Statistical analysis of the migration component of genetic drift

Statistical methods are introduced for analysis of the migration component of genetic drift, i.e., of the stochastic changes that affect allele frequencies during migration between local groups. Attention focuses on alpha M, a parameter that measures the extent to which this component of drift departs from the ideal of independent random sampling, and which can be interpreted as a measure of the extent to which migration is kin-structured. It is shown that alpha M can be estimated from genetic data, even in the absence of information about the genealogical relationships of migrants, and Monte-Carlo simulations are used to approximate the sampling distribution of the estimator under the null hypothesis of independent random sampling. Application of these methods to data from the Aland Islands, Finland, shows that the migration pattern there is consistent with the hypothesis of independent random sampling.     

本科遗传学教学中的遗传漂变概念探讨

遗传漂变是遗传学教学的难点之一,因其涉及随机性和概率,特别容易引起误解。定义中的“抽样误差”常被误解为遗传漂变是由于“抽样”这一研究方法干扰才导致基因频率的随机变化。本文首先对国内外《遗传学》教材中的遗传漂变定义进行了分析比较,发现“抽样误差”的定义为各教材普遍采用,但只有少数教材对“抽样误差”概念进行了正确的解释,多数未作进一步的说明。文章介绍了遗传漂变的研究历史,亦即Wright、 Fisher和Kimura等学者对遗传漂变研究的贡献。进而,特别介绍了近年来国外关于本科生遗传漂变教学的两篇代表性教学研究论文,指出本科生在学习过程中容易出现错误理解是难以避免的现象,对此也提供了初步的解决办法。作者最后结合自己的教学实践,提出本科生教学中遗传漂变仍然采用含有“抽样误差”概念的定义,只是需要对“抽样误差”做进一步的解释,指出“抽样误差”是等位基因世代传递过程中存在的、配子间的随机结合,“相当于”对整个参与交配的配子库中的配子进行的一次“随机抽样”,而与一般遗传学研究中的人为抽样行为无关。本文旨在为本科遗传学教学中关于遗传源变概念的讲解提供借鉴和参考。     

Multinomial-Sampling Models for Random Genetic Drift

Three different derivations of models with multinomial sampling of genotypes in a finite population are presented. The three derivations correspond to the operation of random drift through population regulation, conditioning on the total number of progeny, and culling, respectively. Generations are discrete and nonoverlapping; the diploid population mates at random. Each derivation applies to a single multiallelic locus in a monoecious or dioecious population; in the latter case, the locus may be autosomal or X-linked. Mutation and viability selection are arbitrary; there are no fertility differences. In a monoecious population, the model yields the Wright-Fisher model (i.e., multinomial sampling of genes) if and only if the viabilities are multiplicative. In a dioecious population, the analogous reduction does not occur even for pure random drift. Thus, multinomial sampling of genotypes generally does not lead to multinomial sampling of genes. Although the Wright-Fisher model probably lacks a sound biological basis and may be inaccurate for small populations, it is usually (perhaps always) a good approximation for genotypic multinomial sampling in large populations.     

Low RAPD Variation and Female-Biased Sex Ratio Indicate Genetic Drift in Small Populations of the Dioecious Conifer Taxus Baccata in Switzerland

Small populations are prone to genetic drift as a consequence of random sampling effects. We investigated whether we could detect such random sampling effects in the English yew (Taxus baccata), a dioecious conifer species occurring in scattered populations in Switzerland. Seven pairs of small and large populations were analyzed using random amplified polymorphic DNA (RAPD) marker bands from 20 individuals per population. Several genetic parameters (mean marker band frequency deviation, molecular variance, population differentiation) indicated that small populations experienced genetic drift. These genetic differences between small and large populations of yew were paralleled by an increased sex ratio bias towards a higher number of females in the small populations. Our findings support earlier assumptions that the Swiss occurrences of yew may be described as metapopulation dynamics, characterized by local colonization and extinction events leading to the observed genetic drift.     

PERSPECTIVE: MODELS OF SPECIATION: WHAT HAVE WE LEARNED IN 40 YEARS?

