The evolution of conditional dispersal and reproductive isolation along environmental gradients

Dispersal modulates gene flow throughout a population's spatial range. Gene flow affects adaptation at local spatial scales, and consequently impacts the evolution of reproductive isolation. A recent theoretical investigation has demonstrated that local adaptation along an environmental gradient, facilitated by the evolution of limited dispersal, can lead to parapatric speciation even in the absence of assortative mating. This and other studies assumed unconditional dispersal, so individuals start dispersing without regard to local environmental conditions. However, many species disperse conditionally; their propensity to disperse is contingent upon environmental cues, such as the degree of local crowding or the availability of suitable mates. Here, we use an individual-based model in continuous space to investigate by numerical simulation the relationship between the evolution of threshold-based conditional dispersal and parapatric speciation driven by frequency-dependent competition along environmental gradients. We find that, as with unconditional dispersal, parapatric speciation occurs under a broad range of conditions when reproduction is asexual, and under a more restricted range of conditions when reproduction is sexual. In both the asexual and sexual cases, the evolution of conditional dispersal is strongly influenced by the slope of the environmental gradient: shallow environmental gradients result in low dispersal thresholds and high dispersal distances, while steep environmental gradients result in high dispersal thresholds and low dispersal distances. The latter, however, remain higher than under unconditional dispersal, thus undermining isolation by distance, and hindering speciation in sexual populations. Consequently, the speciation of sexual populations under conditional dispersal is triggered by a steeper gradient than under unconditional dispersal. Enhancing the disruptiveness of frequency-dependent selection, more box-shaped competition kernels dramatically lower the speciation-enabling slope of the environmental gradient.     

Species packing in nonsmooth competition models

Despite the potential for competition to generate equilibrium coexistence of infinitely tightly packed species along a trait axis, prior work has shown that the classical expectation of system-specific limits to the similarity of stably coexisting species is sound. A key reason is that known instances of continuous coexistence are fragile, requiring fine-tuning of parameters: A small alteration of the parameters leads back to the classical limiting similarity predictions. Here we present, but then cast aside, a new theoretical challenge to the expectation of limiting similarity. Robust continuous coexistence can arise if competition between species is modeled as a nonsmooth function of their differences—specifically, if the competition kernel (differential response of species’ growth rates to changes in the density of other species along the trait axis) has a nondifferentiable sharp peak at zero trait difference. We will say that these kernels possess a “kink.” The difference in predicted behavior stems from the fact that smooth kernels do not change to a first-order approximation around their maxima, creating strong competitive interactions between similar species. “Kinked” kernels, on the other hand, decrease linearly even for small species differences, reducing interspecific competition compared with intraspecific competition for arbitrarily small species differences. We investigate what mechanisms would lead to kinked kernels in the first place. It turns out that discontinuities in resource utilization generate them. We argue that such sudden jumps in the utilization of resources are unrealistic, and therefore, one should expect kernels to be smooth in reality.     

The role of gene flow asymmetry along an environmental gradient in constraining local adaptation and range expansion

Theoretically, asymmetric gene flow along an environmental gradient can limit species range expansion by keeping peripheral populations from locally adapting. However, few empirical studies have examined this potentially fundamental evolutionary mechanism. We address this possibility in the cricket Allonemobius socius, which exist along a season‐length gradient where the probability of producing a single generation per year (univoltinism) increases with latitude. As the probability of univoltinism increases northwards, populations are expected to hedge their bets by producing a greater proportion of diapause eggs when exposed to a mild diapause cue. However, gene flow from southern populations may disrupt local adaptation in the north by reducing the proportion of diapause eggs (expected to be 100% in pure univoltine environments). This may limit range expansion along the northern periphery where A. socius compete with A. fasciatus, a sister species that exhibits an invariant diapause‐only egg‐laying strategy. To assess the potential for range limitation, we examined diapause incidence (the proportion of diapause eggs produced under diapause conditions), gene flow symmetry and population structure across nine A. socius populations. We found that gene flow was asymmetric and biased northwards towards the periphery. Furthermore, peripheral populations that inhabited pure univoltine environments produced numerous nondiapause eggs (a southern, bivoltine diapause phenotype), which we assume to be a suboptimal phenotype. These patterns suggest that asymmetric gene flow along the gradient constrains adaptation in peripheral populations, potentially constraining species range expansion.     

