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.     

The Effects of Density Dependence and Immigration on Local Adaptation and Niche Evolution in a Black-Hole Sink Environment

We examine the effects of density dependence and immigration on local adaptation in a "black-hole sink" habitat, i.e., a habitat in which isolated populations of a species would tend to extinction but where a population is demographically maintained by recurrent one-way migration from a separate source habitat in which the species persists. Using a diploid, one-locus model of a discrete-generation sink population maintained by immigration from a fixed source population, we show that a locally favored allele will spread when rare in the sink if the absolute fitness (or, in some cases, the geometric-mean absolute fitness) of heterozygotes with the favored allele is above one in the sink habitat. With density dependence, the criterion for spread can depend on the rate of immigration, because immigration affects local densities and, hence, absolute fitness. Given the successful establishment of a locally favored allele, it will be maintained by a migration-selection balance and the resulting polymorphic population will be sustained deterministically with either stable or unstable dynamics. The densities of stable polymorphic populations tend to exceed densities that would be maintained in the absence of the favored allele. With strong density regulation, spread of the favored allele may destabilize population dynamics. Our analyses show that polymorphic populations which form subsequent to the establishment of favorable alleles have the capacity to persist deterministically without immigration. Finally, we examined the probabilistic rate at which new favored alleles arise and become established in a sink population. Our results suggest that favored alleles are established most readily at intermediate levels of immigration.     

Evolutionary consequences of asymmetric dispersal rates

We study the consequences of asymmetric dispersal rates (e.g., due to wind or current) for adaptive evolution in a system of two habitat patches. Asymmetric dispersal rates can lead to overcrowding of the "downstream" habitat, resulting in a source-sink population structure in the absence of intrinsic quality differences between habitats or can even cause an intrinsically better habitat to function as a sink. Source-sink population structure due to asymmetric dispersal rates has similar consequences for adaptive evolution as a source-sink structure due to habitat quality differences: natural selection tends to be biased toward the source habitat. We demonstrate this for two models of adaptive evolution: invasion of a rare allele that improves fitness in one habitat but reduces it in the other and antagonistic selection on a quantitative trait determined by five additive loci. If a habitat can sustain a population without immigration, the conditions for adaptation to that habitat are most favorable if there is little or no immigration from the other habitat; the influence of emigration depends on the magnitude of the allelic effects involved and other parameters. If, however, the population is initially unable to persist in a given habitat without immigration, our model predicts that the population will be most likely to adapt to that habitat if the dispersal rates in both directions are high. Our results highlight the general message that the effect of gene flow upon local adaptation should depend profoundly on the demographic context of selection.     

Temporal variation can facilitate niche evolution in harsh sink environments

We examine the impact of temporal variation on adaptive evolution in "sink" environments, where a species encounters conditions outside its niche. Sink populations persist because of recurrent immigration from sources. Prior studies have highlighted the importance of demographic constraints on adaptive evolution in sinks and revealed that adaptation is less likely in harsher sinks. We examine two complementary models of population and evolutionary dynamics in sinks: a continuous-state quantitative-genetics model and an individual-based model. In the former, genetic variance is fixed; in the latter, genetic variance varies because of mutation, drift, and sampling. In both models, a population in a constant harsh sink environment can exist in alternative states: local maladaptation (phenotype comparable to immigrants from the source) or adaptation (phenotype near the local optimum). Temporal variation permits transitions between these states. We show that moderate amounts of temporal variation can facilitate adaptive evolution in sinks, permitting niche evolution, particularly for slow or autocorrelated variation. Such patterns of temporal variation may particularly pertain to sinks caused by biotic interactions (e.g., predation). Our results are relevant to the evolutionary dynamics of species' ranges, the fate of exotic invasive species, and the evolutionary emergence of infectious diseases into novel hosts.     

The phenomenology of niche evolution via quantitative traits in a 'black-hole' sink

Previous studies of adaptive evolution in sink habitats (in which isolated populations of a species cannot persist deterministically) have highlighted the importance of demographic constraints in slowing such evolution, and of immigration in facilitating adaptation. These studies have relied upon either single-locus models or deterministic quantitative genetic formulations. We use individual-based simulations to examine adaptive evolution in a 'black-hole' sink environment where fitness is governed by a polygenic character. The simulations track both the number of individuals and their multi-locus genotypes, and incorporate, in a natural manner, both demographic and genetic stochastic processes. In agreement with previous studies, our findings reveal the central parts played by demographic constraints and immigration in adaptation within a sink (adaptation is more difficult in environments with low absolute fitness, and higher immigration can accelerate adaptation). A novel finding is that there is a 'punctuational' pattern in adaptive evolution in sink environments. Populations typically stay maladapted for a long time, and then rapidly shift into a relatively adapted state, in which persistence no longer depends upon recurrent immigration.     

