Controlling for P‐value inflation in allele frequency change in experimental evolution and artificial selection experiments

Experimental evolution studies can be used to explore genomic response to artificial and natural selection. In such studies, loci that display larger allele frequency change than expected by genetic drift alone are assumed to be directly or indirectly associated with traits under selection. However, such studies report surprisingly many loci under selection, suggesting that current tests for allele frequency change may be subject to P‐value inflation and hence be anticonservative. One factor known from genomewide association (GWA) studies to cause P‐value inflation is population stratification, such as relatedness among individuals. Here, we suggest that by treating presence of an individual in a population after selection as a binary response variable, existing GWA methods can be used to account for relatedness when estimating allele frequency change. We show that accounting for relatedness like this effectively reduces false‐positives in tests for allele frequency change in simulated data with varying levels of population structure. However, once relatedness has been accounted for, the power to detect causal loci under selection is low. Finally, we demonstrate the presence of P‐value inflation in allele frequency change in empirical data spanning multiple generations from an artificial selection experiment on tarsus length in two free‐living populations of house sparrow and correct for this using genomic control. Our results indicate that since allele frequencies in large parts of the genome may change when selection acts on a heritable trait, such selection is likely to have considerable and immediate consequences for the eco‐evolutionary dynamics of the affected populations.     

Speed of expansion and extinction in experimental populations

Although the causes of population extinction are well understood, the speed at which populations decline to extinction is not. A testable, counter-intuitive prediction of stochastic population theory is that, on average, for any interior interval of the domain of biologically attainable population sizes, the expected duration of increase equals the expected duration of decline. Here we report the first empirical tests of this hypothesis. Using data from two experiments in which replicate populations of Daphnia magna were observed to go extinct under different experimental conditions, we failed to reject the null hypothesis of no difference between the growth and decline phases in populations under constant conditions and conditions with modest environmental variability, but find strong evidence to reject equal first passage time in highly variable environments. These results confirm the prediction of equal passage times entailed by diffusion models of population dynamics, supporting continued application in both population theory and conservation decision making under the restricted conditions where the approximation can be expected to hold.     

Evolution of host resistance: looking for coevolutionary hotspots at small spatial scales

Natural plant populations are often found to be extremely diverse in their resistance to pathogens. While the potential of pathogens in driving the evolution of resistance in hosts has been widely recognized, empirical evidence linking disease dynamics to host population genetic structure has remained scarce. Here I show that current coevolutionary selection for resistance can be divergent even on a very fine spatial scale. In a natural plant-pathogen metapopulation, disease occurrence patterns were highly aggregated over space and time within host populations. A laboratory inoculation experiment showed higher resistance within areas of the host populations where encounter rates with the pathogen have been high. Higher resistance to sympatric than to allopatric strains of the pathogen suggests that this change has taken place as a response to local selection. These results constitute evidence of adaptive microevolution of resistance resulting from disease epidemics in natural plant-pathogen associations, and highlight the importance of finding the relevant scale at which to address questions of current coevolutionary selection.     

The role of weak selection and high mutation rates in nearly neutral evolution

Neutral dynamics occur in evolution if all types are ‘effectively equal’ in their reproductive success, where the definition of ‘effectively equal’ depends on the population size and the details of mutations. Empirically observed neutral genetic evolution in extremely large clonal populations can only be explained under current models if selection is completely absent. Such models typically consider the case where population dynamics occurs on a different timescale to evolution. However, this assumption is invalid when mutations are not rare in a whole population. We show that this has important consequences for the occurrence of neutral evolution in clonal populations. In highly connected type spaces, neutral dynamics can occur for all population sizes despite significant selective differences, via the forming of effectively neutral networks connecting rare neutral types. Biological implications include an explanation for the high diversity of rare types that survive in large clonal populations, and a theoretical justification for the use of neutral null models.     

When can ecological speciation be detected with neutral loci?