Theoretical studies of speciation have been dominated by numerical simulations aiming to demonstrate that speciation in a certain scenario may occur. What is needed now is a shift in focus to identifying more general rules and patterns in the dynamics of speciation. The crucial step in achieving this goal is the development of simple and general dynamical models that can be studied not only numerically but analytically as well. I review some of the existing analytical results on speciation. I first show why the classical theories of speciation by peak shifts across adaptive valleys driven by random genetic drift run into trouble (and into what kind of trouble). Then I describe the Bateson-Dobzhansky-Muller (BDM) model of speciation that does not require overcoming selection. I describe exactly how the probability of speciation, the average waiting time to speciation, and the average duration of speciation depend on the mutation and migration rates, population size, and selection for local adaptation. The BDM model postulates a rather specific genetic architecture of reproductive isolation. I then show exactly why the genetic architecture required by the BDM model should be common in general. Next I consider the multilocus generalizations of the BDM model again concentrating on the qualitative characteristics of speciation such as the average waiting time to speciation and the average duration of speciation. Finally, I consider two models of sympatric speciation in which the conditions for sympatric speciation were found analytically. A number of important conclusions have emerged from analytical studies. Unless the population size is small and the adaptive valley is shallow, the waiting time to a stochastic transition between the adaptive peaks is extremely long. However, if transition does happen, it is very quick. Speciation can occur by mutation and random drift alone with no contribution from selection as different populations accumulate incompatible genes. The importance of mutations and drift in speciation is augmented by the general structure of adaptive landscapes. Speciation can be understood as the divergence along nearly neutral networks and holey adaptive landscapes (driven by mutation, drift, and selection for adaptation to a local biotic and/or abiotic environment) accompanied by the accumulation of reproductive isolation as a by-product. The waiting time to speciation driven by mutation and drift is typically very long. Selection for local adaptation (either acting directly on the loci underlying reproductive isolation via their pleiotropic effects or acting indirectly via establishing a genetic barrier to gene flow) can significantly decrease the waiting time to speciation. In the parapatric case the average actual duration of speciation is much shorter than the average waiting time to speciation. Speciation is expected to be triggered by changes in the environment. Once genetic changes underlying speciation start, they go to completion very rapidly. Sympatric speciation is possible if disruptive selection and/or assortativeness in mating are strong enough. Sympatric speciation is promoted if costs of being choosy are small (or absent) and if linkage between the loci experiencing disruptive selection and those controlling assortative mating is strong.     

Genetic Drift of HIV Populations in Culture

Populations of Human Immunodeficiency Virus type 1 (HIV-1) undergo a surprisingly large amount of genetic drift in infected patients despite very large population sizes, which are predicted to be mostly deterministic. Several models have been proposed to explain this phenomenon, but all of them implicitly assume that the process of virus replication itself does not contribute to genetic drift. We developed an assay to measure the amount of genetic drift for HIV populations replicating in cell culture. The assay relies on creation of HIV populations of known size and measurements of variation in frequency of a neutral allele. Using this assay, we show that HIV undergoes approximately ten times more genetic drift than would be expected from its population size, which we defined as the number of infected cells in the culture. We showed that a large portion of the increase in genetic drift is due to non-synchronous infection of target cells. When infections are synchronized, genetic drift for the virus is only 3-fold higher than expected from its population size. Thus, the stochastic nature of biological processes involved in viral replication contributes to increased genetic drift in HIV populations. We propose that appreciation of these effects will allow better understanding of the evolutionary forces acting on HIV in infected patients.     

The adaptive value of epigenetic mutation: Limited in large but high in small peripheral populations

The fate of populations during range expansions, invasions and environmental changes is largely influenced by their ability to adapt to peripheral habitats. Recent models demonstrate that stable epigenetic modifications of gene expression that occur more frequently than genetic mutations can both help and hinder adaptation in panmictic populations. However, these models do not consider interactions between epimutations and evolutionary forces in peripheral populations. Here, we use mainland–island mathematical models and simulations to explore how the faster rate of epigenetic mutation compared to genetic mutations interacts with migration, selection and genetic drift to affect adaptation in peripheral populations. Our model focuses on cases where epigenetic marks are stably inherited. In a large peripheral population, where the effect of genetic drift is negligible, our analyses suggest that epimutations with random fitness impacts that occur at rates as high as 10^–3 increase local adaptation when migration is strong enough to overwhelm divergent selection. When migration is weak relative to selection and epimutations with random fitness impacts decrease adaptation, we find epigenetic modifications must be highly adaptively biased to enhance adaptation. Finally, in small peripheral populations, where genetic drift is strong, epimutations contribute to adaptation under a wider range of evolutionary conditions. Overall, our results suggest that epimutations can change outcomes of adaptation in peripheral populations, which has implications for understanding conservation and range expansions and contractions, especially of small populations.     