Sex-biased dispersal and adaptation to marginal habitats

If gene flow occurs through both sexes but only females contribute to population growth, adaptation to marginal (sink) habitats should be differentially affected by male versus female dispersal. Here I address this problem with two models. First, I consider the fate of a rare allele that improves fitness in the marginal habitat but reduces fitness in the core (source) habitat. Then I study the evolution of a polygenic character mediating a trade-off in fitness between the habitats. Both approaches led to qualitatively similar predictions. The effect of a difference in the dispersal rate between the sexes depends on the degree to which immigration from the core habitat boosts the reproductive output from the marginal habitat. This boost is slight if the marginal habitat is able to sustain well a population without immigration. In that case, both female- and male-biased dispersal is more favorable for adaptation to marginal habitats than equal dispersal of both sexes (assuming that the dispersal rate averaged over the sexes is kept constant). In contrast, if the marginal habitat is an absolute sink unable to sustain a population without immigration, the conditions for adaptation to that habitat are least favorable under highly male-biased dispersal and most favorable under highly female-biased dispersal. Under some circumstances, high average (male+female) dispersal is more favorable than low dispersal. Thus, gene flow should not be seen solely as thwarting adaptation to marginal habitats. The results are interpreted in terms of how male and female dispersal affects the relative rate of gene flow from the source to the sink habitat and in the opposite direction. This study predicts that ecological niches of taxa with female-biased dispersal should tend to be broader and more evolutionarily flexible.     

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.     

On the evolutionary stability of sink populations

The evolution of adaptive behaviours can influence population dynamics. Conversely, population dynamics can affect both the rate and direction of adaptive evolution. This paper examines reasons why sink populations – populations maintained by immigration, preventing local extinction – might persist in the habitat repertoire of a species over evolutionary time-scales. Two such reasons correspond to standard explanations for deviations from an ideal free habitat distribution: organisms may not be free to settle in whichever habitat has the highest potential fitness, and may be constrained by costs, perceptual limitations, or mode of dispersal in the acuity of their habitat selectivity. Here, I argue that a third general reason for persistent sink populations is provided by unstable population dynamics in source habitats. I present a simple model illustrating how use of a sink habitat may be selectively advantageous, when a source population has unstable dynamics (which necessarily reflects temporal variation in local fitnesses). Species with unstable local dynamics in high-quality habitats should be selected to utilize a broader range of habitats than species with stable local dynamics, and in particular in some circumstances should utilize sink habitats. This observation has implications for the direction of niche evolution, and the likelihood of niche conservatism.     

Fitness declines towards range limits and local adaptation to climate affect dispersal evolution during climate‐induced range shifts

Dispersal ability will largely determine whether species track their climatic niches during climate change, a process especially important for populations at contracting (low‐latitude/low‐elevation) range limits that otherwise risk extinction. We investigate whether dispersal evolution at contracting range limits is facilitated by two processes that potentially enable edge populations to experience and adjust to the effects of climate deterioration before they cause extinction: (i) climate‐induced fitness declines towards range limits and (ii) local adaptation to a shifting climate gradient. We simulate a species distributed continuously along a temperature gradient using a spatially explicit, individual‐based model. We compare range‐wide dispersal evolution during climate stability vs. directional climate change, with uniform fitness vs. fitness that declines towards range limits (RLs), and for a single climate genotype vs. multiple genotypes locally adapted to temperature. During climate stability, dispersal decreased towards RLs when fitness was uniform, but increased when fitness declined towards RLs, due to highly dispersive genotypes maintaining sink populations at RLs, increased kin selection in smaller populations, and an emergent fitness asymmetry that favoured dispersal in low‐quality habitat. However, this initial dispersal advantage at low‐fitness RLs did not facilitate climate tracking, as it was outweighed by an increased probability of extinction. Locally adapted genotypes benefited from staying close to their climate optima; this selected against dispersal under stable climates but for increased dispersal throughout shifting ranges, compared to cases without local adaptation. Dispersal increased at expanding RLs in most scenarios, but only increased at the range centre and contracting RLs given local adaptation to climate.     

