The evolution of dispersal rates in a heterogeneous time-periodic environment

A reaction-diffusion model for the evolution of dispersal rates is considered in which there is both spatial heterogeneity and temporal periodicity. The model is restricted to two phenotypes because of technical difficulties, but a wide range of mathematical techniques and computational effort are needed to obtain useful answers. We find that the question of selection is a great deal richer than in the autonomous case, where the phenotype with the lowest diffusion is selected for. In the current model either the lower or higher diffuser rate may be selected, or there may be coexistence of phenotypes. The paper raises several open questions and suggests in particular that a mutation-selection multi-phenotypic model would repay study. Received: 17 April 2000 / Revised version: 2 May 2001 / Published online: 12 October 2001     

The evolution of recombination

The selective forces responsible for the evolution of genes mediating recombination are discussed. These genes originated because of their role indna repair. In eukaryotes, their role in repair is not sufficient to account for the evolution of meiosis and syngamy. Therefore, a “hitch-hiking” explanation is required, according to which a recombination gene gets a lift in frequency from the high-fitness genes to which it is linked. Such hitch-hiking models are reviewed: collectively they provide an adequate explanation for the maintenance of sex and recombination in eukaryotes. In prokaryotes, the main selective force favouring recombination isdna repair: the cross-overs caused by recombination may occasionally have important evolutionary effects, but they are the consequences, rather than the causes, of the evolution of recombination in prokaryotes. In both prokaryotes and eukaryotes, recombination genes also cause specific, repeatable and adaptive rearrangements of the genetic material.     

Within-host viral evolution in a heterogeneous environment: insights into the HIV co-receptor switch

A virus infecting a host faces a heterogeneous and a spatially structured environment. Using a mathematical model that incorporates two types of target cells and spatial structuring, we investigate conditions for viral within-host diversification. We show that branching occurs for a wide range of parameters but that it always requires some spatial structure. Applying our model to the case of HIV, we show that it captures three main properties of the 'co-receptor switch' observed in many HIV infections: the initial dominance of virus strains that infect CCR5(+) cells, the late switch in some (but, importantly, not all) HIV infections and the associated drop in the number of uninfected T-cells. This suggests that the co-receptor switch could result from gradual adaptation of the virus population to target cell heterogeneity. More generally, we argue that evolutionary ecology can help us better understand the course of some infections.     

The evolution of plastic recombination

Empirical data suggest that recombination rates may change in response to stress. To study the evolution of plastic recombination, we develop a modifier model using the same theoretical framework used to study conventional (nonplastic) modifiers, thus allowing direct comparison. We examine the evolution of plastic recombination in both haploid and diploid systems. In haploids, a plastic modifier spreads by forming associations with selectively favored alleles. Relative to nonplastic effects, selection on the plastic effects of a modifier is both much stronger and less sensitive to the specifics of the selection regime (e.g., epistasis). In contrast, the evolution of plastic recombination in diploids is much more restricted. Selection on plasticity requires the ability to detect DNA damage or cis-trans effects as may occur through maternal effects on fitness.     

The evolution of migration in a seasonal environment

Despite the fact that migration occurs in a wide variety of taxa worldwide, little is known about the conditions under which migration is expected to evolve from an ancestral resident population. We develop a model that focuses on ecological factors affecting the evolution of migration in a seasonal environment within a genetically explicit framework. We model the evolution of migration for two common types of migration: ‘shared breeding’ where migrants share a breeding ground with residents and migrate to a separate non-breeding area, versus ‘shared non-breeding’, where migrants share a non-breeding ground with residents and migrate to a separate breeding area. Ecologically, migration is more easily established in the shared-breeding case versus the shared-non-breeding case. Genetically, the additive effect of a migratory allele affects its establishment more in the shared-non-breeding case versus the shared-breeding case, whereas the dominance effect of the allele affects its establishment more in the shared-breeding case versus the shared-non-breeding case. Generally, migratory alleles can invade even when residents are competitively superior to migrants during the shared season. Partial migration occurs when the population is polymorphic for migratory and non-migratory alleles, and is dependent upon which season is shared and the additive and dominance behaviour of the migratory allele.     

