GENE FLOW FROM DOMESTICATED SPECIES TO WILD RELATIVES: MIGRATION LOAD IN A MODEL OF MULTIVARIATE SELECTION

Domesticated species frequently spread their genes into populations of wild relatives through interbreeding. The domestication process often involves artificial selection for economically desirable traits. This can lead to an indirect response in unknown correlated traits and a reduction in fitness of domesticated individuals in the wild. Previous models for the effect of gene flow from domesticated species to wild relatives have assumed that evolution occurs in one dimension. Here, I develop a quantitative genetic model for the balance between migration and multivariate stabilizing selection. Different forms of correlational selection consistent with a given observed ratio between average fitness of domesticated and wild individuals offsets the phenotypic means at migration–selection balance away from predictions based on simpler one-dimensional models. For almost all parameter values, correlational selection leads to a reduction in the migration load. For ridge selection, this reduction arises because the distance the immigrants deviates from the local optimum in effect is reduced. For realistic parameter values, however, the effect of correlational selection on the load is small, suggesting that simpler one-dimensional models may still be adequate in terms of predicting mean population fitness and viability.     

Genetic and Statistical Analyses of Strong Selection on Polygenic Traits: What,Me Normal?

We develop a general population genetic framework for analyzing selection on many loci, and apply it to strong truncation and disruptive selection on an additive polygenic trait. We first present statistical methods for analyzing the infinitesimal model, in which offspring breeding values are normally distributed around the mean of the parents, with fixed variance. These show that the usual assumption of a Gaussian distribution of breeding values in the population gives remarkably accurate predictions for the mean and the variance, even when disruptive selection generates substantial deviations from normality. We then set out a general genetic analysis of selection and recombination. The population is represented by multilocus cumulants describing the distribution of haploid genotypes, and selection is described by the relation between mean fitness and these cumulants. We provide exact recursions in terms of generating functions for the effects of selection on non-central moments. The effects of recombination are simply calculated as a weighted sum over all the permutations produced by meiosis. Finally, the new cumulants that describe the next generation are computed from the non-central moments. Although this scheme is applied here in detail only to selection on an additive trait, it is quite general. For arbitrary epistasis and linkage, we describe a consistent infinitesimal limit in which the short-term selection response is dominated by infinitesimal allele frequency changes and linkage disequilibria. Numerical multilocus results show that the standard Gaussian approximation gives accurate predictions for the dynamics of the mean and genetic variance in this limit. Even with intense truncation selection, linkage disequilibria of order three and higher never cause much deviation from normality. Thus, the empirical deviations frequently found between predicted and observed responses to artificial selection are not caused by linkage-disequilibrium-induced departures from normality. Disruptive selection can generate substantial four-way disequilibria, and hence kurtosis; but even then, the Gaussian assumption predicts the variance accurately. In contrast to the apparent simplicity of the infinitesimal limit, data suggest that changes in genetic variance after 10 or more generations of selection are likely to be dominated by allele frequency dynamics that depend on genetic details.     

The West Pacific diversity hotspot as a source or sink for new species? Population genetic insights from the Indo‐Pacific parrotfish Scarus rubroviolaceus

We used a population genetic approach to quantify major population subdivisions and patterns of migration within a broadly distributed Indo-Pacific parrotfish. We genotyped 15 microsatellite loci in Scarus rubroviolaceus collected from 20 localities between Africa and the Americas. A STRUCTURE model indicates the presence of four major populations: Eastern Pacific, Hawaii, Central-West Pacific and a less well-differentiated Indian Ocean. We used the isolation and migration model to estimate splitting times, population sizes and migration patterns between sister population pairs. To eliminate loci under selection, we used BayeScan to select loci for three isolation and migration models: Eastern Pacific and Central-West Pacific, Hawaii and the Central-West Pacific, and Indian Ocean and the Central-West Pacific. To test the assumption of a stepwise mutation model (SMM), we used likelihood to test the SMM against a two-phase model that allowed mutational complexity. A posteriori, minor departures from SMM were estimated to affect ≤2% of the alleles in the data. The data were informative about the contemporary and ancestral population sizes, migration rates and the splitting time in the eastern Pacific/Central-West Pacific comparison. The model revealed a splitting time ～17,000 BP, a larger contemporary N(e) in the Central-West Pacific than in the eastern Pacific and a strong bias of east to west migration. These characteristics support the Center of Accumulation model of peripatric diversification in low-diversity peripheral sites and perhaps migration from those sites to the western Pacific diversity hotspot.     

