Multilocus selection in subdivided populations I. Convergence properties for weak or strong migration

The dynamics and equilibrium structure of a deterministic population-genetic model of migration and selection acting on multiple multiallelic loci is studied. A large population of diploid individuals is distributed over finitely many demes connected by migration. Generations are discrete and nonoverlapping, migration is irreducible and aperiodic, all pairwise recombination rates are positive, and selection may vary across demes. It is proved that, in the absence of selection, all trajectories converge at a geometric rate to a manifold on which global linkage equilibrium holds and allele frequencies are identical across demes. Various limiting cases are derived in which one or more of the three evolutionary forces, selection, migration, and recombination, are weak relative to the others. Two are particularly interesting. If migration and recombination are strong relative to selection, the dynamics can be conceived as a perturbation of the so-called weak-selection limit, a simple dynamical system for suitably averaged allele frequencies. Under nondegeneracy assumptions on this weak-selection limit which are generic, every equilibrium of the full dynamics is a perturbation of an equilibrium of the weak-selection limit and has the same stability properties. The number of equilibria is the same in both systems, equilibria in the full (perturbed) system are in quasi-linkage equilibrium, and differences among allele frequencies across demes are small. If migration is weak relative to recombination and epistasis is also weak, then every equilibrium is a perturbation of an equilibrium of the corresponding system without migration, has the same stability properties, and is in quasi-linkage equilibrium. In both cases, every trajectory converges to an equilibrium, thus no cycling or complicated dynamics can occur.      

Competition and the Effect of Spatial Resource Heterogeneity on Evolutionary Diversification

A model is presented to explore how the form of selection arising from competition for resources is affected by spatial resource heterogeneity. The model consists of a single species occupying two patches connected by migration, where the two patches can differ in the type of resources that they contain. The main goal is to determine the conditions under which competition for resources results in disruptive selection (i.e., selection favoring a polymorphism) since it is this form of selection that will give rise to the evolutionary diversification of resource exploitation strategies. In particular, comparing the conditions giving rise to disruptive selection when the two patches are identical to the conditions when they contain different resources reveals the effect of spatial resource heterogeneity. Results show that when the patches are identical, the conditions giving rise to disruptive selection are identical to those that give rise to character displacement in previous models. When the patches are different, the conditions giving rise to disruptive selection can be either more or less stringent depending upon demographic parameters such as the intrinsic rate of increase and the migration rate. Surprisingly, spatial resource heterogeneity can actually make forms of evolutionary diversification such as character displacement less likely. It is also found that results are dependent on how the resource exploitation strategies and the spatial resource heterogeneity affect the population dynamics. One robust conclusion however, is that spatial resource heterogeneity always has a disruptive effect when the migration rate between patches is low.     

Evolution of migration in a metapopulation

In this paper a general deterministic discrete-time metapopulation model with a finite number of habitat patches is analysed within the framework of adaptive dynamics. We study a general model and prove analytically that (i) if the resident populations state is a fixed point, then the resident strategy with no migration is an evolutionarily stable strategy, (ii) a mutant population with no migration can invade any resident population in a fixed point state, (iii) in the uniform migration case the strategy not to migrate is attractive under small mutational steps so that selection favours low migration. Some of these results have been previously observed in simulations, but here they are proved analytically in a general case. If the resident population is in a two-cyclic orbit, then the situation is different. In the uniform migration case the invasion behaviour depends both on the type of the residents attractor and the survival probability during migration. If the survival probability during migration is low, then the system evolves towards low migration. If the survival probability is high enough, then evolutionary branching can happen and the system evolves to a situation with several coexisting types. In the case of out-of-phase attractor, evolutionary branching can happen with significantly lower survival probabilities than in the in-phase attractor case. Most results in the two-cyclic case are obtained by numerical simulations. Also, when migration is not uniform we observe in numerical simulations in the two-cyclic orbit case selection for low migration or evolutionary branching depending on the survival probability during migration.     