The evolution of sex dimorphism in recombination

Sex dimorphism in recombination is widespread on both sex chromosomes and autosomes. Various hypotheses have been proposed to explain these dimorphisms. Yet no theoretical model has been explored to determine how heterochiasmy--the autosomal dimorphism--could evolve. The model presented here shows three circumstances in which heterochiasmy is likely to evolve: (i) a male-female difference in haploid epistasis, (ii) a male-female difference in cis-epistasis minus trans-epistasis in diploids, or (iii) a difference in epistasis between combinations of genes inherited maternally or paternally. These results hold even if sources of linkage disequilibria besides epistasis, such as migration or Hill-Robertson interference, are considered and shed light on previous verbal models of sex dimorphism in recombination rates. Intriguingly, these results may also explain why imprinted regions on the autosomes of humans or sheep are particularly heterochiasmate.     

The evolution of sex and recombination

The evolution and maintenance of sexual reproduction, and the associated process of genetic recombination, are still controversial issues. Two recent books have provided overviews of the ideas and observations in this field. This article reviews some of the major ideas that have been proposed to account for sex and recombination, and comments on the results of attempts at empirical tests. While there is now an impressive body of well-formulated evolutionary models, it has proved hard to discriminate between them, either experimentally or by means of comparative data. It may well be that there is no unitary selective advantage to sex and recombination, but that a variety of forces are involved.     

Competition for space in a heterogeneous environment

We consider effects of competition for space in a heterogeneous environment, making use of nonlinear interaction-diffusion equations. Competition for space is assumed to mean mutual repulsive interactions that force other individuals to disperse from a crowded region. In other words, we are concerned with density-dependent dispersal forced by population pressures. Spatial heterogeneity is incorporated in the growth rates, and the environment is assumed to have a favorable habitat for two populations surrounded by largely hostile regions. Space-independent migration rates are assumed. We ignore the usual density-dependence in the growth rates to focus our attention on density-dependence in the migration rates. Our main conclusion is that two populations can coexist if the interspecific repulsive forces are weaker than the intraspecific ones. It is also emphasized that density-dependent dispersal in a heterogeneous environment is not always a stabilizing agent, and that either of two populations may become extinct by competition for space. Finally, the resemblance of our results to those from Lotka-Volterra competition equations is suggested.     

Body condition dependent dispersal in a heterogeneous environment

We find the evolutionarily stable dispersal behaviour of a population that inhabits a heterogeneous environment where patches differ in safety (the probability that a juvenile individual survives until reproduction) and productivity (the total competitive weight of offspring produced by the local individual), assuming that these characteristics do not change over time. The body condition of clonally produced offspring varies within and between families. Offspring compete for patches in a weighted lottery, and dispersal is driven by kin competition. Survival during dispersal may depend on body condition, and competitive ability increases with increasing body condition. The evolutionarily stable strategy predicts that families abandon patches which are too unsafe or do not produce enough successful dispersers. From families that invest in retaining their natal patches, individuals stay in the patch that are less suitable for dispersal whereas the better dispersers disperse. However, this clear within-family pattern is often not reflected in the population-wide body condition distribution of dispersers or non-dispersers. This may be an explanation why empirical data do not show any general relationship between body condition and dispersal. When all individuals are equally good dispersers, then there exist equivalence classes defined by the competitive weight that remains in a patch. An equivalence class consists of infinitely many dispersal strategies that are selectively neutral. This provides an explanation why very diverse patterns found in body condition dependent dispersal data can all be equally evolutionarily stable.     