It is not yet clear under what conditions empirical studies can reliably detect progress toward ecological speciation through the analysis of allelic variation at neutral loci. We use a simulation approach to investigate the range of parameter space under which such detection is, and is not, likely. We specifically test for the conditions under which divergent natural selection can cause a ‘generalized barrier to gene flow’ that is present across the genome. Our individual‐based numerical simulations focus on how population divergence at neutral loci varies in relation to recombination rate with a selected locus, divergent selection on that locus, migration rate and population size. We specifically test whether genetic differences at neutral markers are greater between populations in different environments than between populations in similar environments. We find that this expected signature of ecological speciation can be detected under part of the parameter space, most consistently when divergent selection is strong and migration is intermediate. By contrast, the expected signature of ecological speciation is not reliably detected when divergent selection is weak or migration is low or high. These findings provide insights into the strengths and weaknesses of using neutral markers to infer ecological speciation in natural systems.     

Consequences of population structure on genes under balancing selection

This paper describes a new approach to modeling population structure for genes under strong balancing selection of the type seen in plant self-incompatibility systems and the major histocompatibility complex (MHC) system of vertebrates. Simple analytic solutions for the number of alleles maintained at equilibrium and the expected proportion of alleles shared between demes at various levels are derived and checked against simulation results. The theory accurately captures the dynamics of allele number in a subdivided population and identifies important values of m (migration rate) at which allele number and distribution change qualitatively. Starting from a panmictic population, as migration among demes decreases a qualitative change in dynamics is seen at approximately m(crit) approximately equal to the square root of(s/4piNT) where NT is the total population size and s is a measure of the strength of selection. At this point, demes can no longer maintain their panmictic allele number, due to increasing isolation from the total population. Another qualitative change occurs at a migration rate on the same order of magnitude as the mutation rate, mu. At this point, the demes are highly differentiated for allele complement, and the total number of alleles in the population is increased. Because in general u < m<(crit) at intermediate migration rates slightly fewer alleles may be maintained in the total population than are maintained at panmixia. Within this range, total allele number may not be the best indicator of whether a population is effectively panmictic, and some caution should be used when interpreting samples from such populations. The theory presented here can help to analyze data from genes under balancing selection in subdivided populations.     

Evolutionary game dynamics in finite populations

We introduce a model of stochastic evolutionary game dynamics in finite populations which is similar to the familiar replicator dynamics for infinite populations. Our focus is on the conditions for selection favoring the invasion and/or fixation of new phenotypes. For infinite populations, there are three generic selection scenarios describing evolutionary game dynamics among two strategies. For finite populations, there are eight selection scenarios. For a fixed payoff matrix a number of these scenarios can occur for different population sizes. We discuss several examples with unexpected behavior.     

Habitat selection reduces extinction of populations subject to Allee effects

Theoretical studies indicate that a single population under an Allee effect will decline to extinction if reduced below a particular threshold, but the existence of multiple local populations connected by random dispersal improves persistence of the global population. An additional process that can facilitate persistence is the existence of habitat selection by dispersers. Using analytic and simulation models of population change, I found that when habitat patches exhibiting Allee effects are connected by dispersing individuals, habitat selection by these dispersers increases the likelihood that patches persist at high densities, relative to results expected by random settlement. Populations exhibiting habitat selection also attain equilibrium more quickly than randomly dispersing populations. These effects are particularly important when Allee effects are large and more than two patches exist. Integrating habitat selection into population dynamics may help address why some studies have failed to find extinction thresholds in populations, despite well-known Allee effects in many species.     

When maladaptive gene flow does not increase selection

Populations receiving high maladaptive gene flow are expected to experience strong directional selection—because gene flow pulls mean phenotypes away from local fitness peaks. We tested this prediction by means of a large and replicated mark‐recapture study of threespine stickleback (Gasterosteus aculeatus) in two stream populations. One of the populations (outlet) experiences high gene flow from the lake population and its morphology is correspondingly poorly adapted. The other population (inlet) experiences very low gene flow from the lake population and its morphology is correspondingly well adapted. Contrary to the above prediction, selection was not stronger in the outlet than in the inlet, a result that forced us to consider potential reasons for why maladaptive gene flow might not increase selection. Of particular interest, we show by means of a simple population genetic model that maladaptive gene flow can—under reasonable conditions—decrease the strength of directional selection. This outcome occurs when immigrants decrease mean fitness in the resident population, which decreases the strength of selection against maladapted phenotypes. We argue that this previously unrecognized effect of gene flow deserves further attention in theoretical and empirical studies.     

