pairs in the linked case evolved from randomly mating populations, populations must have passed through states of equally weak assortative mating during the speciation process. It is interesting then to ask why evolution should not follow the same trajectory to speciation a second time. The answer lies in the strength of the effect of assortative mating alleles before and after disturbance.
Speciation can occur in the predisturbance environment because the behavioral effect of each assortative mating allele is large. Speciation requires disruptive selection on the marker phenotype. In general, choosy females that prefer common males are more likely to find and mate with their preferred males than equally choosy females that prefer rare males. Thus, assortative mating by female choice tends to stabilize common male marker phenotypes (Otto et al. 2008). However, this effect can be weakened or even reversed if females that prefer rare males are choosier than females that prefer common males. Early in the speciation process, intermediate marker phenotypes are common, assortative mating behavior is weak, and the density of assortative mating alleles is nearly uniform across female marker phenotypes. Thus, sexual selection favors common males and inhibits the creation of offspring with extreme marker phenotypes (see Appendix S1). However, rare females with extreme marker phenotypes are most likely to pass their extreme marker phenotypes on to their offspring when they mate assortatively, and as a result assortative mating alleles become concentrated in individuals with extreme marker phenotypes. As a result, females with extreme marker phenotypes discriminate against intermediate males more strongly than intermediate females discriminate against extreme males. This weakens the stabilizing effect of sexual selection that favors common males. If the behavioral effect of each assortative mating allele is large, the difference in choosiness between extreme and intermediate females is great. Stabilizing sexual selection becomes weak, and disruptive ecological selection can overcome stabilizing sexual selection. Phenotypic modes and eventually incipient species are able to develop on the marker trait axis.
Because disturbances reduce the behavioral effect of each assortative mating allele, they weaken the effect of linkage disequilibria between assortative mating and marker loci. Stabilizing sexual selection overcomes disruptive viability selection on the marker phenotype, and modes on the marker trait axis are unable to reemerge. As stabilizing sexual selection eliminates more and more rare marker phenotypes, intermediate marker phenotypes become more common and the stabilizing effect of sexual selection increases. Over time, this positive feedback mechanism leads to the effective fixation of a single marker phenotype in the population (Fig. 5). Mutation maintains a small amount of variation at marker loci even when the marker phenotype is effectively fixed, but strong sexual selection makes the effectively fixed state highly stable.
Interestingly, if species pairs collapse and incipient species do not reemerge rapidly, weak or moderate disturbances cause effective fixation more quickly than stronger disturbances (Fig. 6). This is because assortative mating behavior in the hybrid swarm after a weak disturbance remains stronger than after a strong disturbance, and thus the stabilizing effect of sexual selection on the marker phenotype is greater.
SLOW ONSET DISTURBANCES
Incipient species pairs were more resistant to slow-onset than to rapid-onset disturbances (Fig. 7). Hybridization in response to slow-onset disturbances begins gradually. Because hybrids are rare, sexual selection against rare hybrid males causes the frequency of assortative mating alleles in the population to increase. If the increased frequency of assortative mating alleles is able to offset the reduced behavioral effect of those alleles, reproductive isolation between the incipient species is maintained or restored. However, if it becomes sufficiently strong, even a slow-onset disturbance can cause the collapse of an incipient species pair.
In both the linked and unlinked cases, incipient species pairs were often able to reemerge after a disturbance was removed from the system (Fig. 8). The mean time from the correction of a disturbance to species reemergence was 68 (first decile 14, ninth decile 134) generations in the linked case and 89 (first decile 14, ninth decile 257) generations in the unlinked case. Incipient species were most likely to reemerge if the disturbance was of a short duration. Counterintuitively, incipient species were more likely to reemerge after a strong disturbance than after a moderate disturbance of the same duration. Because the density of assortative mating alleles is maintained or increased in the population during a disturbance, individuals show strong assortative mating behavior as soon as the disturbance is removed. However, the reemergence of incipient species pairs requires not only strong assortative mating but also sufficient variability at marker trait loci, and is therefore possible only if disturbances are removed before the marker phenotype has become effectively fixed. Because moderate disturbances cause marker phenotypes to become effectively fixed more quickly than stronger disturbances (Fig. 6), the window of opportunity for the reemergence of incipient species pairs is longer when disturbances are severe.
Incipient species pairs that reemerged after a disturbance was removed from a system were often phenotypically different from those that existed before species collapse (Fig. 9). If some marker loci became fixed during the disturbance, marker phenotypes in the reemerged species often failed to reach the extreme values exhibited by the precollapse species pair (i.e., −1 and +1). In the unlinked case, the clustering of marker and ecological phenotypes was often reversed in the new species pair. The probability that phenotypes in the new species differed from those before species collapse increased with the duration of the disturbance.