IS THE POPULATION SIZE OF A SPECIES RELEVANT TO ITS EVOLUTION?

Abstract This paper examines aspects of genetic draft, the stochastic force induced by substitutions at one locus on the dynamics of a closely linked locus. Of particular interest is the role of population size on genetic draft. Remarkably, the rate of substitution of weakly selected advantageous mutations decreases with increasing population size, whereas that for deleterious mutations increases with population size. This dependency on population size is the opposite of that for genetic drift. Moreover, these rates are only weakly dependent on population size, again contrary to the strong dependency of drift‐based dynamics. Four models of the strongly selected loci responsible for genetic draft are examined. Three of these exhibit a very weak dependency on population size, which implies that their induced effects will also be weakly dependent on population size. Together, these results suggest that population size and binomial sampling may not be relevant to a species' evolution. If this is the case, then a number of evolutionary conundrums are resolved.     

MIGRATION AND GENETIC DRIFT IN HUMAN POPULATIONS

In humans and many other species, mortality is concentrated early in the life cycle, and is low during the ages of dispersal and reproduction. Yet precisely the opposite is assumed by classical population-genetics models of migration and genetic drift. We introduce a model in which population regulation occurs before migration. In contrast to the conventional model, our model implies that geographic variation in the allele frequencies of newborns should exceed that of adults. Thus, it is important to distinguish genetic variation of adults from that of newborns in species with human-like life cycles. Classical models deal with the variance of group allele frequencies about the allele frequency of a hypothetical “continent” or “foundation stock.” Empirical studies, however, can only measure “reduced” variance, i.e., variance about the current population mean. Our model deals with reduced variance, and should therefore be more relevant to field studies. We show that reduced variance converges faster, which implies that populations are more likely to be at equilibrium with respect to reduced than unreduced variance. To summarize the effect of migration on genetic population structure, we introduce a new parameter, the effective migration rate. Unlike most population structure statistics, it does not confound the effects of mobility and population size, and it should therefore be useful for comparisons between populations. Finally, we show that the difference between geographic variation of newborn and adult allele frequencies contains information about both effective population size and effective migration rate.     

Beads and Dice in a Genetic Drift Exercise

Natural selection driving adaptive changes is a powerful and intuitive explanation for the evolution of the living world around us. Evolution at the molecular level, however, is chiefly ruled by random genetic drift. The idea that an advantageous allele may be lost by chance in a natural population is rather difficult to explore in the classroom. Low-cost and hands-on educational resources are needed to make genetic drift more intuitive among students. In this exercise, we use colored beads and the roll of a die to simulate drift and selection jointly affecting the fate of the genetic variants in an evolving population. Our aim is to teach students that natural selection does not determine but simply influences the fate of advantageous alleles because random genetic drift is always present. We have been using this exercise successfully for over a decade for the Biological Sciences students at the Federal University of Rio de Janeiro.     

Genetic variability and drift load in populations of an aquatic snail

Abstract Population genetic theory predicts that in small populations, random genetic drift will fix and accumulate slightly deleterious mutations, resulting in reduced reproductive output. This genetic load due to random drift (i.e., drift load) can increase the extinction risk of small populations. We studied the relationship between genetic variability (indicator of past population size) and reproductive output in eight isolated, natural populations of the hermaphroditic snail Lymnaea stagnalis . In a common laboratory environment, snails from populations with the lowest genetic variability mature slower and have lower fecundity than snails from genetically more variable populations. This result suggests that past small population size has resulted in increased drift load, as predicted. The relationship between genetic variability and reproductive output is independent of the amount of nonrandom mating within populations. However, reproductive output and the current density of snails in the populations were not correlated. Instead, data from the natural populations suggest that trematode parasites may determine, at least in part, population densities of the snails.     