Evolutionary game dynamics in finite populations with strong selection and weak mutation

We study stochastic game dynamics in finite populations. To this end we extend the classical Moran process to incorporate frequency-dependent selection and mutation. For 2 x 2 games, we give a complete analysis of the long-run behavior when mutation rates are small. For 3 x 3 coordination games, we provide a simple rule to determine which strategy will be selected in large populations. The expected motion in our model resembles the standard replicator dynamics when the population is large, but is qualitatively different when the population is small. Our analysis shows that even in large finite populations the behavior of a replicator-like system can be different from that of the standard replicator dynamics. As an application, we consider selective language dynamics. We determine which language will be spoken in finite large populations. The results have an intuitive interpretation but would not be expected from an analysis of the replicator dynamics.     

THE EFFICACY OF DIVERGENCE HITCHHIKING IN GENERATING GENOMIC ISLANDS DURING ECOLOGICAL SPECIATION

Genes under divergent selection flow less readily between populations than other loci. This observation has led to verbal “divergence hitchhiking” models of speciation in which decreased interpopulation gene flow surrounding loci under divergent selection can generate large regions of differentiation within the genome (genomic islands). The efficacy of this model in promoting speciation depends on the size of the region affected by divergence hitchhiking. Empirical evidence is mixed, with examples of both large and small genomic islands. To address these empirical discrepancies and to formalize the theory, we present mathematical models of divergence hitchhiking, which examine neutral differentiation around selected sites. For a single locus under selection, regions of differentiation do not extend far along a chromosome away from a selected site unless both effective population sizes and migration rates are low. When multiple loci are considered, regions of differentiation can be larger. However, with many loci under selection, genome‐wide divergence occurs and genomic islands are erased. The results show that divergence hitchhiking can generate large regions of differentiation, but that the conditions under which this occurs are limited. Thus, speciation may often require multifarious selection acting on many, isolated and physically unlinked genes. How hitchhiking promotes further adaptive divergence warrants consideration.     

Language dynamics in finite populations

Any mechanism of language acquisition can only learn a restricted set of grammars. The human brain contains a mechanism for language acquisition which can learn a restricted set of grammars. The theory of this restricted set is universal grammar (UG). UG has to be sufficiently specific to induce linguistic coherence in a population. This phenomenon is known as "coherence threshold". Previously, we have calculated the coherence threshold for deterministic dynamics and infinitely large populations. Here, we extend the framework to stochastic processes and finite populations. If there is selection for communicative function (selective language dynamics), then the analytic results for infinite populations are excellent approximations for finite populations; as expected, finite populations need a slightly higher accuracy of language acquisition to maintain coherence. If there is no selection for communicative function (neutral language dynamics), then linguistic coherence is only possible for finite populations.     

A metapopulation perspective on genetic diversity and differentiation in partially self-fertilizing plants

Abstract.— Partial self-fertilization is common in higher plants. Mating system variation is known to have important consequences for how genetic variation is distributed within and among populations. Selfing is known to reduce effective population size, and inbreeding species are therefore expected to have lower levels of genetic variation than comparable out crossing taxa. However, several recent empirical studies have shown that reductions in genetic diversity within populations of inbreeding species are far greater than the expected reductions based on the reduced effective population size. Two different processes have been argued to cause these patterns, selective sweeps (or hitchhiking) and background selection. Both are expected to be most effective in reducing genetic variation in regions of low recombination rates. Selfing is known to reduce the effective recombination rate, and inbreeding taxa are thus thought to be particularly vulnerable to the effects of hitchhiking or background selection. Here I propose a third explanation for the lower-than-expected levels of genetic diversity within populations of selfing species; recurrent extinctions and recolonizations of local populations, also known as metapopulation dynamics. I show that selfing in a metapopulation setting can result in large reductions in genetic diversity within populations, far greater than expected based the lower effective population size inbreeding species is expected to have. The reason for this depends on an interaction between selfing and pollen migration.     