Our model predicts that an environmental disturbance that reduces the ability of individuals to identify and discriminate against heterospecific mates can lead to increased hybridization between incipient species, and potentially to the collapse of an incipient species pair into a hybrid swarm. In some cases, incipient species may reemerge following a collapse. Reemergence will be most likely if the disturbance is temporary. If the disturbance persists for many generations, sexual selection in the population after disturbance can eliminate variability at marker loci, and incipient species may be unable to reemerge. Because sexual selection will be stronger after moderate than after strong disturbances, marker loci may fix more quickly after moderate disturbances, and collapse resulting from moderate disturbances may be more likely to be permanent than collapse resulting from strong disturbances. Finally, our model predicts that the resistance and resilience of populations to disturbance may depend on the genetic architecture underlying the marker and ecological traits. In particular, species pairs may be more likely to survive or reemerge after a disturbance if the marker and ecological loci are coadapted and/or linked than if the marker and ecological loci are unlinked and the marker and ecological phenotypes are selectively independent.
Although the collapse of incipient species pairs into hybrid swarms has sometimes been called “speciation in reverse” (Seehausen 2006; Taylor et al. 2006; Seehausen et al. 2008a), disturbances in our model did not simply reverse speciation processes. The homogenization of easily observed traits such as ecological and marker phenotypes may make species collapse look like speciation in reverse. However, disturbances did not reverse the invasion of assortative mating alleles into model populations, and as a result the evolutionary potential of hybrid swarms was different from that of the original randomly mating parental population. In some cases, an increase in the frequency of assortative mating alleles after a disturbance led to the reemergence of reproductive isolation and of incipient species pairs. Because species reemergence requires only a strengthening rather than a de novo evolution of assortative mating behavior, and because the evolution of assortative mating is slowest in its early stages (see Appendix S1), the reemergence of species pairs after disturbance was faster than the initial speciation process. In other cases, assortative mating behavior in the hybrid swarm eliminated variation at marker loci, and incipient species were unable to reemerge. Effective fixation of the marker phenotype is strongly stable. Sexual selection against rare marker phenotypes prevents the accumulation of new variation at marker loci, and sexual selection against the male offspring of females that accept mates with rare marker phenotypes prevents assortative mating in the population from relaxing. Thus, once marker loci have become effectively fixed, the potential for future speciation based on the same marker trait may be permanently eliminated.
In empirical studies, when the members of some hybrid swarms have been introduced into environments similar to those experienced by the parental species, hybrids have shown mating that is assortative according to the same marker phenotypes used by the parental species (van der Sluijs et al. 2008a). This result is predicted by our model, which suggests that we have captured an important property of species collapse processes that has previously been underappreciated. It is not yet known whether assortative mating in hybridizing populations evolves to become stronger, as predicted by our model, or slowly decays over time. This may be a fruitful area for empirical research.
The continued presence of assortative mating alleles in hybrid populations after species collapse makes the reemergence of incipient species possible if disturbed environments can be repaired. In such cases, species reemergence does not require the evolution or even the strengthening of assortative mating, but requires only that sexual selection due to assortative mating alleles already present in the population reestablish reproductively isolated modes on the marker trait axis. Thus, incipient species may reemerge very quickly. However, because assortative mating behavior in hybrid swarms can homogenize the marker phenotype over time, the reemergence of incipient species may be most likely if the disturbance can be quickly corrected. If incipient species do reemerge, we do not expect these species to be identical to the parental species pair. In our model, even short bouts of hybridization often resulted in substantial homogenization of parental species. If the distribution of resources in the restored system is similar to that in the system before disturbance, ecological phenotypes in the reemerged species may be similar to those in the parental species. However, the distribution of neutral variation between the species may be quite different, and some alleles that were present in the parental species may be absent from the reemerged species. Moreover, marker phenotypes in the reemerged species may be different, and in the unlinked case the clustering of marker and ecological phenotypes may be reversed, from those of the incipient species before collapse. Thus, although conservation practitioners may sometimes be able to repopulate ecological niches by quickly correcting disturbances after species collapse, in general it will not be possible to resurrect species pairs that have been lost through hybridization.
Species pairs in the linked case were less vulnerable to collapse through hybridization and more likely to reemerge after hybridization than species pairs in the unlinked case. This is because linkage and coadaptation help to maintain linkage disequilibria between marker and ecological loci, and linkage disequilibria can convert disruptive ecological selection into divergent selection on the marker phenotype. Moreover, coadaptation helps to avoid fixation of marker loci under sexual selection in a hybrid swarm, and variability at marker loci is necessary for species reemergence. Thus, the same attributes that allow speciation to occur in our sympatric model also make species pairs more resistant and more resilient to hybridization. For this reason, we hypothesize that species pairs that evolve in parapatry or allopatry may be more vulnerable to collapse through hybridization than those that evolve in sympatry. Cade (1983) makes a similar argument based on the empirical observation that species with long sympatric histories tend to exhibit stronger barriers to reproduction than parapatric species or recently reintroduced species. This hypothesis will require testing with explicitly spatial models of speciation and species collapse.