Evolutionary dynamics and strong Allee effects

We describe the dynamics of an evolutionary model for a population subject to a strong Allee effect. The model assumes that the carrying capacity k(u), inherent growth rate r(u), and Allee threshold a(u) are functions of a mean phenotypic trait u subject to evolution. The model is a plane autonomous system that describes the coupled population and mean trait dynamics. We show bounded orbits equilibrate and that the Allee basin shrinks (and can even disappear) as a result of evolution. We also show that stable non-extinction equilibria occur at the local maxima of k(u) and that stable extinction equilibria occur at local minima of r(u). We give examples that illustrate these results and demonstrate other consequences of an Allee threshold in an evolutionary setting. These include the existence of multiple evolutionarily stable, non-extinction equilibria, and the possibility of evolving to a non-evolutionary stable strategy (ESS) trait from an initial trait near an ESS.     

Competition and evolution along environmental gradients: patterns, boundaries and sympatric divergence

The present study examined how competitive interactions and environmental conditions generate species boundaries and determine species distributions. A spatially explicit, quantitative genetic, two-species competition model was used to manipulate the strengths of competition, gene flow and local adaptation along environmental gradients. This allowed us to assess the long-term persistence of each species and whether the ranges they inhabited had boundaries in space or were unlimited. We found that a species boundary arises along less steep environmental gradients when the strength of stabilizing selection and diversifying selection are similar. We also found that a species boundary may arise along shallow environmental gradients if interspecific competition is more intense than intraspecific, which relaxes previous requirements for steep gradients for generating range limits. We determined an analytical form for the critical environmental gradient as a function of ecological and genetic parameters at which a species boundary is expected to arise by competition. Results suggest an alternative to resource competition as an explanation for phenotypic divergence between sympatric competitors. Competitors sharing a trait that is under stabilizing selection along an environmental gradient may segregate spatially and evolve in different regions, with phenotypic sympatric divergence reflecting the resulting clines. Along various types of environmental gradients, variation in stabilizing selection intensities could lead to contrasting patterns in the distribution of species. For stabilizing selection strengths in accord with field data estimates, this study predicts that the level of sympatric character divergence would be limited along environmental gradients.     

Allee effects, immigration, and the evolution of species' niches

Theoretical studies of adaptation to sink environments (with conditions outside the niche requirements of a species) have shown that immigration from source habitats can either facilitate or inhibit local adaptation. Here, we examine the influence of immigration on the evolution of local adaptation, given an Allee effect (i.e., at low densities, absolute fitness increases with population density). We consider a deterministic model for evolution at a haploid locus, and a stochastic individual-based model for evolution of a quantitative trait, and several kinds of Allee effects. We demonstrate that increased immigration can greatly facilitate adaptive evolution in the sink; with greater immigration, local population sizes rise, and because of the Allee effect, there is a positive indirect effect of immigration on local fitness. This makes it easier for alleles of modest effect to be captured by natural selection, transforming the sink into a locally adapted population that can persist without immigration.     

Parallel evolution and ecological selection: replicated character displacement in spadefoot toads

Ecological character displacement—trait evolution stemming from selection to lessen resource competition between species—is most often inferred from a pattern in which species differ in resource-use traits in sympatry but not in allopatry, and in which sympatric populations within each species differ from conspecific allopatric populations. Yet, without information on population history, the presence of a divergent phenotype in multiple sympatric populations does not necessarily imply that there has been repeated evolution of character displacement. Instead, such a pattern may arise if there has been character displacement in a single ancestral population, followed by gene flow carrying the divergent phenotype into multiple, derived, sympatric populations. Here, we evaluate the likelihood of such historical events versus ongoing ecological selection in generating divergence in trophic morphology between multiple populations of spadefoot toad (Spea multiplicata) tadpoles that are in sympatry with a heterospecific and those that are in allopatry. We present both phylogenetic and population genetic evidence indicating that the same divergent trait, which minimizes resource competition with the heterospecific, has arisen independently in multiple sympatric populations. These data, therefore, provide strong indirect support for competition''s role in divergent trait evolution.     

