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.     

The risk of a mosquito-borne infection in a heterogeneous environment

A common assumption about malaria, dengue, and other mosquito-borne infections is that the two main components of the risk of human infection—the rate at which people are bitten (human biting rate) and the proportion of mosquitoes that are infectious—are positively correlated. In fact, these two risk factors are generated by different processes and may be negatively correlated across space and time in heterogeneous environments. Uneven distribution of blood-meal hosts and larval habitat creates a spatial mosaic of demograPhic sources and sinks. Moreover, mosquito populations fluctuate temporally, forced by environmental variables such as rainfall, temperature, and humidity. These sources of spatial and temporal heterogeneity in the distribution of mosquito populations generate variability in the human biting rate, in the proportion of mosquitoes that are infectious, and in the risk of human infection. To understand how heterogeneity affects the epidemiology of mosquito-borne infections, we developed a set of simple models that incorporate heterogeneity in a stepwise fashion. These models predict that the human biting rate is highest shortly after the mosquito densities peak, near breeding sites where adult mosquitoes emerge, and around the edges of areas where humans are aggregated. In contrast, the proportion of mosquitoes that are infectious reflects the age structure of mosquito populations; it peaks where old mosquitoes are found, far from mosquito breeding habitat, and when mosquito population density is declining. Finally, we show that estimates for the average risk of infection that are based on the average entomological inoculation rate are strongly biased in heterogeneous environments.     

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.     

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 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 recombination in changing environments

Recombination generates under-represented genotypes by breaking down linkage disequilibrium between genes. Recent analyses have specified the conditions under which recombination is favored. These conditions are surprisingly sensitive to the form of selection and environmental change. This quantification makes it possible to use empirical measurements of critical parameters such as the form of epistasis, the rate of mutation, and the frequency of beneficial sweeps to assess different hypotheses for the evolution of recombination.     

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.     

Probability of fixation in a heterogeneous environment

We investigate the probability of fixation of a new mutation arising in a metapopulation that ranges over a heterogeneous selective environment. Using simulations, we test the performance of several approximations of this probability, including a new analytical approximation based on separation of the timescales of selection and migration. We extend all approximations to multideme metapopulations with arbitrary population structure. Our simulations show that no single approximation produces accurate predictions of fixation probabilities for all cases of potential interest. At the limits of low and high migration, previously published approximations are found to be highly accurate. The new separation-of-timescales approach provides the best approximations for intermediate rates of migration among habitats, provided selection is not too intense. For nonzero migration and relatively strong selection, all approximations perform poorly. However, the probability of fixation is bounded above and below by the approximations based on low and high migration limits. Surprisingly, in our simulations with symmetric migration, heterogeneous selection in a metapopulation never decreased-and sometimes substantially increased-the probability of fixation of a new allele compared to metapopulations experiencing homogeneous selection with the same mean selection intensity.     

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.     

The evolution of recombination in permanent translocation heterozygotes

The evolution of a selectively neutral locus that controls the degree to which alleles at a single selected locus are linked with a particular set of chromosomes in a permanent translocation heterozygote is studied. With complete selfing and fitness overdominance a new allele at the modifying locus will increase in frequency if it increases the linkage of all alleles at the selected locus to a particular set of chromosomes. With random mating a new allele at the modifying locus will increase when rare if it increases the linkage of alleles at the selected locus to a particular set of chromosomes. In addition, a parameter analogous to the coefficient of linkage disequilibrium in usual two-locus models with random mating must be nonzero if a new allele at the modifying locus is to increase in frequency at a geometric rate when rare. With mixed selfing and random mating a new allele at the modifying locus will apparently increase when rare only if it increases the linkage of alleles at the selected locus to a particular set of chromosomes.     

Fixation probabilities in a spatially heterogeneous environment

 We consider a simple model of a one-locus, two-allele population inhibiting a two-patch system and experiencing spatially heterogeneous viability selection. The populaton size is finite. We use a diffusion approximation and singular perturbation techniques to find the probability of fixation of a mutant allele. We focus on situations in which each allele is advantageous in one patch and deleterious in the other patch. Our theoretical results support the previous conclusions that, under certain conditions, small populations respond faster to selection than do large populations. We emphasize that knowledge of the dependence of migration rates on population size is crucial in evaluating the effects of population size on the rate of evolution.     

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.     

The evolution of mate choice in a fluctuating environment

This paper analyzes the evolutionary dynamics of a locus controlling the degree of female mating preference in a temporally fluctuating environment. Preference for mating with males with respect to their genotypes at a locus that is subject to temporally varying natural selection pressure is considered first. With weak selection and free recombination between the choice locus and the selected locus, preference for mating with heterozygotes appears to be favored. With strong selection, preference for homozygous mates may be favored. In each case, choice alleles may increase from very low initial frequencies to near fixation, in contrast to previous models of mate choice in varying environments. Linkages between the two loci has complex effects on the strength and direction of selection for mate choice. Preference for mating with males with the currently fitter genotypes at the locus under natural selection is also modelled. Provided that the environmental period is not too short, a rare allele conferring such preference may be favored and spread to fixation. Strong natural selection, tight linkage and a short environmental period may produce polymorphism for the level of mate choice.     

Divergent evolution of dispersal in a heterogeneous landscape

The evolution of dispersal is investigated in a landscape of many patches with fluctuating carrying capacities and spatial heterogeneity in temporal fluctuations. Although asynchronous temporal fluctuations select for dispersal, spatial heterogeneity in the distribution of fluctuating environmental variables selects against it. We find evolutionary branching in dispersal rate leading to the evolutionarily stable coexistence of a high- and a low-dispersal phenotype. We study how the opposing forces of selection for and against dispersal change with the relative size and the environmental qualities of the source and sink habitats. Our results suggest that the evolution of dispersal dimorphism could be a first step towards speciation and local adaptation.     

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 Hill-Robertson effect and the evolution of recombination

In finite populations, genetic drift generates interference between selected loci, causing advantageous alleles to be found more often on different chromosomes than on the same chromosome, which reduces the rate of adaptation. This "Hill-Robertson effect" generates indirect selection to increase recombination rates. We present a new method to quantify the strength of this selection. Our model represents a new beneficial allele (A) entering a population as a single copy, while another beneficial allele (B) is sweeping at another locus. A third locus affects the recombination rate between selected loci. Using a branching process model, we calculate the probability distribution of the number of copies of A on the different genetic backgrounds, after it is established but while it is still rare. Then, we use a deterministic model to express the change in frequency of the recombination modifier, due to hitchhiking, as A goes to fixation. We show that this method can give good estimates of selection for recombination. Moreover, it shows that recombination is selected through two different effects: it increases the fixation probability of new alleles, and it accelerates selective sweeps. The relative importance of these two effects depends on the relative times of occurrence of the beneficial alleles.     

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.