Mathematical modelling of mosquito dispersal in a heterogeneous environment

Mosquito dispersal is a key behavioural factor that affects the persistence and resurgence of several vector-borne diseases. Spatial heterogeneity of mosquito resources, such as hosts and breeding sites, affects mosquito dispersal behaviour and consequently affects mosquito population structures, human exposure to vectors, and the ability to control disease transmission. In this paper, we develop and simulate a discrete-space continuous-time mathematical model to investigate the impact of dispersal and heterogeneous distribution of resources on the distribution and dynamics of mosquito populations. We build an ordinary differential equation model of the mosquito life cycle and replicate it across a hexagonal grid (multi-patch system) that represents two-dimensional space. We use the model to estimate mosquito dispersal distances and to evaluate the effect of spatial repellents as a vector control strategy. We find evidence of association between heterogeneity, dispersal, spatial distribution of resources, and mosquito population dynamics. Random distribution of repellents reduces the distance moved by mosquitoes, offering a promising strategy for disease control.     

The evolution of dispersal in random environment

In this paper we introduce a stochastic model for a population living and migrating between s sites without distinction in the states between residents and immigrants. The evolutionary stable strategies (ESS) is characterized by the maximization of a stochastic growth rate. We obtain that the expectation of reproductive values, normalized by some random quantity, are constant on all sites and that the expectation of the normalized vector population structure is proportional to eigenvector of the dispersion matrix associated to eigenvalue one, which are, in some way, analogous to the results obtained in the deterministic case.     

Sex allocation and dispersal in a heterogeneous two-patch environment

We investigate the evolution of sex allocation and dispersal in a two-habitat environment using a game theoretic analysis. One habitat is of better quality than the other and increased habitat quality influences the competitive ability of offspring in a sex-specific manner. Unlike previous work, we allow incomplete mixing of the population during mating. We discuss three special cases involving the evolution of sex allocation under fixed levels of dispersal between habitats. In these special cases, stable sex-allocation behaviors can be both biased and unbiased. When sex-allocation behavior and dispersal rates co-evolve we identify two basic outcomes. First-when sex-specific differences in the consequences of spatial heterogeneity are large-we predict the evolution of biased sex-allocation behavior in both habitats, with dispersal by males in one direction and dispersal by females in the other direction. Second-when sex-specific differences are small-unbiased sex-allocation is predicted with no dispersal between habitats.     

The evolution of recombination under domestication: a test of two hypotheses

The successful domestication of wild plants has been one of the most important human accomplishments of the last 10,000 yr. Though our empirical knowledge of the genetic mechanisms of plant domestication is still relatively limited, there exists a large body of theory that offers a host of hypotheses on the genetics of domestication. Two of these that have not been addressed concern the role of recombination in the process of domestication. The first predicts an increase in recombination rate through domestication, while the second argues that recombination rate should serve as a preadaptation to domestication. This study makes use of data on chiasma frequencies available from almost a century of plant cytogenetical literature to test these two hypotheses. The results support the hypothesis that domestication selects for an increase in recombination, and in rejecting the preadaptation hypothesis, they suggest directions for future research into the possibility of preadaptation to domestication.     

Assessing rapid evolution in a changing environment

Climate change poses a serious threat to species persistence. Effective modelling of evolutionary responses to rapid climate change is therefore essential. In this review we examine recent advances in phylogenetic comparative methods, techniques normally used to study adaptation over long periods, which allow them to be applied to the study of adaptation over shorter time scales. This increased applicability is largely due to the emergence of more flexible models of character evolution and the parallel development of molecular technologies that can be used to assess adaptive variation at loci scattered across the genome. The merging of phylogenetic and population genetic approaches to the study of adaptation has significant potential to advance our understanding of rapid responses to environmental change.     