Pleiotropic Models of Polygenic Variation, Stabilizing Selection, and Epistasis

We show that in polymorphic populations many polygenic traits pleiotropically related to fitness are expected to be under apparent ``stabilizing selection' independently of the real selection acting on the population. This occurs, for example, if the genetic system is at a stable polymorphic equilibrium determined by selection and the nonadditive contributions of the loci to the trait value either are absent, or are random and independent of those to fitness. Stabilizing selection is also observed if the polygenic system is at an equilibrium determined by a balance between selection and mutation (or migration) when both additive and nonadditive contributions of the loci to the trait value are random and independent of those to fitness. We also compare different viability models that can maintain genetic variability at many loci with respect to their ability to account for the strong stabilizing selection on an additive trait. Let V(m) be the genetic variance supplied by mutation (or migration) each generation, V(g) be the genotypic variance maintained in the population, and n be the number of the loci influencing fitness. We demonstrate that in mutation (migration)-selection balance models the strength of apparent stabilizing selection is order V(m)/V(g). In the overdominant model and in the symmetric viability model the strength of apparent stabilizing selection is approximately 1/(2n) that of total selection on the whole phenotype. We show that a selection system that involves pairwise additive by additive epistasis in maintaining variability can lead to a lower genetic load and genetic variance in fitness (approximately 1/(2n) times) than an equivalent selection system that involves overdominance. We show that, in the epistatic model, the apparent stabilizing selection on an additive trait can be as strong as the total selection on the whole phenotype.     

MAINTENANCE OF POLYGENIC VARIATION IN SPATIALLY STRUCTURED POPULATIONS: ROLES FOR LOCAL MATING AND GENETIC REDUNDANCY

Although heritable genetic variation is critical to the evolutionary process, we know little about how it is maintained. Obviously, mutation-selection balance must play a role, but there is considerable doubt over whether it can account for heritabilities as high as 0.5, which are commonly found in natural populations. Most models of mutation-selection balance assume panmictic populations. In this paper we use Monte Carlo simulations to examine the effect of isolation by distance on the variation maintained by mutation in a polygenic trait subject to optimizing selection. We show that isolation by distance can substantially increase the total variation maintained in continuous populations over a wide range of dispersal patterns, but only if more than one genotype produces the optimal phenotype (genetic redundancy). Isolation by distance alone has only a slight effect on the variation maintained in the total population for neutral alleles. The combined effect of isolation by distance and genetic redundancy, however, allows the maintenance of substantial variation despite strong stabilizing selection. The mechanism is straightforward. Isolation by distance allows mutation and drift to operate independently in different parts of the population. Because of their independent evolutionary histories, different parts of the population independently draw from the available set of redundant genotypes. Because the genotypes are redundant, selection does not discriminate among them, and they will persist until eliminated by drift. The population as a whole maintains many distinct genotypes. We show that this process allows mutation to maintain high levels of variation, even under strong stabilizing selection, and that over a moderate range of dispersal patterns the amount of variation maintained in the entire population is independent of both the strength of selection and the variance of the dispersal distance. Furthermore, we show that individual heterozygosity is increased in locally mating populations when selection is strong. Finally, our simulations provide a rough picture of how selection and the dispersal pattern influence the spatial distribution of genetic and phenotypic variation.     