Evolutionary dynamics and strong Allee effects

We describe the dynamics of an evolutionary model for a population subject to a strong Allee effect. The model assumes that the carrying capacity k(u), inherent growth rate r(u), and Allee threshold a(u) are functions of a mean phenotypic trait u subject to evolution. The model is a plane autonomous system that describes the coupled population and mean trait dynamics. We show bounded orbits equilibrate and that the Allee basin shrinks (and can even disappear) as a result of evolution. We also show that stable non-extinction equilibria occur at the local maxima of k(u) and that stable extinction equilibria occur at local minima of r(u). We give examples that illustrate these results and demonstrate other consequences of an Allee threshold in an evolutionary setting. These include the existence of multiple evolutionarily stable, non-extinction equilibria, and the possibility of evolving to a non-evolutionary stable strategy (ESS) trait from an initial trait near an ESS.     

Highly Replicated Evolution of Parapatric Ecotypes

Parallel evolution of ecotypes occurs when selection independently drives the evolution of similar traits across similar environments. The multiple origins of ecotypes are often inferred based on a phylogeny that clusters populations according to geographic location and not by the environment they occupy. However, the use of phylogenies to infer parallel evolution in closely related populations is problematic because gene flow and incomplete lineage sorting can uncouple the genetic structure at neutral markers from the colonization history of populations. Here, we demonstrate multiple origins within ecotypes of an Australian wildflower, Senecio lautus. We observed strong genetic structure as well as phylogenetic clustering by geography and show that this is unlikely due to gene flow between parapatric ecotypes, which was surprisingly low. We further confirm this analytically by demonstrating that phylogenetic distortion due to gene flow often requires higher levels of migration than those observed in S. lautus. Our results imply that selection can repeatedly create similar phenotypes despite the perceived homogenizing effects of gene flow.     

The role of recombination,niche‐specific gene pools and flexible genomes in the ecological speciation of bacteria

Bacteria diversify into genetic clusters analogous to those observed in sexual eukaryotes, but the definition of bacterial species is an ongoing problem. Recent work has focused on adaptation to distinct ecological niches as the main driver of clustering, but there remains debate about the role of recombination in that process. One view is that homologous recombination occurs too rarely for gene flow to constrain divergent selection. Another view is that homologous recombination is frequent enough in many bacterial populations that barriers to gene flow are needed to permit divergence. Niche‐specific gene pools have been proposed as a general mechanism to limit gene flow. We use theoretical models to evaluate additional hypotheses that evolving genetic architecture, specifically the effect sizes of genes and gene gain and loss, can limit gene flow between diverging populations. Our model predicts that (a) in the presence of gene flow and recombination, ecological divergence is concentrated in few loci of large effect and (b) high rates of gene flow plus recombination promote gene loss and favor the evolution of niche‐specific genes. The results show that changing genetic architecture and gene loss can facilitate ecological divergence, even without niche‐specific gene pools. We discuss these results in the context of recent studies of sympatric divergence in microbes.     

Ecological speciation along an elevational gradient in a tropical passerine bird?

Local adaptation of populations along elevational gradients is well known, but conclusive evidence that such divergence has resulted in the origin of distinct species in parapatry remains lacking. We integrated morphological, vocal, genetic and behavioural data to test predictions pertaining to the hypothesis of parapatric ecological speciation associated with elevation in populations of a tropical montane songbird, the Grey‐breasted Wood‐wren (Henicorhina leucophrys: Troglodytidae), from the Sierra Nevada de Santa Marta, Colombia. We confirmed that two distinct populations exist along the elevational gradient. Phylogenetic analyses tentatively indicate that the two populations are not sister taxa, suggesting they did not differentiate from a single ancestor along the gradient, but rather resulted from separate colonization events. The populations showed marked divergence in morphometrics, vocalizations and genetic variation in mitochondrial and nuclear loci, and little to no evidence of hybridization. Individuals of both populations responded more strongly to their own local songs than to songs from another elevation. Although the two forms do not appear to have differentiated locally in parapatry, morphological and vocal divergence along the elevational gradient is consistent with adaptation, suggesting a possible link between adaptive evolution in morphology and songs and the origin of reproductive isolation via a behavioural barrier to gene flow. The adaptive value of phenotypic differences between populations requires additional study.     

