Evolution Of Dispersal Rates Research Articles

Eco-evolutionary feedbacks following changes in spatial connectedness.

Humans are drastically changing the spatial configuration of habitats. The associated changes in habitat connectedness impose strong selection on dispersal, and dispersal related traits. Evolutionary responses do, however, strongly feedback on the metapopulation dynamics, by further constraining or improving connectivity and impacting local population and food web dynamics. Because these spatial eco-evolutionary interactions occur at contemporary time scales, unique evidence on its importance is especially emerging in the field of entomology as many insects have short generation times and a huge reproductive potential. We review the ecological feedbacks originating from the evolution of dispersal rate, dispersal syndromes and genetic diversity on metapopulation dynamics and range expansions. We thus close the eco-evolutionary loop for insect and arachnid spatial dynamics.

Dispersal evolution and resource matching in a spatially and temporally variable environment.

Metapopulations may consist of patches of different quality, and are often disturbed by extrinsic processes causing variation of patch quality. The persistence of such metapopulations then depends on the species' dispersal strategy. In a temporally constant environment, the evolution of dispersal rates follows the resource matching rule, i.e. at the evolutionarily stable dispersal strategy the number of competitors in each patch matches the resource availability in each patch. Here, we investigate how the distribution of individuals resulting from convergence stable dispersal strategies would match the distribution of resources in an environment which is temporally variable due to extrinsic disturbance. We develop an analytically tractable asexual model with two qualities of patches. We show that convergence stable dispersal rates are such that resource matching is predicted in expectation before habitat quality variation, and that the distribution of individuals undermatches resources after habitat quality variation. The overall flow of individuals between patches matches the overall flow of resources between patches resulting from environmental variation. We show that these conclusions can be generalized to organisms with sexual reproduction, and to a metapopulation with three qualities of patches when there is no mutational correlation between dispersal rates.

Stochastic population growth in spatially heterogeneous environments

Classical ecological theory predicts that environmental stochasticity increases extinction risk by reducing the average per-capita growth rate of populations. For sedentary populations in a spatially homogeneous yet temporally variable environment, a simple model of population growth is a stochastic differential equation dZ(t) = μZ(t)dt + σZ(t)dW(t), t ≥ 0, where the conditional law of Z(t+Δt)-Z(t) given Z(t) = z has mean and variance approximately z μΔt and z²σ²Δt when the time increment Δt is small. The long-term stochastic growth rate lim(t→∞) t⁻¹ log Z(t) for such a population equals μ − σ²/2 . Most populations, however, experience spatial as well as temporal variability. To understand the interactive effects of environmental stochasticity, spatial heterogeneity, and dispersal on population growth, we study an analogous model X(t) = (X¹(t) , . . . , X(n)(t)), t ≥ 0, for the population abundances in n patches: the conditional law of X(t+Δt) given X(t) = x is such that the conditional mean of X(i)(t+Δt) − X(i)(t) is approximately [x(i)μ(i) + Σ(j) (x(j) D(ji) − x(i) D(i j) )]Δt where μ(i) is the per capita growth rate in the ith patch and D(ij) is the dispersal rate from the ith patch to the jth patch, and the conditional covariance of X(i)(t+Δt)− X(i)(t) and X(j)(t+Δt) − X(j)(t) is approximately x(i)x(j)σ(ij)Δt for some covariance matrix Σ = (σ(ij)). We show for such a spatially extended population that if S(t) = X¹(t)+· · ·+ X(n)(t) denotes the total population abundance, then Y(t) = X(t)/S(t), the vector of patch proportions, converges in law to a random vector Y(∞) as t → ∞, and the stochastic growth rate lim(t→∞) t⁻¹ log S(t) equals the space-time average per-capita growth rate Σ(i)μ(i)E[Y(i)(∞)] experienced by the population minus half of the space-time average temporal variation E[Σ(i,j) σ(i j)Y(i)(∞) Y(j)(∞)] experienced by the population. Using this characterization of the stochastic growth rate, we derive an explicit expression for the stochastic growth rate for populations living in two patches, determine which choices of the dispersal matrix D produce the maximal stochastic growth rate for a freely dispersing population, derive an analytic approximation of the stochastic growth rate for dispersal limited populations, and use group theoretic techniques to approximate the stochastic growth rate for populations living in multi-scale landscapes (e.g. insects on plants in meadows on islands). Our results provide fundamental insights into "ideal free" movement in the face of uncertainty, the persistence of coupled sink populations, the evolution of dispersal rates, and the single large or several small (SLOSS) debate in conservation biology. For example, our analysis implies that even in the absence of density-dependent feedbacks, ideal-free dispersers occupy multiple patches in spatially heterogeneous environments provided environmental fluctuations are sufficiently strong and sufficiently weakly correlated across space. In contrast, for diffusively dispersing populations living in similar environments, intermediate dispersal rates maximize their stochastic growth rate.