The effects of sexual selection on trait divergence in a peripheral population with gene flow

The unique aspects of speciation and divergence in peripheral populations have long sparked much research. Unidirectional migration, received by some peripheral populations, can hinder the evolution of distinct differences from their founding populations. Here, we explore the effects that sexual selection, long hypothesized to drive the divergence of distinct traits used in mate choice, can play in the evolution of such traits in a partially isolated peripheral population. Using population genetic continent‐island models, we show that with phenotype matching, sexual selection increases the frequency of an island‐specific mating trait only when female preferences are of intermediate strength. We identify regions of preference strength for which sexual selection can instead cause an island‐specific trait to be lost, even when it would have otherwise been maintained at migration‐selection balance. When there are instead separate preference and trait loci, we find that sexual selection can lead to low trait frequencies or trait loss when female preferences are weak to intermediate, but that sexual selection can increase trait frequencies when preferences are strong. We also show that novel preference strengths almost universally cannot increase, under either mating mechanism, precluding the evolution of premating isolation in peripheral populations at the early stages of species divergence.     

COMPARISON OF NON‐GAUSSIAN QUANTITATIVE GENETIC MODELS FOR MIGRATION AND STABILIZING SELECTION

The balance between stabilizing selection and migration of maladapted individuals has formerly been modeled using a variety of quantitative genetic models of increasing complexity, including models based on a constant expressed genetic variance and models based on normality. The infinitesimal model can accommodate nonnormality and a nonconstant genetic variance as a result of linkage disequilibrium. It can be seen as a parsimonious one‐parameter model that approximates the underlying genetic details well when a large number of loci are involved. Here, the performance of this model is compared to several more realistic explicit multilocus models, with either two, several or a large number of alleles per locus with unequal effect sizes. Predictions for the deviation of the population mean from the optimum are highly similar across the different models, so that the non‐Gaussian infinitesimal model forms a good approximation. It does, however, generally estimate a higher genetic variance than the multilocus models, with the difference decreasing with an increasing number of loci. The difference between multilocus models depends more strongly on the effective number of loci, accounting for relative contributions of loci to the variance, than on the number of alleles per locus.     

Sensory trait variation contributes to biased dispersal of threespine stickleback in flowing water

Gene flow is widely thought to homogenize spatially separate populations, eroding effects of divergent selection. The resulting theory of ‘migration–selection balance’ is predicated on a common assumption that all genotypes are equally prone to dispersal. If instead certain genotypes are disproportionately likely to disperse, then migration can actually promote population divergence. For example, previous work has shown that threespine stickleback (Gasterosteus aculeatus) differ in their propensity to move up‐ or downstream (‘rheotactic response’), which may facilitate genetic divergence between adjoining lake and stream populations of stickleback. Here, we demonstrate that intraspecific variation in a sensory system (superficial neuromast lines) contributes to this variation in swimming behaviour in stickleback. First, we show that intact neuromasts are necessary for a typical rheotactic response. Next, we showed that there is heritable variation in the number of neuromasts and that stickleback with more neuromasts are more likely to move downstream. Variation in pectoral fin shape contributes to additional variation in rheotactic response. These results illustrate how within‐population quantitative variation in sensory and locomotor traits can influence dispersal behaviour, thereby biasing dispersal between habitats and favouring population divergence.     

Red Queen dancing in the lek: effects of mating skew on host–parasite interactions

The RQH (Red Queen hypothesis), which argues that hosts need to be continuously finding new ways to avoid parasites that are able to infect common host genotypes, has been at the center of discussions on the maintenance of sex. This is because diversity is favored under the host–parasite coevolution based on negative frequency‐dependent selection, and sexual reproduction is a mechanism that generates genetic diversity in the host population. Together with parasite infections, sexual organisms are usually under sexual selection, which leads to mating skew or mating success biased toward males with a particular phenotype. Thus, strong mating skew would affect genetic variance in a population and should affect the benefit of the RQH. However, most models have investigated the RQH under a random mating system and not under mating skew. In this study, I show that sexual selection and the resultant mating skew may increase parasite load in the hosts. An IBM (individual‐based model), which included host–parasite interactions and sexual selection among hosts, demonstrates that mating skew influenced parasite infection in the hosts under various conditions. Moreover, the IBM showed that the mating skew evolves easily in cases of male–male competition and female mate choice, even though it imposes an increased risk of parasite infection on the hosts. These findings indicated that whether the RQH favored sexual reproduction depended on the condition of mating skew. That is, consideration of the host mating system would provide further understanding of conditions in which the RQH favors sexual reproduction in real organisms.     