Long-distance migrating species of birds travel in larger groups

How individuals migrate over long distances is an enduring mystery of animal migration. Strong selection pressure for travelling in groups has been suggested in long-distance migrating species. Travelling in groups can reduce the energetic demands of long migration, increase navigational accuracy and favour group foraging at migratory halts. Nevertheless, this hypothesis has received scant attention. I examined evolutionary transitions in migration distance in all North American breeding species of birds. I documented 72 evolutionary shifts in migration distance in the pool of 409 species. In contrasting clades, long-distance migration, as opposed to short-distance migration, was associated with a larger travelling group size. No other transitions occurred alongside in other traits such as group size in the non-breeding season or body mass. The results suggest that larger group sizes have been beneficial in the evolution of long-distance migration in a large clade of birds.     

The evolution of outsider exclusion

The rate of migration between different parts of a population can be important in determining evolutionary outcomes. This paper presents a mathematical model in which some individuals act to exclude immigrants from their group. It is shown that outsider exclusion can be favoured by evolution, even when outsider excluders incur a large cost. In addition, it is shown that the evolutionary mechanism which causes increases in the frequency of outsider excluders is a form of kin selection or group selection. A second model shows that a similar mechanisms can act to favour the evolution of reluctance to mate with immigrants.     

Evolution of migration in a periodically changing environment

The ability to migrate can evolve in response to various forces. In particular, when selection is heterogeneous in space but constant in time, local adaptation induces a fitness cost on immigrants and selects against migration. The evolutionary outcome, however, is less clear when selection also varies temporally. Here, we present a two-locus model analyzing the effects of spatial and temporal variability in selection on the evolution of migration. The first locus is under temporally varying selection (various periodic functions are considered, but a general nonparametric framework is used), and the second locus is a modifier controlling migration ability. First, we study the dynamics of local adaptation and derive the migration rate that maximizes local adaptation as a function of the speed and geometry of the fluctuations in the environment. Second, we derive an analytical expression for the evolutionarily stable migration rate. When there is no cost of migration, we show that higher migration rates are favored when selection changes fast. When migration is costly, however, the evolutionarily stable migration rate is maximal for an intermediate speed of the variation of selection. This model may help in understanding the evolution of migration in a broad range of scenarios and, in particular, in host-parasite systems, where selection is thought to vary quickly in both space and time.     

Migration rates, frequency-dependent selection and the self-incompatibility locus in Leavenworthia (brassicaceae)

Loci subject to negative frequency-dependent selection are expected to exhibit higher effective migration rates compared to reference loci. Although the number of gene copies transferred between populations by migration is the same for all genes, those subject to negative frequency-dependent selection are more likely to be retained in the immigrant population because rare alleles are selectively favored. So far, evidence for this prediction has been indirect, based on summary statistics rather than on migration rate estimates. Here, we introduce an approximate Bayesian procedure to jointly estimate migration rates at two predefined sets of loci between two populations. We applied the procedure to compare migration rate estimates at the self-incompatibility locus (S-locus) with that at 10 reference loci in two plant species, Leavenworthia alabamica and L. crassa (Brassicaceae). The maximum likelihood estimate for the proportion of migrants (m) was four times higher at the S-locus than at reference loci, but the difference was not statistically significant. Lack of significance might be due to insufficient data, but perhaps also to the recent divergence of the two species (311 ka), because we also show using simulations that the effective migration rate at the S-locus is expected to increase with increasing divergence time. These findings aid in understanding the evolutionary dynamics of negative frequency-dependent selection and they suggest that divergence time should be accounted for when employing migration rates to help detect negative frequency-dependent selection.     