Acquired immunity and stochasticity in epidemic intervals impede the evolution of host disease resistance

Disease can generate intense selection pressure on host populations, but here we show that acquired immunity in a population subject to repeated disease outbreaks can impede the evolution of genetic disease resistance by maintaining susceptible genotypes in the population. Interference between the life-history schedule of a species and periodicity of the disease has unintuitive effects on selection intensity, and stochasticity in outbreak period further reduces the rate of spread of disease-resistance alleles. A general age-structured population genetic model was developed and parameterized using empirical data for phocine distemper virus (PDV) epizootics in harbor seals. Scenarios with acquired immunity had lower levels of epizootic mortality compared with scenarios without acquired immunity for the first PDV outbreaks, but this pattern was reversed after about five disease cycles. Without acquired immunity, evolution of disease resistance was more rapid, and long-term population size variation is efficiently dampened. Acquired immunity has the potential to significantly influence rapid evolutionary dynamics of a host population in response to age-structured disease selection and to alter predicted selection intensities compared with epidemiological models that do not consider such feedback. This may have important implications for evolutionary population dynamics in a range of human, agricultural, and wildlife disease settings.     

Adaptation to larval crowding in Drosophila ananassae leads to the evolution of population stability

Density-dependent selection is expected to lead to population stability, especially if r and K tradeoff. Yet, there is no empirical evidence of adaptation to crowding leading to the evolution of stability. We show that populations of Drosophila ananassae selected for adaptation to larval crowding have higher K and lower r, and evolve greater stability than controls. We also show that increased population growth rates at high density can enhance stability, even in the absence of a decrease in r, by ensuring that the crowding adapted populations do not fall to very low sizes. We discuss our results in the context of traits known to have diverged between the selected and control populations, and compare our results with previous work on the evolution of stability in D. melanogaster. Overall, our results suggest that density-dependent selection may be an important factor promoting the evolution of relatively stable dynamics in natural populations.     

Transposable element number in mixed mating populations

Theoretical population genetic studies of transposable elements focus almost exclusively on random mating species, whereas many plants reproduce through partial or substantial self-fertilization. Here I develop computer simulation and analytic approximations of simplified element dynamics (transposition balanced by selective elimination) in partially self-fertilizing populations, using Ty1-copia elements for biological inspiration. Under the most plausible models and parameter values, element numbers decrease with self-fertilization when element insertions are deleterious, but may increase when ectopic exchange regulates element number. Conclusions for models of ectopic exchange depend in part on parameters for which little firm empirical evidence is available. Small changes in selfing rate can lead to abrupt changes in element number when homozygous and heterozygous elements have markedly different fitness effects. Equilibrium element numbers can be sensitive to population size, especially at high selfing rates. Elements are frequently lost in small highly selfing populations under the deleterious insertion model. In contrast, small highly selfing populations can accumulate very large numbers of elements under ectopic exchange. Empirical data on element number and localization in plants with different mating systems suggests that deleterious insertion, rather than ectopic exchange, may regulate element number. Limitations to available empirical data, especially the lack of comparison between closely related species differing in mating system, mean that this conclusion is tentative.     

Does animal behavior underlie covariation between hosts' exposure to infectious agents and susceptibility to infection? Implications for disease dynamics

Animal behavior is unique in influencing both components of the process of transmission of disease: exposure to infectious agents, and susceptibility to infection once exposed. To date, the influence of behavior on exposure versus susceptibility has largely been considered separately. Here, we ask whether these two key mechanisms act in concert in natural populations, whereby individuals who are most exposed to infectious agents or have the most contact with conspecifics are also the most susceptible or infectious. We propose three mechanisms that can generate covariation between these two key elements of the transmission of disease within and among hosts, and we provide empirical examples of each. We then use a mathematical model to examine the effect of this covariation on the dynamics of disease at the population level. First, we show that the empirical mechanisms generating covariation between behavioral and physiological components of disease transmission are widespread and include endocrine mediators of behavior, mate choice, group size, sickness behaviors, and behavioral avoidance of infectious conspecifics. The diversity of these empirical mechanisms underscores the potential importance and breadth of covariation in the disease process. Second, we show mathematically that the variability in hosts' exposure to infectious agents and susceptibility or infectiousness, and how tightly they are coupled, strongly influences the ability of a disease to invade a host population. Overall, we propose that covariation between behavioral and physiological components of transmission is likely widespread in natural populations, and can have important consequences for the dynamics of disease at the population level as well as for our understanding of sexual selection, social behavior, and animal communication.     