Bayesian analysis of multivariate mixed models for a prospective cohort study using skew‐elliptical distributions

Classical multivariate mixed models that acknowledge the correlation of patients through the incorporation of normal error terms are widely used in cohort studies. Violation of the normality assumption can make the statistical inference vague. In this paper, we propose a Bayesian parametric approach by relaxing this assumption and substituting some flexible distributions in fitting multivariate mixed models. This strategy allows for the skewness and the heavy tails of error‐term distributions and thus makes inferences robust to the violation. This approach uses flexible skew‐elliptical distributions, including skewed, fat, or thin‐tailed distributions, and imposes the normal model as a special case. We use real data obtained from a prospective cohort study on the low back pain to illustrate the usefulness of our proposed approach.     

Hybrid zone structure and the potential role of selection in hybridizing populations of native westslope cutthroat trout (Oncorhynchus clarki lewisi) and introduced rainbow trout (O. mykiss)

Introgressive hybridization is a common feature of many zones of contact between divergent lineages of fishes. This is particularly common when taxa that are normally allopatric come into artificial (human-induced) secondary contact. We examined 18 native populations of westslope cutthroat trout (Oncorhynchus clarki lewisi, WCT) to determine the extent of introgressive hybridization with introduced rainbow trout (O. mykiss, RBT) and the genetic structure of hybridizing populations in the upper Kootenay River, southeastern British Columbia, Canada. Using four diagnostic nuclear loci we calculated a hybrid index, inbreeding coefficient, FIS, and the linkage disquilibrium correlation coefficient, Rij, for each locality to determine the distribution of genotypes in each population. We also categorized the 142 hybrid individuals found across localities into four hybrid classes based on their genotypes. The majority of localities (11/18) showed a unimodal distribution of genotypes skewed towards genotypes of WCT. Two localities, however (lower Gold Creek and Lodgepole Creek) showed a flat to bimodal distribution and one site (lower Bull River) showed a unimodal distribution skewed towards RBT genotypes. The majority of hybrid individuals were classified genotypically as WCT backcrosses (59%) and post-F1 individuals (24%). We found a skewed ratio of pure WCT to pure RBT (17:1) and only four F1 hybrids (3%), suggesting that the spread of RBT alleles may be facilitated by hybrids straying to neighbouring populations. We also tested for the action of selection in one population using cohort analyses, but found little evidence of differential selection between pure WCT and hybrid individuals. Pooled across age classes there were significant differences in genotypic frequencies among loci suggesting differential introgression. There was no asymmetry to the hybridization between rainbow trout and westslope cutthroat trout because both species' mitochondrial DNA haplotypes were observed at similar frequencies in the hybrids. Our analyses suggest that hybrid swarms are likely to form in the upper Kootenay River drainage and that certain native WCT populations in British Columbia are at risk of local genomic extinction.     

The effects of the mating system on the evolution of migration in a spatially heterogeneous population

Summary Verbal explanations for the evolution of migration and dispersal often invoke inbreeding depression as an important force. Experimental work on plant populations indicates that while inbreeding depression may favor increased migration rates, adaptation to local environments may reduce the advantage to migrants. We formalize and test this hypothesis using a two-locus genetic model that incorporates lowered fitness in offspring produced by self-fertilization, and habitat differentiation. We also use the model to address questions about the general theory of genetic modifiers and the modifier reduction principle. We find that even under conditions when migration would increase the mean fitness of a population, migration may not be favored. This result is due to the associations that develop between genotypes at a locus subject to overdominant selection and at a neutral locus controlling the migration rate. Thus, it appears that, in this model, the forces of local adaptation, which favor a reduction in the migration rate, overwhelm those of inbreeding depression, which may favor dispersal.     