Migration and the evolution of sexual dichromatism: evolutionary loss of female coloration with migration among wood-warblers

The mechanisms underlying evolutionary changes in sexual dimorphism have long been of interest to biologists. A striking gradient in sexual dichromatism exists among songbirds in North America, including the wood-warblers (Parulidae): males are generally more colourful than females at northern latitudes, while the sexes are similarly ornamented at lower latitudes. We use phylogenetically controlled comparative analysis to test three non-mutually exclusive hypotheses for the evolution of sexual dichromatism among wood-warblers. The first two hypotheses focus on the loss of female coloration with the evolution of migration, either owing to the costs imposed by visual predators during migration, or owing to the relaxation of selection for female social signalling at higher latitudes. The third hypothesis focuses on whether sexual dichromatism evolved owing to changes in male ornamentation as the strength of sexual selection increases with breeding latitude. To test these hypotheses, we compared sexual dichromatism to three variables: the presence of migration, migration distance, and breeding latitude. We found that the presence of migration and migration distance were both positively correlated with sexual dichromatism, but models including breeding latitude alone were not strongly supported. Ancestral state reconstruction supports the hypothesis that the ancestral wood-warblers were monochromatic, with both colourful males and females. Combined, these results are consistent with the hypotheses that the evolution of migration is associated with the relaxation of selection for social signalling among females and that there are increased predatory costs along longer migratory routes for colourful females. These results suggest that loss of female ornamentation can be a driver of sexual dichromatism and that social or natural selection may be a stronger contributor to variation in dichromatism than sexual selection.     

The process of evolutionary migration in species of Selaginella

The variation in three species ofSelaginella that occur in areas south and north of glaciated and periglacial regions is analysed. In each species the southern populations are more variable than the northern ones. These geographic patterns of variation are related to post-Wisconsin climatic changes and to the northward migration of each species. The geographic differentiation and migration of the species are seen as related phenomena. The concept of evolutionary migra tion-the operation of natural selection and of migration in mutually supportive roles-is discussed and applied to the examples inSelaginella. The possible broad significance of the process of evolutionary migration in floras directly under the influence of Wisconsin and post-Wisconsin environments is indicated.     

Stochastic processes are key determinants of short-term evolution in influenza a virus

Understanding the evolutionary dynamics of influenza A virus is central to its surveillance and control. While immune-driven antigenic drift is a key determinant of viral evolution across epidemic seasons, the evolutionary processes shaping influenza virus diversity within seasons are less clear. Here we show with a phylogenetic analysis of 413 complete genomes of human H3N2 influenza A viruses collected between 1997 and 2005 from New York State, United States, that genetic diversity is both abundant and largely generated through the seasonal importation of multiple divergent clades of the same subtype. These clades cocirculated within New York State, allowing frequent reassortment and generating genome-wide diversity. However, relatively low levels of positive selection and genetic diversity were observed at amino acid sites considered important in antigenic drift. These results indicate that adaptive evolution occurs only sporadically in influenza A virus; rather, the stochastic processes of viral migration and clade reassortment play a vital role in shaping short-term evolutionary dynamics. Thus, predicting future patterns of influenza virus evolution for vaccine strain selection is inherently complex and requires intensive surveillance, whole-genome sequencing, and phenotypic analysis.     

General models of multilocus evolution

In 1991, Barton and Turelli developed recursions to describe the evolution of multilocus systems under arbitrary forms of selection. This article generalizes their approach to allow for arbitrary modes of inheritance, including diploidy, polyploidy, sex linkage, cytoplasmic inheritance, and genomic imprinting. The framework is also extended to allow for other deterministic evolutionary forces, including migration and mutation. Exact recursions that fully describe the state of the population are presented; these are implemented in a computer algebra package (available on the Web at http://helios.bto.ed.ac.uk/evolgen). Despite the generality of our framework, it can describe evolutionary dynamics exactly by just two equations. These recursions can be further simplified using a "quasi-linkage equilibrium" (QLE) approximation. We illustrate the methods by finding the effect of natural selection, sexual selection, mutation, and migration on the genetic composition of a population.     

Phenotypic evolution under gene-culture transmission in structured populations.

I consider a simple model for the evolution of a quantitative character is structured populations when an offspring's phenotype is determined partly by his or her genetic constitution and partly by cultural transmission of the parental phenotype. Analysis of the model indicates that when individual and group selection are in the same direction, phenotypic evolution always proceeds faster under gene-culture vs. purely genetic transmission. When individual and group selection are countervailing, altruistic characters evolve faster under gene-culture transmission when individual selection is weak and migration among groups is limited, with increased individual selection and migration tending to decrease the advantage of gene-culture transmission over purely genetic transmission. Given the prevalence of cultural transmission in higher species, these results suggest that contrary to what is often assumed, group selection may indeed by a potent evolutionary force in the evolution of altruistic characters.     