Strong effects of heterosis on the evolution of dispersal rates

When dispersal is limited, crosses between different regions may generate progeny of higher fitness than crosses within regions, due to the fact that individuals from the same region are more likely to share the same recessive deleterious alleles. This phenomenon (termed heterosis) generates a selective force favouring dispersal; however, the importance of heterosis on dispersal evolution has been a subject for debate. In this paper, we use computer simulations representing deleterious mutations occurring over a whole genome (of arbitrary map length R) to explore the magnitude of heterosis, and its effect on the evolution of dispersal. These results show that heterosis may have important effects on dispersal when it is in the upper range of values observed in natural populations, which occurs in our simulations when the genomic deleterious mutation rate U is also in the upper range of observed values. Comparing the results with extrapolations from an analytical two-locus model indicates that the effect of heterosis is mainly driven by pairwise associations between the locus affecting dispersal and selected loci when U is not too high (roughly, U < 0.5), whereas higher order associations become important for higher values of U.

Social Evolution: The Decline and Fall of Genetic Kin Recognition

Animals should benefit from the ability to recognise their kin, yet curiously this faculty is often absent. New theory confirms that genetic kin recognition is inherently unstable, explaining its rarity.

Can the assumption of a non‐random search improve our prediction of butterfly fluxes between resource patches?

Abstract. 1. Understanding dispersal patterns that enable small, spatially isolated populations to survive in fragmented landscapes has become an important issue in conservation biology and landscape management. However, for most of the species of interest it is not known whether dispersing individuals navigate or follow systematic search strategies, as opposed to moving randomly.2. Recently it was shown that individuals of the butterfly species Maniola jurtina do not seek resources by means of random flight. If true, this may be problematic for existing metapopulation models, including those based on the evolution of dispersal rates in metapopulations.3. The study tested to what extent the non‐random dispersal patterns described in the literature can explain M. jurtina fluxes in its natural habitat.4. A model based on literature assumptions of M. jurtina movements is presented in the work reported here, and its predictions are compared with 2 years of capture–recapture data on its fluxes in two landscapes.5. The model provides a good fit to the data and gives better predictions than the model based only on patch sizes and distances between patches.6. Thus, if data are available about the actual landscape under consideration, the model should be preferred to simpler approaches; however, in general theoretical considerations the simple approach based on patch size and the degree of its isolation will retain its value.

Foray search: an effective systematic dispersal strategy in fragmented landscapes.

In the absence of evidence to the contrary, population models generally assume that the dispersal trajectories of animals are random, but systematic dispersal could be more efficient at detecting new habitat and may therefore constitute a more realistic assumption. Here, we investigate, by means of simulations, the properties of a potentially widespread systematic dispersal strategy termed "foray search." Foray search was more efficient in detecting suitable habitat than was random dispersal in most landscapes and was less subject to energetic constraints. However, it also resulted in considerably shorter net dispersed distances and higher mortality per net dispersed distance than did random dispersal, and it would therefore be likely to lead to lower dispersal rates toward the margins of population networks. Consequently, the use of foray search by dispersers could crucially affect the extinction-colonization balance of metapopulations and the evolution of dispersal rates. We conclude that population models need to take the dispersal trajectories of individuals into account in order to make reliable predictions.

Evolution of density- and patch-size-dependent dispersal rates.