Selection on skewed characters and the paradox of stasis

Observed phenotypic responses to selection in the wild often differ from predictions based on measurements of selection and genetic variance. An overlooked hypothesis to explain this paradox of stasis is that a skewed phenotypic distribution affects natural selection and evolution. We show through mathematical modeling that, when a trait selected for an optimum phenotype has a skewed distribution, directional selection is detected even at evolutionary equilibrium, where it causes no change in the mean phenotype. When environmental effects are skewed, Lande and Arnold's (1983) directional gradient is in the direction opposite to the skew. In contrast, skewed breeding values can displace the mean phenotype from the optimum, causing directional selection in the direction of the skew. These effects can be partitioned out using alternative selection estimates based on average derivatives of individual relative fitness, or additive genetic covariances between relative fitness and trait (Robertson–Price identity). We assess the validity of these predictions using simulations of selection estimation under moderate sample sizes. Ecologically relevant traits may commonly have skewed distributions, as we here exemplify with avian laying date — repeatedly described as more evolutionarily stable than expected — so this skewness should be accounted for when investigating evolutionary dynamics in the wild.     

TESTING MODELS OF MIGRATION AND ISOLATION AMONG POPULATIONS OF CHINOOK SALMON (ONCORHYNCHUS TSCHAWYTSCHA)

The chinook salmon (Oncorhynchus tschawytscha) is a behaviorally, morphologically, and ecologically variable species distributed over a large geographic range. Although previous genetic surveys have revealed considerable genetic differences among populations with different life history types and from different major river drainages, it is not clear to what degree these genetically distinct populations are connected by low levels of gene flow. The work described in this paper addresses this question by surveying DNA restriction site variation at six nuclear genes from nine populations encompassing most of the species's North American range, and then attempting to fit the patterns of variation observed at these genes to five different evolutionary models using computer simulations of the coalescent process. Two commonly used constant population size models, one hypothesizing no migration among populations and one hypothesizing equal rates of migration among populations, were found to be statistically inconsistent with the observed patterns of variation. The other three models, which involved either recent divergence among populations coupled with large changes in populations size, unequal migration rates among populations, or selection, were all found to be consistent with the observed patterns of variation. Assuming selective neutrality, these results suggest that either the populations have all descended from a common ancestral population within the last ~50,000 years and have all suffered large declines in effective population size since that time, or that they have a more ancient divergence time but are connected by low levels of gene flow. These conclusions rest on the assumption of selective neutrality. With the methods employed, it was not possible to simultaneously test hypotheses of both selective neutrality and population structure.     

Drawing inferences about the coancestry coefficient

The coancestry coefficient, also known as the population structure parameter, is of great interest in population genetics. It can be thought of as the intraclass correlation of pairs of alleles within populations and it can serve as a measure of genetic distance between populations. For a general class of evolutionary models it determines the distribution of allele frequencies among populations. Under more restrictive models it can be regarded as the probability of identity by descent of any pair of alleles at a locus within a random mating population. In this paper we review estimation procedures that use the method of moments or are maximum likelihood under the assumption of normally distributed allele frequencies. We then consider the problem of testing hypotheses about this parameter. In addition to parametric and non-parametric bootstrap tests we present an asymptotically-distributed chi-square test. This test reduces to the contingency-table test for equal sample sizes across populations. Our new test appears to be more powerful than previous tests, especially for loci with multiple alleles. We apply our methods to HapMap SNP data to confirm that the coancestry coefficient for humans is strictly positive.     

Evolutionary stability under the replicator and the gradient dynamics

We unite two general models for evolutionary change under the forces of selection, mutation and reproduction, a genetic model (replicator dynamics) and a cultural model (gradient dynamics). Under the assumption of normality, we find that the mean and variance dynamics are essentially identical under the two models and we relate these to the ESS and convergence stability conditions.     

Effect of migration and environmental heterogeneity on the maintenance of quantitative genetic variation: a simulation study