The breakdown of premating isolation has often been hypothesized to link environmental change to species collapse (e.g., Wiegand 1935; Mecham 1960; Seehausen et al. 1997; Taylor et al. 2006), and we have focused on that mechanism here. However, some researchers have proposed that incipient species pairs might also collapse if environmental change were to create ecological selection favoring hybrids (Hendry et al. 2006; Taylor et al. 2006; Grant and Grant 2008; Seehausen et al. 2008a; Behm et al. 2010). For example, two incipient species might specialize on food particles of different sizes. If a disturbance were to replace large and small particles with particles of intermediate size, hybrids might be favored over parental species. Ribiero and Caticha (2009) investigated the conditions under which such ecological selection might lead to the collapse of incipient species pairs, and found that sexual selection against hybrids should make species collapse uncommon unless ecological selection favoring hybrids is strong. In our model, the reemergence of incipient species pairs after collapse often depended on disruptive ecological selection in the hybrid swarm. Thus, although weak-to-moderate selection favoring hybrids may be unlikely to cause the collapse of incipient species pairs, it may be sufficient to prevent species reemergence after a collapse in which premating isolation has been weakened. This might be true of the Enos Lake stickleback system, where it has been suggested that environmental change has disturbed both premating reproductive isolation and postmating selection against hybrids (Taylor et al. 2006; Behm et al. 2010).
We focused our investigation on systems described by two parameter sets: the linked case that favors the evolution of assortative mating and reproductive isolation in sympatric populations (parameters in appendix Table S1), and the unlinked case in which speciation may be possible only in parapatry or allopatry (parameters in appendix Table S1, but d= 0 and ρ= 0.5). By holding system parameters (e.g., carrying capacity, the strength of competition between phenotypes, and the strength of viability selection) constant, we were able to investigate thoroughly how disturbance parameters (e.g., strength, duration, and rate of onset) affect the probabilities of species collapse and reemergence. The parameters that describe a disturbance may be measurable in the field, and in some cases may be at least partially under the control of ecosystem managers. Thus, we believe our results are of both scientific and practical importance. A mechanistic understanding of the processes that lead to species collapse and reemergence, as well as spot checks in other parts of parameter space, suggest that our qualitative results should hold under other parameter sets that favor adaptive speciation. Nonetheless, the parameters we held constant may have quantitative effects on the probabilities of species collapse and reemergence, and some of those effects may be counterintuitive. The effects of these parameters on speciation processes have been extensively studied elsewhere (e.g., Dieckmann and Doebeli 1999; Gavrilets and Vose 2005; Burger et al. 2006; Otto et al. 2008; Pennings et al. 2008), but investigation of their effects on species collapse may reward effort. One parameter value of particular interest is s, effect size of each assortative mating allele. This effect size is known to affect the probability of speciation (Gavrilets and Vose 2005, 2009; Gavrilets et al. 2007; Pennings et al. 2008;), and we show here that it can also affect the probability of re-speciation after species collapse. Although we have held this parameter constant in our model, in nature it may be subject to evolution, particularly when assortative mating is governed by multiple loci or multiple alleles at a single locus. A more thorough understanding of how the distribution of effect sizes of assortative mating alleles evolves would advance our understanding of both speciation and species collapse processes.
In summary, we used a simple model to show that a disturbance that weakens premating isolation between incipient ecological species can sometimes lead to species collapse through hybridization. Whether a particular species pair collapses is likely to depend on the strength, speed, and duration of the disturbance, as well as on the genetic architecture underlying resource use and mate choice in the species pair. Our results support the hypothesis that incipient species may sometimes reemerge if disturbances can be corrected, but suggest that species after reemergence will often be different than the original species pair. Thus, the restoration of habitats after species collapse may not be sufficient to conserve or restore biodiversity.
Associate Editor: M. Doebeli
The authors thank A. R. Ives, A. D. Peters, M. G. Turner, and D. I. Bolnick for helpful comments on this manuscript. RTG was supported by an NSF predoctoral fellowship, by NSF grant DEB-0816613 to A. R. Ives, and by the National Institute for Mathematical and Biological Synthesis, an Institute sponsored by NSF, the U.S. Department of Homeland Security, and the U.S. Department of Agriculture through NSF Award #EF-0832858, with additional support from The University of Tennessee, Knoxville. JEB was supported by NSF grant DGE-0549369 IGERT: Training Program on Biodiversity Conservation and Sustainable Development in Southwest China.