The evolution of phenotypic traits in a predator-prey system subject to Allee effect

This paper considers the evolution of phenotypic traits in a community comprising the populations of predators and prey subject to Allee effect. The evolutionary model is constructed from a deterministic approximation of the stochastic process of mutation and selection. Firstly, we investigate the ecological and evolutionary conditions that allow for continuously stable strategy and evolutionary branching. We find that the strong Allee effect of prey facilitates the formation of continuously stable strategy in the case that prey population undergoes evolutionary branching if the Allee effect of prey is not strong enough. Secondly, we show that evolutionary suicide is impossible for prey population when the intraspecific competition of prey is symmetric about the origin. However, evolutionary suicide can occur deterministically on prey population if prey individuals undergo strong asymmetric competition and are subject to Allee effect. Thirdly, we show that the evolutionary model with symmetric interactions admits a stable limit cycle if the Allee effect of prey is weak. Evolutionary cycle is a likely outcome of the process, which depends on the strength of Allee effect and the mutation rates of predators and prey.     

GENETIC MODELS OF ADAPTATION AND GENE FLOW IN PERIPHERAL POPULATIONS

We investigate the interplay between gene flow and adaptation in peripheral populations of a widespread species. Models are developed for the evolution of a quantitative trait under clinally varying selection in a species whose density decreases from the center of the range to its periphery. Two major results emerge. First, gene flow from populations at the range center can be a strong force that inhibits peripheral populations from evolving to their local ecological optima. As a result, peripheral populations experience persistent directional selection. Second, response to local selection pressures can cause rapid and substantial evolution when a peripheral population is isolated from gene flow. The amount of evolutionary change depends on gene flow, selection, the ecological gradient, and the trait's heritability. Rapid divergence can also occur between the two halves of a formerly continuous population that is divided by a vicariant event. A general conclusion is that disruption of gene flow can cause evolutionary divergence, perhaps leading to speciation, in the absence of contributions from random genetic drift.     

Phylogenetic diversity,trait diversity and niches: species assembly of ferns along a tropical elevational gradient

Aim To analyse the structure of pteridophyte assemblages, based on phylogenetic relatedness and trait properties, along an elevational gradient. Ecological theory predicts that co‐occurring species may be: randomly selected from a regional pool; ecologically sorted so that they are functionally different hence resulting in reduced competition (overdispersion); or functionally similar as an adaptation to specific ecological conditions (clustering). Location Braulio Carrillo National Park and Cerro de la Muerte, Costa Rica, Central America. Methods We used an empirical dataset of the quantitative pattern of species occurrences and individual numbers of ferns within 156 plots along a tropical elevational gradient to test whether directed ecological sorting might cause deviations in patterns of trait and phylogenetic diversity. Mean pairwise distances of species based on phylogenetic and trait properties were compared with two different sets of null assemblages, one maintaining species frequency distributions (constrained) and one not (unconstrained). Results Applying different null models resulted in varying degrees of overdispersion and clustering, but overall patterns of deviation from random expectations remained the same. Contrary to theoretical predictions, phylogenetic and trait diversity were relatively independent from one another. Phylogenetic diversity showed no patterns along the elevational gradient, whereas trait diversity showed significant trends for epiphytes. Main conclusions Under stressful environmental conditions (drought at low elevations and frost at high elevations), epiphytic fern assemblages tended to be clustered with respect to trait characteristics, which suggests environmental filtering. Conversely, under less extreme environmental conditions (middle of the transect), the sorting was biased towards high differentiation (overdispersion), presumably because of interspecific competition and trait shifts among closely related species (character displacement).     