Study on a Brazilian isolate. I. Population structure and random genetic drift

A number of parameters were evaluated in order to determine the level of isolation of a small Brazilian community existing in partial geographic isolation and thereby evaluate the random genetic drift potential in the population. On a theoretical basis, it is concluded that the probability of genetic drift is low but cannot be excluded. The relatively small proportion of migrants (26%), the limited individual mobility, as given by marital distance (29 +/- 7 km), the mean migrational distance (46 +/- 11 km), the small effective size (122), and the value of the product Neme (26) agree with the possibility of genetic drift in this population. The observed coefficient of inbreeding (0.00239) is lower than that expected (0.0066) for random mating, suggesting some pressures against consanguineous marriage.     

Genetic structuring in fluctuating populations

The effect of genetic drift in spatially distributed dispersal-linked and density-regulated populations is studied in a classical one-locus two-allele system. We analyse emergence of genetic differentiation assuming random drift only, where the noise-like variability is due to demographic stochasticity. We find emergence of clusters of sub-units with local allele fixation and persistence of both alleles in lengthy simulations. We demonstrate that local allele fixation (extending over a number of adjoining spatial sub-units) – without global loss of alleles – may occur when the carrying capacities of local patches are small, under a full range population dynamic regimes, when dispersal rate is small, and when redistribution (through dispersal) does not act as global mixer. These results are novel. The key to the observations is that drift is simultaneously influenced by distance-dependent dispersal, demographic stochasticity and autocorrelated population fluctuations due to delayed-density dependence. These are standard elements of contemporary population models in spatially structured context. With stable large populations, no stochasticity and dispersal limited to neighbours only, our model collapses to the stepping-stone model, while with dispersal being random and global, the model collapses to Wright's island model.     

Microevolution in island forms: the roles of drift and directional selection in morphological divergence of a passerine bird

Abstract.— Theory predicts that in small isolated populations random genetic drift can lead to phenotypic divergence; however this prediction has rarely been tested quantitatively in natural populations. Here we utilize natural repeated island colonization events by members of the avian species complex, Zosterops lateralis , to assess whether or not genetic drift alone is an adequate explanation for the observed patterns of microevolutionary divergence in morphology. Morphological and molecular genetic characteristics of island and mainland populations are compared to test three predictions of drift theory: (1) that the pattern of morphological change is idiosyncratic to each island; (2) that there is concordance between morphological and neutral genetic shifts across island populations; and (3) for populations whose time of colonization is known, that the rate of morphological change is sufficiently slow to be accounted for solely by genetic drift. Our results are not consistent with these predictions. First, the direction of size shifts was consistently towards larger size, suggesting the action of a nonrandom process. Second, patterns of morphological divergence among recently colonized populations showed little concordance with divergence in neutral genetic characters. Third, rate tests of morphological change showed that effective population sizes were not small enough for random processes alone to account for the magnitude of microevolutionary change. Altogether, these three lines of evidence suggest that drift alone is not an adequate explanation of morphological differentiation in recently colonized island Zosterops and therefore we suggest that the observed microevolutionary changes are largely a result of directional natural selection.     

Dynamics of Fst for the island model

F(st) is a measure of genetic differentiation in a subdivided population. Sewall Wright observed that F(st)=1/1+2Nm in a haploid diallelic infinite island model, where N is the effective population size of each deme and m is the migration rate. In demonstrating this result, Wright relied on the infinite size of the population. Natural populations are not infinite and therefore they change over time due to genetic drift. In a finite population, F(st) becomes a random variable that evolves over time. In this work we ask, given an initial population state, what are the dynamics of the mean and variance of F(st) under the finite island model? In application both of these quantities are critical in the evaluation of F(st) data. We show that after a time of order N generations the mean of F(st) is slightly biased below 1/1+2Nm. Further we show that the variance of F(st) is of order 1/d where d is the number of demes in the population. We introduce several new mathematical techniques to analyze coalescent genealogies in a dynamic setting.     

A Statistical Test of a Neutral Model Using the Dynamics of Cytonuclear Disequilibria

In this paper we use cytonuclear disequilibria to test the neutrality of mtDNA markers. The data considered here involve sample frequencies of cytonuclear genotypes subject to both statistical sampling variation as well as genetic sampling variation. First, we obtain the dynamics of the sample cytonuclear disequilibria assuming random drift alone as the source of genetic sampling variation. Next, we develop a test statistic using cytonuclear disequilibria via the theory of generalized least squares to test the random drift model. The null distribution of the test statistic is shown to be approximately chi-squared using an asymptotic argument as well as computer simulation. Power of the test statistic is investigated under an alternative model with drift and selection. The method is illustrated using data from cage experiments utilizing different cytonuclear genotypes of Drosophila melanogaster. A program for implementing the neutrality test is available upon request.     