Inbreeding effects on pair fecundity and population persistence

Despite strong empirical evidence of the harmful effects of inbreeding on fecundity, spontaneous recessive deleterious mutations are generally considered as acting on survival only in evolutionary models and population viability analyses. In this study, we modelled a species with separate sexes to assess the effect of selection on fecundity in small populations on the risk of extinction. We showed that the impact of inbreeding on short-term fitness changes and that population dynamics are strongly influenced by phenotypic interactions among males and females during reproduction. In particular, population persistence was found to be highly sensitive to the level at which selection acts (i.e. individual vs. pair) and to asymmetry among sexes (in terms of mutation rates and mutational effects).  © 2005 The Linnean Society of London, Biological Journal of the Linnean Society , 2005, 86 , 467–476.     

The evolution of stability in a competitive system

The characteristics governing the dynamics of populations can evolve and this evolution can either be towards stability or chaos. Yet it is not obvious how or why such population characteristics can evolve through selection on individuals. In this paper we construct a mathematical model, inspired by experimental results, illustrating the dynamics of a population of competing Drosophila. We demonstrate how selection of life history characteristics and stability influence one another as a population interacts with its environment. We generalize this result and show that population stability can evolve as a consequence of selection on individuals.     

Inertia: the discrepancy between individual and common good in dispersal and prospecting behaviour

The group selection debate of the 1960s made it clear that evolution does not necessarily increase population performance. Individuals can be selected to have traits that diminish a common good and make population persistence difficult. At the extreme, the discrepancy between levels of selection is predicted to make traits evolve towards values at which a population can no longer persist (evolutionary suicide). Dispersal and prospecting are prime examples of traits that have a strong influence on population persistence under environmental and demographic stochasticity. Theory predicts that an ‘optimal’ dispersal strategy from a population point of view can differ considerably from that produced by individual‐level selection. Because dispersal is frequently risky or otherwise costly, individuals are often predicted to disperse less than would be ideal for population performance (persistence or size). We define this discrepancy as ‘inertia’ and examine current knowledge of its occurrence and effects on population dynamics in nature. We argue that inertia is potentially widespread but that a framework is currently lacking for predicting precisely the extent to which it has a real influence on population persistence. The opposite of inertia, ‘hypermobility’ (more dispersal by individuals than would maximize population performance) remains a possibility: it is known that highest dispersal rates do not lead to best expected population performance, and examples of such high dispersal evolving exist at least in the theoretical literature. We also show, by considering prospecting behaviour, that similar issues arise in species with advanced cognitive and learning abilities. Individual prospecting strategies and the information acquired during dispersal are known to influence the decisions and therefore the fate of individuals and, as a corollary, populations. Again, the willingness of individuals to sample environments might evolve to levels that are not optimal for populations. This conflict can take intriguing forms. For example, better cognitive abilities of individuals may not always lead to better population‐level performance. Simulation studies have found that ‘blind’ dispersal can lead to better connected metapopulations than cognitively more advanced habitat choice rules: the latter can lead to too many individuals sticking to nearby safe habitat. The study of the mismatch between individual and population fitness should not be a mere intellectual exercise. Population managers typically need to take a population‐level view of performance, which may necessitate human intervention if it differs from what is selected for. We conclude that our knowledge of inertia and hypermobility would advance faster if theoretical studies—without much additional effort—quantified the population consequences of the evolving traits and compared this with hypothetical (not selectively favoured) dispersal rules, and if empirical studies were similarly conducted with the differing levels of selection in mind.