CONSUMER–RESOURCE INTERACTIONS AND THE EVOLUTION OF MIGRATION

Theoretical studies have demonstrated that selection will favor increased migration when fitnesses vary both temporally and spatially, but it is far from clear how pervasive those theoretical conditions are in nature. Although consumer–resource interactions are omnipresent in nature and can generate spatial and temporal variation, it is unknown even in theory whether these dynamics favor the evolution of migration. We develop a mathematical model to address whether and how migration evolves when variability in fitness is determined at least in part by consumer–resource coevolutionary interactions. Our analyses show that such interactions can drive the evolution of migration in the resource, consumer, or both species and thus supplies a general explanation for the pervasiveness of migration. Over short time scales, we show the direction of change in migration rate is determined primarily by the state of local adaptation of the species involved: rates increase when a species is locally maladapted and decrease when locally adapted. Our results reveal that long‐term evolutionary trends in migration rates can differ dramatically depending on the strength or weakness of interspecific interactions and suggest an explanation for the evolutionary divergence of migration rates among interacting species.     

Evolution of complex life cycles of amphibians: bridging the gap between metapopulation dynamics and life history evolution

Current evolutionary models for amphibian life cycles reflect tradeoffs in size-specific growth and mortality rates between the aquatic and terrestrial stages. A limitation of these models is that they do not incorporate evolutionary phenomena that are associated with metapopulation structure. In this work I address components of the evolution of complex life cycles (CLCs) that are tied to the metapopulation dynamics of amphibians that use seasonal wetlands that vary in hydroperiod. In particular, I describe how selection for the minimum length of the larval period affects metapopulation viability and the selection/migration equilibrium. Selection to increase the minimum length of the larval period functionally reduces the number of viable breeding sites on the landscape, increases the average distance between neighboring sites, and increases the risk of metapopulation extinction. Within a metapopulation, asymmetric gene flow between populations that are adapted to different hydroperiods tends to swamp local selection for long larval periods at sites with long hydroperiods. The evolutionary stability of CLCs of many species with metapopulation structure may reflect the fact that extremely small metamorphs cannot survive on land, while lineages with long larval periods incur a high risk of metapopulation extinction. I encourage theorists to more carefully consider how life history traits and metapopulation viability are related for these and other taxa.     

Natural selection on fecundity variance in subdivided populations: kin selection meets bet hedging

In a series of seminal articles in 1974, 1975, and 1977, J. H. Gillespie challenged the notion that the "fittest" individuals are those that produce on average the highest number of offspring. He showed that in small populations, the variance in fecundity can determine fitness as much as mean fecundity. One likely reason why Gillespie's concept of within-generation bet hedging has been largely ignored is the general consensus that natural populations are of large size. As a consequence, essentially no work has investigated the role of the fecundity variance on the evolutionary stable state of life-history strategies. While typically large, natural populations also tend to be subdivided in local demes connected by migration. Here, we integrate Gillespie's measure of selection for within-generation bet hedging into the inclusive fitness and game theoretic measure of selection for structured populations. The resulting framework demonstrates that selection against high variance in offspring number is a potent force in large, but structured populations. More generally, the results highlight that variance in offspring number will directly affect various life-history strategies, especially those involving kin interaction. The selective pressures on three key traits are directly investigated here, namely within-generation bet hedging, helping behaviors, and the evolutionary stable dispersal rate. The evolutionary dynamics of all three traits are markedly affected by variance in offspring number, although to a different extent and under different demographic conditions.     