Development of genetic differentiation and postzygotic isolation in experimental metapopulations of spider mites

We studied the development of genetic differentiation and postzygotic isolation in experimental metapopulations of the two-spotted spider mite, Tetranychus urticae Koch. A genetically diverse starter population was made by allowing six inbred sublines to interbreed. Then three migration patterns were tested: no migration, or one or three immigrants per subpopulation per generation. Variations in four traits were investigated: allozymes, acaricide resistance, diapause, and hatchability. In the allozymes, acaricide resistance, and diapause, genetic variation among subpopulations became high in metapopulations with no migration, but not in the others, which showed that one immigrant is enough to prevent genetic differentiation. Hatchability, which was decreased by interbreeding among the six sublines, gradually recovered in succeeding generations. In metapopulations with no migration, hatchability was reduced again after in-migration at the 15th generation. Different karyotypes or coadapted gene complexes can survive in different subpopulations by genetic drift, and both Wolbachia-infected and -noninfected subpopulations may be selected, which would lead to postzygotic isolation between isolated subpopulations. Our results indicate that sampling effects such as genetic drift or stochastic loss of Wolbachia produce postzygotic isolation in laboratory populations of spider mite.     

Basal metabolic rate of aged mice is affected by random genetic drift but not by selective breeding for high early-age locomotor activity or chronic wheel access

The study of correlated evolution can lead to new insights about the inheritance patterns of complex traits. In order to better understand the evolution of metabolic rate, we tested whether voluntary activity levels and basal metabolic rate are genetically correlated in 90-wk-old mice (Mus domesticus) from replicated lines of the sixteenth generation of an artificial selection experiment for high early-age wheel-running activity. We measured basal rates of oxygen consumption and carbon dioxide production and also computed the respiratory exchange ratio. Half of the individuals from both selected and control lines had been allowed free access to running wheels since 4 wk of age, while the other half were in standard cages. This design allowed testing of hypotheses about (1) genetic correlations between voluntary activity and metabolic rate and (2) lifetime training effects on metabolic traits. Selection group did not have a significant effect on metabolic traits; therefore, this study does not support some of the implicit assumptions of the aerobic capacity model for the evolution of vertebrate energetics. Activity group also did not affect metabolic rate, indicating that lifetime training does not alter basal metabolism in these mice. However, strong replicate line-within-selection-group differences were detected, indicating the occurrence of random genetic drift. In females, this divergence in metabolic traits attributable to drift was independent of body mass, but in males it was probably caused by a correlated response to selection involving body mass. This study is the first to show such effects of random genetic drift on metabolic traits.     

The impact of random frequency-dependent mutations on the average population fitness

ABSTRACT: BACKGROUND: In addition to selection, the process of evolution is accompanied by stochastic effects, such as changing environmental conditions, genetic drift and mutations. Commonly it is believed that without genetic drift, advantageous mutations quickly fixate in a halpoid population due to strong selection and lead to a continuous increase of the average fitness. This conclusion is based on the assumption of constant fitness. However, for frequency dependent fitness, where the fitness of an individual depends on the interactions with other individuals in the population, this does not hold. RESULTS: We propose a mathematical model that allows to understand the consequences of random frequency dependent mutations on the dynamics of an infinite large population. The frequencies of different types change according to the replicator equations and the fitness of a mutant is random and frequency dependent. To capture the interactions of different types, we employ a payoff matrix of variable size and thus are able to accommodate an arbitrary number of mutations. We assume that at most one mutant type arises at a time. The payoff entries to describe the mutant type are random variables obeying a probability distribution which is related to the fitness of the parent type. CONCLUSIONS: We show that a random mutant can decrease the average fitness under frequency dependent selection, based on analytical results for two types, and on simulations for n types. Interestingly, in the case of at most two types the probabilities to increase or decrease the average fitness are independent of the concrete probability density function. Instead, they only depend on the probability that the payoff entries of the mutant are larger than the payoff entries of the parent type.