The evolution of strong reciprocity: cooperation in heterogeneous populations

How do human groups maintain a high level of cooperation despite a low level of genetic relatedness among group members? We suggest that many humans have a predisposition to punish those who violate group-beneficial norms, even when this imposes a fitness cost on the punisher. Such altruistic punishment is widely observed to sustain high levels of cooperation in behavioral experiments and in natural settings. We offer a model of cooperation and punishment that we call STRONG RECIPROCITY: where members of a group benefit from mutual adherence to a social norm, strong reciprocators obey the norm and punish its violators, even though as a result they receive lower payoffs than other group members, such as selfish agents who violate the norm and do not punish, and pure cooperators who adhere to the norm but free-ride by never punishing. Our agent-based simulations show that, under assumptions approximating likely human environments over the 100000 years prior to the domestication of animals and plants, the proliferation of strong reciprocators when initially rare is highly likely, and that substantial frequencies of all three behavioral types can be sustained in a population. As a result, high levels of cooperation are sustained. Our results do not require that group members be related or that group extinctions occur.     

The ideal free distribution of clonal plant's ramets among patches in a heterogeneous environment

The plastic response of clonal plant to different patch quality is not always the same and the degree is different too. So the result of this kind of foraging behaviour is different. In order to make clear whether the ramtes stay in favourable patches and get the quantitative relationship between the ramets distribution among patches and the available resource amount in heterogeneous environment, we develop a theoretical work under ideal free distribution (IFD) theory framework by neglecting some morphological plasticity of the spacer in this article. The results of our general model show that the ramet distribution should obey input matching rule at equilibrium. That means the ratio of ramet number in different patches should be equal to the ratio of available resource amount in these patches. We also use the simulation to predict the distribution pattern under history mattering. The results show that the initial ramets number has significant influence on the final distribution: over matching and under matching both can occur. More initial ramets in favourable patch result in over matching and more initial ramets in unfavourable patch result in under matching. The degree of the deviation from input matching rule is great when the difference of patches is small. These results prove that ideal free distribution theory works the same with animals. The ramets can stay in favourable patches sometimes in spite of the plasticity of the spacer, and the distribution depends on both patch quality and the history factors. But these results are true only when the functional response is type II.     

Intraguild predation with evolutionary dispersal in a spatially heterogeneous environment

Journal of Mathematical Biology - In many cases, the motility of species in a certain region can depend on the conditions of the local habitat, such as the availability of food and other resources...     

The effects of migration and drift on local adaptation to a heterogeneous environment

Local adaptation experiments are widely used to quantify the levels of adaptation within a heterogeneous environment. However, theoretical studies generally focus on the probability of fixation of alleles or the mean fitness of populations, rather than local adaptation as it is commonly measured experimentally or in field studies. Here, we develop mathematical models and use them to generate analytical predictions for the level of local adaptation as a function of selection, migration and genetic drift. First, we contrast mean fitness and local adaptation measures and show that the latter can be expressed in a simple and general way as a function of the spatial covariance between population mean phenotype and local environmental conditions. Second, we develop several approximations of a population genetics model to show that the system exhibits different behaviours depending on the rate of migration. The main insights are the following: with intermediate migration, both genetic drift and migration decrease local adaptation; with low migration, drift decreases local adaptation but migration speeds up adaptation; with high migration, genetic drift has no effect on local adaptation. Third, we extend this analysis to cases where the trait under selection is continuous using classical quantitative genetics theory. Finally, we discuss these results in the light of recent experimental work on local adaptation.     

Host-parasite interaction as a factor in the evolution of genetic recombination

A model of the rec-system evolution determined by species interactions of the host-parasite type has been studied. In contrast to known formalizations, the genetic structure of both populations is clearly represented in our model, which makes it possible to set the mode of their interrelations in a more natural and biologically consistent way. The numerical analysis has revealed the situations, where nondecreasing oscillations of the linkage disequilibrium coefficient and, consequently, the selection favourable for higher recombination occur in a system. The evolutionary advantage of recombination has been demonstrated both in terms of population mean fitness and in the models with locus modifier of recombination.