Dangerously few liaisons: a review of mate-finding Allee effects

In this paper, we review mate-finding Allee effects from ecological and evolutionary points of view. We define ‘mate-finding’ as mate searching in mobile animals, and also as the meeting of gametes for sessile animals and plants (pollination). We consider related issues such as mate quality and choice, sperm limitation and physiological stimulation of reproduction by conspecifics, as well as discussing the role of demographic stochasticity in generating mate-finding Allee effects. We consider the role of component Allee effects due to mate-finding in generating demographic Allee effects (at the population level). Compelling evidence for demographic Allee effects due to mate-finding (as well as via other mechanisms) is still limited, due to difficulties in censusing rare populations or a failure to identify underlying mechanisms, but also because of fitness trade-offs, population spatial structure and metapopulation dynamics, and because the strength of component Allee effects may vary in time and space. Mate-finding Allee effects act on individual fitness and are thus susceptible to change via natural selection. We believe it is useful to distinguish two routes by which evolution can act to mitigate mate-finding Allee effects. The first is evolution of characteristics such as calls, pheromones, hermaphroditism, etc. which make mate-finding more efficient at low density, thus eliminating the Allee effect. Such adaptations are very abundant in the natural world, and may have arisen to avoid Allee effects, although other hypotheses are also possible. The second route is to avoid low density via adaptations such as permanent or periodic aggregation. In this case, the Allee effect is still present, but its effects are avoided. These two strategies may have different consequences in a world where many populations are being artificially reduced to low density: in the first case, population growth rate can be maintained, while in the second case, the mechanism to avoid Allee effects has been destroyed. It is therefore in these latter populations that we predict the greatest evidence for mate-finding Allee effects and associated demographic consequences. This idea is supported by the existing empirical evidence for demographic Allee effects. Given a strong effect that mate-finding appears to have on individual fitness, we support the continuing quest to find connections between component mate-finding Allee effects (individual reproductive fitness) and the demographic consequences. There are many reasons why such studies are difficult, but it is important, particularly given the increasing number of populations and species of conservation concern, that the ecological community understands more about how widespread demographic Allee effects really are, and why.     

Canalization breakdown and evolution in a source-sink system

Understanding the process of adaptation to novel environments may help to elucidate several ecological phenomena, from the stability of species range margins to host-pathogen specificity and persistence in degraded habitats. We study evolution in one type of novel environment: a sink habitat where populations cannot persist without recurrent immigration from a source population. Previous studies on source-sink evolution have focused on how extrinsic environmental factors influence adaptation to a sink, but few studies have examined how intrinsic genetic factors influence adaptation. We use an individual-based model to explore how genetic canalization that evolves in gene regulation networks influences the adaptation of a population to a sink. We find that as canalization in the regulation network increases, the probability of adaptation to the novel habitat decreases. When adaptation to the habitat does occur, it is usually preceded by a breakdown of canalization. As evolution continues in the novel habitat, canalization reemerges, but a legacy of the breakdown may remain, even after several generations. We also find that environmental noise tends to increase the probability of adaptation to the novel habitat. Our results suggest that the details of genetic architecture can significantly influence the likelihood of niche evolution in novel environments.     

Allee effects and resilience in stochastic populations

Allee effects, or positive functional relationships between a population’s density (or size) and its per unit abundance growth rate, are now considered to be a widespread if not common influence on the growth of ecological populations. Here we analyze how stochasticity and Allee effects combine to impact population persistence. We compare the deterministic and stochastic properties of four models: a logistic model (without Allee effects), and three versions of the original model of Allee effects proposed by Vito Volterra representing a weak Allee effect, a strong Allee effect, and a strong Allee effect with immigration. We employ the diffusion process approach for modeling single-species populations, and we focus on the properties of stationary distributions and of the mean first passage times. We show that stochasticity amplifies the risks arising from Allee effects, mainly by prolonging the amount of time a population spends at low abundance levels. Even weak Allee effects become consequential when the ubiquitous stochastic forces affecting natural populations are accounted for in population models. Although current concepts of ecological resilience are bound up in the properties of deterministic basins of attraction, a complete understanding of alternative stable states in ecological systems must include stochasticity.     

具有Allee效应的合作进化

Allee效应对物种的续存是潜在的干扰因素,在很大程度上将增加种群局部甚至全局灭绝的可能性。对许多物种,尤其是濒临物种更容易受其影响。将Allee效应引入囚徒困境博弈模型,通过理论分析与数值模拟相结合的方法分析讨论了Allee效应对合作进化的影响。研究结果表明:在恶劣的环境条件下,Allee效应极易使物种灭绝,不利于合作进化;在相对优越的环境条件下(死亡率较低),Allee效应促进合作进化,且Allee效应强度越强,更有利于合作进化,不过种群的空间斑块占有率也会随着Allee效应强度的增强而降低,使物种最终灭绝。     

The effect of mating system on invasiveness: some genetic load may be advantageous when invading new environments