The paradox of high genetic variation observed in traits under stabilizing selection is a long‐standing problem in evolutionary theory, as mutation rates appear too low to explain observed levels of standing genetic variation under classic models of mutation–selection balance. Spatially or temporally heterogeneous environments can maintain more standing genetic variation within populations than homogeneous environments, but it is unclear whether such conditions can resolve the above discrepancy between theory and observation. Here, we use individual‐based simulations to explore the effect of various types of environmental heterogeneity on the maintenance of genetic variation (V_A) for a quantitative trait under stabilizing selection. We find that V_A is maximized at intermediate migration rates in spatially heterogeneous environments and that the observed patterns are robust to changes in population size. Spatial environmental heterogeneity increased variation by as much as 10‐fold over mutation–selection balance alone, whereas pure temporal environmental heterogeneity increased variance by only 45% at max. Our results show that some combinations of spatial heterogeneity and migration can maintain considerably more variation than mutation–selection balance, potentially reconciling the discrepancy between theoretical predictions and empirical observations. However, given the narrow regions of parameter space required for this effect, this is unlikely to provide a general explanation for the maintenance of variation. Nonetheless, our results suggest that habitat fragmentation may affect the maintenance of V_A and thereby reduce the adaptive capacity of populations.     

Hitchhiking effect of a beneficial mutation spreading in a subdivided population

A central problem in population genetics is to detect and analyze positive natural selection by which beneficial mutations are driven to fixation. The hitchhiking effect of a rapidly spreading beneficial mutation, which results in local removal of standing genetic variation, allows such an analysis using DNA sequence polymorphism. However, the current mathematical theory that predicts the pattern of genetic hitchhiking relies on the assumption that a beneficial mutation increases to a high frequency in a single random-mating population, which is certainly violated in reality. Individuals in natural populations are distributed over a geographic space. The spread of a beneficial allele can be delayed by limited migration of individuals over the space and its hitchhiking effect can also be affected. To study this effect of geographic structure on genetic hitchhiking, we analyze a simple model of directional selection in a subdivided population. In contrast to previous studies on hitchhiking in subdivided populations, we mainly investigate the range of sufficiently high migration rates that would homogenize genetic variation at neutral loci. We provide a heuristic mathematical analysis that describes how the genealogical structure at a neutral locus linked to the locus under selection is expected to change in a population divided into two demes. Our results indicate that the overall strength of genetic hitchhiking--the degree to which expected heterozygosity decreases--is diminished by population subdivision, mainly because opportunity for the breakdown of hitchhiking by recombination increases as the spread of the beneficial mutation across demes is delayed when migration rate is much smaller than the strength of selection. Furthermore, the amount of genetic variation after a selective sweep is expected to be unequal over demes: a greater reduction in expected heterozygosity occurs in the subpopulation from which the beneficial mutation originates than in its neighboring subpopulations. This raises a possibility of detecting a "hidden" geographic structure of population by carefully analyzing the pattern of a selective sweep.     

A network approach to modeling population aggregation and genetic control of pest insects

Historically, models of the invasion and biological control of insect pests have omitted heterogeneities in the spatial structure of the targeted populations. In this study, we use stochastic network simulations to examine explicitly population heterogeneity as a function of landscape structure and insect behavior. We show that when insects are distributed non-randomly across a heterogeneous landscape, control can be significantly hindered. However, when insect populations are clustered as a result of limited dispersal, genetic control efficiency can be enhanced. In developing the model, we relax a key assumption of previous theoretical studies of genetic control: that released genetic control insects remain homogenously distributed irrespective of the spatial structure of the wild type populations. Here, this behavior (termed the ‘coverage proportion’) is parameterized and its properties are explored. We show that landscape heterogeneity and limited dispersal have little effect on the critical coverage proportion necessary for control.     

A Bayesian Approach to Joint Mixed‐Effects Models with a Skew‐Normal Distribution and Measurement Errors in Covariates

Summary In recent years, nonlinear mixed‐effects (NLME) models have been proposed for modeling complex longitudinal data. Covariates are usually introduced in the models to partially explain intersubject variations. However, one often assumes that both model random error and random effects are normally distributed, which may not always give reliable results if the data exhibit skewness. Moreover, some covariates such as CD4 cell count may be often measured with substantial errors. In this article, we address these issues simultaneously by jointly modeling the response and covariate processes using a Bayesian approach to NLME models with covariate measurement errors and a skew‐normal distribution. A real data example is offered to illustrate the methodologies by comparing various potential models with different distribution specifications. It is showed that the models with skew‐normality assumption may provide more reasonable results if the data exhibit skewness and the results may be important for HIV/AIDS studies in providing quantitative guidance to better understand the virologic responses to antiretroviral treatment.