Based on a marginal value approach, we derive a nonlinear expression for evolutionarily stable (ES) dispersal rates in a metapopulation with global dispersal. For the general case of density-dependent population growth, our analysis shows that individual dispersal rates should decrease with patch capacity and-beyond a certain threshold-increase with population density. We performed a number of spatially explicit, individual-based simulation experiments to test these predictions and to explore further the relevance of variation in the rate of population increase, density dependence, environmental fluctuations and dispersal mortality on the evolution of dispersal rates. They confirm the predictions of our analytical approach. In addition, they show that dispersal rates in metapopulations mostly depend on dispersal mortality and inter-patch variation in population density. The latter is dominantly driven by environmental fluctuations and the rate of population increase. These conclusions are not altered by the introduction of neighbourhood dispersal. With patch capacities in the order of 100 individuals, kin competition seems to be of negligible importance for ES dispersal rates except when overall dispersal rates are low.

Perturbations of Periodic Competitive Parabolic Systems

It is shown that the competitive exclusion and coexistence in two species periodic competitive parabolic systems are robust under a class of perturbations. This result is also applied to a reaction-diffusion model for the evolution of dispersal rates.

Evolution of reduced dispersal mortality and 'fat-tailed' dispersal kernels in autocorrelated landscapes.

Models describing the evolution of dispersal strategies have mostly focused on the evolution of dispersal rates. Taking trees as a model for organisms with undirected, passive dispersal, we have developed an individual-based, spatially explicit simulation tool to investigate the evolution of the dispersal kernel, P(r), and its resulting cumulative seed-density distribution, D(r). Simulations were run on a variety of fractal landscapes differing in the fraction of suitable habitat and the spatial autocorrelation. Starting from a uniform D(r), evolution led to an increase in the fraction of seeds staying in the home cell, a reduction of the dispersal mortality (arrival in unsuitable habitat), and the evolution of 'fat-tailed' D(r) in autocorrelated landscapes and approximately uniform D(r) in random landscapes. The evolutionary process was characterized by long periods of stasis with a few bouts of rapid change in the dispersal rate.

Interactions between spatial and temporal scales in the evolution of dispersal rate

The evolution of dispersal rate is studied with a model of several local populations linked by dispersal. Three dispersal strategies are considered where all, half or none of the offspring disperse. The spatial scale (number of patches) and the temporal scale (probability of local extinction) of the environment are critical in determining the selective advantage of the different dispersal strategies. The results from the simulations suggest that an interaction between group selection and individual selection results in a different outcome in relation to the spatial and temporal scales of the environment. Such an interaction is able to maintain a polymorphism in dispersal strategies. The maintenance of this polymorphism is also scale-dependent. This study suggests a mechanism for the short-term evolution of dispersal, and provides a testable prediction of this hypothesis, namely that loss of dispersal abilities should be more frequent in spatially more continuous environments, or in temporally more stable environments.

Evolution of Dispersal Rates in Metapopulation Models: Branching and Cyclic Dynamics in Phenotype Space

Evolution of Dispersal Rates in Metapopulation Models: Branching and Cyclic Dynamics in Phenotype Space

Dispersal and Dynamics

Mixing and asynchrony of interactions can be expected to stabilize the dynamics of populations. One way such mixing occurs is by dispersal, and Hastings and Gyllenberg et al. have shown that symmetric dispersal between two local populations governed by logistic difference equations can simplify the dynamics. These results are extended here by using a more flexible difference equation and allowing asymmetric dispersal. Although there are some instances where dispersal is destabilizing, its stabilizing effect is enhanced by asymmetry. In addition, very high dispersal rates can induce a stable equilibrium of the metapopulation despite highly chaotic local dynamics. If this equilibrium loses stability, the route to intermittent chaos can be observed. Two new conditions under which dispersal can be stabilizing are discussed. One occurs when the timing of reproduction and dispersal differs in the two patches of the metapopulation. This enlarges the asynchrony of the interactions, and simple dynamics due to dispersal are more likely. The second works by slightly adjusting dispersal rates to control chaotic dynamics. The control can replace chaos by a stable equilibrium. The evolution of dispersal rates is discussed. Since obtaining general criteria for invasion into a population with chaotic dynamics is difficult, no clear conclusions are possible as to whether evolution leads to more stable metapopulations. However, a mutant that controls chaos can invade a resident having the same local dynamics but no control mechanism, so that evolution can lead from chaos to a stable equilibrium.

On the Evolutionary Stability of Dispersal to Sink Habitats

On the Evolutionary Stability of Dispersal to Sink Habitats