The role of adaptation in determining invasion success has been acknowledged recently, notably through the accumulation of case studies of rapid evolution during bioinvasions. Despite this growing body of empirical evidence, there is still a need to develop the theoretical background of invasions with adaptation. Specifically, the impact of mating system on the dynamics of adaptation during invasion of a new environment remains only partially understood. Here, we analyze a simulation demo-genetic model of bioinvasion accounting for partial asexuality rates. We simulate two levels of recurrent immigration from a source population at mutation–drift–selection equilibrium to a new empty environment with a different adaptive landscape (black-hole sink). Adaptation relies on a quantitative trait coded explicitly by 10 loci under mutation, selection and genetic drift. Using this model, we confirm previous results on the positive effects on invasiveness of migration, mutation and similarity of local phenotypic optima. We further show how the invasion dynamics of the introduced population is affected by the rate of asexuality. Purely asexual species have lower invasion success in terms of probability and time to invasion than species with other mating systems. Among species with mixed mating systems, the greatest invasiveness is observed for species with high asexual rates. We suggest that this pattern is due to inflated genetic variance in the source population through the Hill-Robertson effect (i.e., clonal interference). An interesting consequence is that species with the highest genetic load in their source environment have greatest invasiveness in the new environment.     

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.     

Population dynamic consequences of allee effects

We take a well-known dynamic model of an isolated, unstructured population and modify this to include a factor that allows for a reduction in fitness due to declining population sizes, often termed an Allee effect. Analysis of the behaviour of this model is carried out on two fronts - determining the equilibrium values and examining the stability of these equilibria. Our results point to the stabilising effect on population dynamics of the Allee effect and an unexpected increase in stability with increased competition due to the interaction between competitive and Allee effects.     

Population models with Allee effect: a new model

In this paper, we develop several population models with Allee effects. We start by defining the Allee effect as a phenomenon in which individual fitness increases with increasing density. Based on this biological assumption, we develop several fitness functions that produce corresponding models with Allee effects. In particular, a rational fitness function yields a new mathematical model, which is the focus of our study. Then we study the dynamics of 2-periodic systems with Allee effects and show the existence of an asymptotically stable 2-periodic carrying capacity.     

Population models with Allee effect: a new model

In this paper, we develop several population models with Allee effects. We start by defining the Allee effect as a phenomenon in which individual fitness increases with increasing density. Based on this biological assumption, we develop several fitness functions that produce corresponding models with Allee effects. In particular, a rational fitness function yields a new mathematical model, which is the focus of our study. Then we study the dynamics of 2-periodic systems with Allee effects and show the existence of an asymptotically stable 2-periodic carrying capacity.     

On the mechanistic underpinning of discrete-time population models with Allee effect

The Allee effect means reduction in individual fitness at low population densities. There are many discrete-time population models with an Allee effect in the literature, but most of them are phenomenological. Recently, Geritz and Kisdi [2004. On the mechanistic underpinning of discrete-time population models with complex dynamics. J. Theor. Biol. 228, 261-269] presented a mechanistic underpinning of various discrete-time population models without an Allee effect. Their work was based on a continuous-time resource-consumer model for the dynamics within a year, from which they derived a discrete-time model for the between-year dynamics. In this article, we obtain the Allee effect by adding different mate finding mechanisms to the within-year dynamics. Further, by adding cannibalism we obtain a higher variety of models. We thus present a generator of relatively realistic, discrete-time Allee effect models that also covers some currently used phenomenological models driven more by mathematical convenience.     

LOCAL ADAPTATION,PHENOTYPIC DIFFERENTIATION,AND HYBRID FITNESS IN DIVERGED NATURAL POPULATIONS OF ARABIDOPSIS LYRATA

Selection for local adaptation results in genetic differentiation in ecologically important traits. In a perennial, outcrossing model plant Arabidopsis lyrata, several differentiated phenotypic traits contribute to local adaptation, as demonstrated by fitness advantage of the local population at each site in reciprocal transplant experiments. Here we compared fitness components, hierarchical total fitness and differentiation in putatively ecologically important traits of plants from two diverged parental populations from different continents in the native climate conditions of the populations in Norway and in North Carolina (NC, U.S.A.). Survival and number of fruits per inflorescence indicated local advantage at both sites and aster life‐history models provided additional evidence for local adaptation also at the level of hierarchical total fitness. Populations were also differentiated in flowering start date and floral display. We also included reciprocal experimental F₁ and F₂ hybrids to examine the genetic basis of adaptation. Surprisingly, the F₂ hybrids showed heterosis at the study site in Norway, likely because of a combination of beneficial dominance effects from different traits. At the NC site, hybrid fitness was mostly intermediate relative to the parental populations. Local cytoplasmic origin was associated with higher fitness, indicating that cytoplasmic genomes also may contribute to the evolution of local adaptation.