Locally adapted traits maintained in the face of high gene flow

Gene flow between phenotypically divergent populations can disrupt local adaptation or, alternatively, may stimulate adaptive evolution by increasing genetic variation. We capitalised on historical Trinidadian guppy transplant experiments to test the phenotypic effects of increased gene flow caused by replicated introductions of adaptively divergent guppies, which were translocated from high‐ to low‐predation environments. We sampled two native populations prior to the onset of gene flow, six historic introduction sites, introduction sources and multiple downstream points in each basin. Extensive gene flow from introductions occurred in all streams, yet adaptive phenotypic divergence across a gradient in predation level was maintained. Descendants of guppies from a high‐predation source site showed high phenotypic similarity with native low‐predation guppies in as few as ~12 generations after gene flow, likely through a combination of adaptive evolution and phenotypic plasticity. Our results demonstrate that locally adapted phenotypes can be maintained despite extensive gene flow from divergent populations.     

Interspecific Competition, Environmental Gradients, Gene Flow, and the Coevolution of Species' Borders

Darwin viewed species range limits as chiefly determined by an interplay between the abiotic environment and interspecific interactions. Haldane argued that species' ranges could be set intraspecifically when gene flow from a species' populous center overwhelms local adaptation at the periphery. Recently, Kirkpatrick and Barton have modeled Haldane's process with a quantitative genetic model that combines density-dependent local population growth with dispersal and gene flow across a linear environmental gradient in optimum phenotype. To address Darwin's ideas, we have extended the Kirkpatrick and Barton model to include interspecific competition and the frequency-dependent selection that it generates, as well as stabilizing selection on a quantitative character. Our model includes local population growth, movements over space, natural selection, and gene flow. It simultaneously addresses the evolution of character displacement and species borders. It reproduces the Kirkpatrick and Barton single-species result that limited ranges can be produced with sufficiently steep environmental gradients and strong dispersal. Further, in the absence of environmental gradients or barriers to dispersal, interspecific competition will not limit species ranges at evolutionary equilibrium. However, interspecific competition can interact with environmental gradients and gene flow to generate limited ranges with much less extreme gradient and dispersal parameters than in the single-species case. Species display character displacement in sympatry, yet the reduction in competition that results from this displacement does not necessarily allow the two species to become sympatric everywhere. When species meet, competition reduces population densities in the region of overlap, which, in turn, intensifies the asymmetry in gene flow from center to margin. This reduces the ability of each species to adapt to local physical conditions at their range limits. If environmental gradients are monotonic but not linear, the transition zone between species at coevolutionary equilibrium occurs where the environmental gradient is steepest. If productivity gradients are also introduced into the model, then patterns similar to Rapoport's rule emerge. Interacting species respond to climate change, as it affects the optimal phenotype over space, by a combination of range shifts and local evolution in mean phenotype, while solitary species respond solely by range shifts. Finally, we compare empirical estimates for intrinsic growth rates and diffusion coefficients for several species to those needed by the single-species model to produce a stable limited range. These empirical values are generally insufficient to produce limited ranges in the model suggesting a role for interspecific interactions.     

Modelling and estimating pollen movement in oilseed rape (Brassica napus) at the landscape scale using genetic markers

Understanding patterns of pollen movement at the landscape scale is important for establishing management rules following the release of genetically modified (GM) crops. We use here a mating model adapted to cultivated species to estimate dispersal kernels from the genotypes of the progenies of male-sterile plants positioned at different sampling sites within a 10 x 10-km oilseed rape production area. Half of the pollen clouds sampled by the male-sterile plants originated from uncharacterized pollen sources that could consist of both large volunteer and feral populations, and fields within and outside the study area. The geometric dispersal kernel was the most appropriate to predict pollen movement in the study area. It predicted a much larger proportion of long-distance pollination than previously fitted dispersal kernels. This best-fitting mating model underestimated the level of differentiation among pollen clouds but could predict its spatial structure. The estimation method was validated on simulated genotypic data, and proved to provide good estimates of both the shape of the dispersal kernel and the rate and composition of pollen issued from uncharacterized pollen sources. The best dispersal kernel fitted here, the geometric kernel, should now be integrated into models that aim at predicting gene flow at the landscape level, in particular between GM and non-GM crops.     