Domestication and fitness in the wild: A multivariate view

Domesticated species continually escaping and interbreeding with wild relatives impose a migration load on wild populations. As domesticated stocks become increasingly different as a result of artificial and natural selection in captivity, fitness of escapees in the wild is expected to decline, reducing the effective rate of migration into wild populations. Recent theory suggest that this may alleviate and eventually eliminate the resulting migration load. I develop a multivariate model of trait and wild fitness evolution resulting from the joint effects of artificial and natural selection in the captive environment. Initially, the evolutionary trajectory is dominated by the effects of artificial selection causing a fast initial decline in fitness of escapees in the wild. In later phases, through the counteracting effects of correlational multivariate natural selection in captivity, the mean phenotype is pushed in directions of weak stabilizing selection, allowing a sustained response in the trait subject to artificial selection. Provided that there is some alignment between the adaptive landscapes in the wild and in captivity, these phases are associated with slower rates of decline in wild fitness of the domesticated stock, suggesting that detrimental effects on wild populations are likely to remain a concern in the foreseeable future.     

Evolutionary responses by native species to major anthropogenic changes to their ecosystems: Pacific salmon in the Columbia River hydropower system

The human footprint is now large in all the Earth's ecosystems, and construction of large dams in major river basins is among the anthropogenic changes that have had the most profound ecological consequences, particularly for migratory fishes. In the Columbia River basin of the western USA, considerable effort has been directed toward evaluating demographic effects of dams, yet little attention has been paid to evolutionary responses of migratory salmon to altered selective regimes. Here we make a first attempt to address this information gap. Transformation of the free-flowing Columbia River into a series of slack-water reservoirs has relaxed selection for adults capable of migrating long distances upstream against strong flows; conditions now favour fish capable of migrating through lakes and finding and navigating fish ladders. Juveniles must now be capable of surviving passage through multiple dams or collection and transportation around the dams. River flow patterns deliver some groups of juvenile salmon to the estuary later than is optimal for ocean survival, but countervailing selective pressures might constrain an evolutionary response toward earlier migration timing. Dams have increased the cost of migration, which reduces energy available for sexual selection and favours a nonmigratory life history. Reservoirs are a benign environment for many non-native species that are competitors with or predators on salmon, and evolutionary responses are likely (but undocumented). More research is needed to tease apart the relative importance of evolutionary vs. plastic responses of salmon to these environmental changes; this research is logistically challenging for species with life histories like Pacific salmon, but results should substantially improve our understanding of key processes. If the Columbia River is ever returned to a quasinatural, free-flowing state, remaining populations might face a Darwinian debt (and temporarily reduced fitness) as they struggle to re-evolve historical adaptations.     

Experimental evolution in Heterandria formosa, a livebearing fish: group selection on population size

Group selection has historically been an important and controversial subject in evolutionary biology. There is now a compelling body of evidence, both theoretical and experimental, that group selection not only can be effective, but can be effective in situations when individual selection is not. However, experiments in which true population-level traits have been shown to evolve in response to group selection are currently limited to two species of flour beetle in the genus Tribolium and RNA viruses. Here we report the results of an experiment wherein we imposed group selection via differential extinction for increased and decreased population size at 6-week intervals, a true population-level trait, in the poeciliid fish Heterandria formosa. In contrast to most other group selection experiments, we observed no evolutionary response after six rounds of group selection in either the up- or down-selected lines. Populational heritability for population size was low, if not actually negative. Our results suggest that group selection via differential extinction may be effective only if population sizes are very small and/or migration rates are low.     

Evolution in metacommunities

A metacommunity can be defined as a set of communities that are linked by migration, and extinction and recolonization. In metacommunities, evolution can occur not only by processes that occur within communities such as drift and individual selection, but also by among-community processes, such as divergent selection owing to random differences among communities in species composition, and group and community-level selection. The effect of these among-community-level processes depends on the pattern of migration among communities. Migrating units may be individuals (migrant pool model), groups of individuals (single-species propagule pool model) or multi-species associations (multi-species propagule pool model). The most interesting case is the multi-species propagule pool model. Although this pattern of migration may a priori seem rare, it becomes more plausible in small well-defined 'communities' such as symbiotic associations between two or a few species. Theoretical models and experimental studies show that community selection is potentially an effective evolutionary force. Such evolution can occur either through genetic changes within species or through changes in the species composition of the communities. Although laboratory studies show that community selection can be important, little is known about how important it is in natural populations.