The community context of species' borders: ecological and evolutionary perspectives

Species distributional limits may coincide with hard dispersal barriers or physiological thresholds along environmental gradients, but they may also be influenced by species interactions. We explore a number of models of interspecific interactions that lead to (sometimes abrupt) distribution limits in the presence and absence of environmental gradients. We find that gradients in competitive ability can lead to spatial segregation of competitors into distinct ranges, but that spatial movement tends to broaden the region of sympatry between the two species, and that Allee effects tend to sharpen these boundaries. We generalize these simple models to include metapopulation dynamics and other types of interactions including predator–prey and host–parasite interactions. We derive conditions for range limits in each case. We also consider models that include coevolution and gene flow and find that character displacement along environmental gradients can lead to stable parapatric distributions. We conclude that it is essential to consider coevolved species interactions as a potential mechanism limiting species distributions, particularly when barriers to dispersal are weak and environmental gradients are gradual.     

Do different rates of gene flow underlie variation in phenotypic and phenological clines in a montane grasshopper community?

Species responses to environmental change are likely to depend on existing genetic and phenotypic variation, as well as evolutionary potential. A key challenge is to determine whether gene flow might facilitate or impede genomic divergence among populations responding to environmental change, and if emergent phenotypic variation is dependent on gene flow rates. A general expectation is that patterns of genetic differentiation in a set of codistributed species reflect differences in dispersal ability. In less dispersive species, we predict greater genetic divergence and reduced gene flow. This could lead to covariation in life‐history traits due to local adaptation, although plasticity or drift could mirror these patterns. We compare genome‐wide patterns of genetic structure in four phenotypically variable grasshopper species along a steep elevation gradient near Boulder, Colorado, and test the hypothesis that genomic differentiation is greater in short‐winged grasshopper species, and statistically associated with variation in growth, reproductive, and physiological traits along this gradient. In addition, we estimate rates of gene flow under competing demographic models, as well as potential gene flow through surveys of phenological overlap among populations within a species. All species exhibit genetic structure along the elevation gradient and limited gene flow. The most pronounced genetic divergence appears in short‐winged (less dispersive) species, which also exhibit less phenological overlap among populations. A high‐elevation population of the most widespread species, Melanoplus sanguinipes, appears to be a sink population derived from low elevation populations. While dispersal ability has a clear connection to the genetic structure in different species, genetic distance does not predict growth, reproductive, or physiological trait variation in any species, requiring further investigation to clearly link phenotypic divergence to local adaptation.     

Overcoming Allee effects through evolutionary,genetic, and demographic rescue

Despite the amplified threats of extinction facing small founder populations, successful colonization sometimes occurs, bringing devastating ecological and economic consequences. One explanation may be rapid evolution, which can increase mean fitness in populations declining towards extinction, permitting persistence and subsequent expansion. Such evolutionary rescue may be particularly important, given Allee effects. When a population is introduced at low density, individuals often experience a reduction in one or more components of fitness due to novel selection pressures that arise from diminished intraspecific interactions and positive density dependence (i.e. component Allee effects). A population can avoid extinction if it can adapt and recover on its own (i.e. evolutionary rescue), or if additional immigration sustains the population (i.e. demographic rescue) or boosts its genetic variation that facilitates adaptation (i.e. genetic rescue). These various forms of rescue have often been invoked as possible mechanisms for specific invasions, but their relative importance to invasion is not generally understood. Within a spatially explicit modelling framework, we consider the relative impact of each type of rescue on the probability of successful colonization, when there is evolution of a multi-locus quantitative trait that influences the strength of component Allee effects. We demonstrate that when Allee effects are important, the effect of demographic rescue via recurrent immigration overall provides the greatest opportunity for success. While highlighting the role of evolution in the invasion process, we underscore the importance of the ecological context influencing the persistence of small founder populations.