The Distribution of Gene Frequencies in Populations

Determining gene flow and the influence of selection across the equatorial barrier of the East Pacific Rise in the tube-dwelling polychaete Alvinella pompejana

Background

Comparative phylogeography recently performed on the mitochondrial cytochrome oxidase I (mtCOI) gene from seven deep-sea vent species suggested that the East Pacific Rise fauna has undergone a vicariant event with the emergence of a north/south physical barrier at the Equator 1-2 Mya. Within this specialised fauna, the tube-dwelling polychaete Alvinella pompejana showed reciprocal monophyly at mtCOI on each side of the Equator (9°50'N/7°25'S), suggesting potential, ongoing allopatric speciation. However, the development of a barrier to gene flow is a long and complex process. Secondary contact between previously isolated populations can occur when physical isolation has not persisted long enough to result in reproductive isolation between genetically divergent lineages, potentially leading to hybridisation and subsequent allelic introgression. The present study evaluates the strength of the equatorial barrier to gene flow and tests for potential secondary contact zones between A. pompejana populations by comparing the mtCOI gene with nuclear genes.

Results

Allozyme frequencies and the analysis of nucleotide polymorphisms at three nuclear loci confirmed the north/south genetic differentiation of Alvinella pompejana populations along the East Pacific Rise. Migration was oriented north-to-south with a moderate allelic introgression between the two geographic groups over a narrow geographic range just south of the barrier. Multilocus analysis also indicated that southern populations have undergone demographic expansion as previously suggested by a multispecies approach. A strong shift in allozyme frequencies together with a high level of divergence between alleles and a low number of 'hybrid' individuals were observed between the northern and southern groups using the phosphoglucomutase gene. In contrast, the S-adenosylhomocysteine hydrolase gene exhibited reduced diversity and a lack of population differentiation possibly due to a selective sweep or hitch-hiking.

Conclusions

The equatorial barrier leading to the separation of East Pacific Rise vent fauna into two distinct geographic groups is still permeable to migration, with a probable north-to-south migration route for A. pompejana. This separation also coincides with demographic expansion in the southern East Pacific Rise. Our results suggest that allopatry resulting from ridge offsetting is a common mechanism of speciation for deep-sea hydrothermal vent organisms.

Cryptic variation between species and the basis of hybrid performance

Crosses between closely related species give two contrasting results. One result is that species hybrids may be inferior to their parents, for example, being less fertile [1]. The other is that F1 hybrids may display superior performance (heterosis), for example with increased vigour [2]. Although various hypotheses have been proposed to account for these two aspects of hybridisation, their biological basis is still poorly understood [3]. To gain further insights into this issue, we analysed the role that variation in gene expression may play. We took a conserved trait, flower asymmetry in Antirrhinum, and determined the extent to which the underlying regulatory genes varied in expression among closely related species. We show that expression of both genes analysed, CYC and RAD, varies significantly between species because of cis-acting differences. By making a quantitative genotype-phenotype map, using a range of mutant alleles, we demonstrate that the species lie on a plateau in gene expression-morphology space, so that the variation has no detectable phenotypic effect. However, phenotypic differences can be revealed by shifting genotypes off the plateau through genetic crosses. Our results can be readily explained if genomes are free to evolve within an effectively neutral zone in gene expression space. The consequences of this drift will be negligible for individual loci, but when multiple loci across the genome are considered, we show that the variation may have significant effects on phenotype and fitness, causing a significant drift load. By considering these consequences for various gene-expression-fitness landscapes, we conclude that F1 hybrids might be expected to show increased performance with regard to conserved traits, such as basic physiology, but reduced performance with regard to others. Thus, our study provides a new way of explaining how various aspects of hybrid performance may arise through natural variation in gene activity.

The Dynamics of Finite Haploid Populations with Overlapping Generations. II. the Diffusion Approximation

The dynamics of a gene in a haploid population can be explained approximately by considering the average reproductive value of the gene. The dynamics of the average reproductive value are similar to those of a gene in a population with nonoverlapping generations with the following modifications: The effective population size, N(e), replaces N; the average mutation rates micro* and nu* replace micro and nu; the average overall selection r*+(T-1)s** replaces s; and time is measured in terms of generations, T. The implications of the average selection coefficient to adaptive life histories are discussed.

Surprising fitness consequences of GC-biased gene conversion: I. Mutation load and inbreeding depression

GC-biased gene conversion (gBGC) is a recombination-associated process mimicking selection in favor of G and C alleles. It is increasingly recognized as a widespread force in shaping the genomic nucleotide landscape. In recombination hotspots, gBGC can lead to bursts of fixation of GC nucleotides and to accelerated nucleotide substitution rates. It was recently shown that these episodes of strong gBGC could give spurious signatures of adaptation and/or relaxed selection. There is also evidence that gBGC could drive the fixation of deleterious amino acid mutations in some primate genes. This raises the question of the potential fitness effects of gBGC. While gBGC has been metaphorically termed the "Achilles' heel" of our genome, we do not know whether interference between gBGC and selection merely has practical consequences for the analysis of sequence data or whether it has broader fundamental implications for individuals and populations. I developed a population genetics model to predict the consequences of gBGC on the mutation load and inbreeding depression. I also used estimates available for humans to quantitatively evaluate the fitness impact of gBGC. Surprising features emerged from this model: (i) Contrary to classical mutation load models, gBGC generates a fixation load independent of population size and could contribute to a significant part of the load; (ii) gBGC can maintain recessive deleterious mutations for a long time at intermediate frequency, in a similar way to overdominance, and these mutations generate high inbreeding depression, even if they are slightly deleterious; (iii) since mating systems affect both the selection efficacy and gBGC intensity, gBGC challenges classical predictions concerning the interaction between mating systems and deleterious mutations, and gBGC could constitute an additional cost of outcrossing; and (iv) if mutations are biased toward A and T alleles, very low gBGC levels can reduce the load. A robust prediction is that the gBGC level minimizing the load depends only on the mutational bias and population size. These surprising results suggest that gBGC may have nonnegligible fitness consequences and could play a significant role in the evolution of genetic systems. They also shed light on the evolution of gBGC itself.

Reproductive value and fluctuating selection in an age-structured population

Fluctuations in age structure caused by environmental stochasticity create autocorrelation and transient fluctuations in both population size and allele frequency, which complicate demographic and evolutionary analyses. Following a suggestion of Fisher, we show that weighting individuals of different age by their reproductive value serves as a filter, removing temporal autocorrelation in population demography and evolution due to stochastic age structure. Assuming weak selection, random mating, and a stationary distribution of environments with no autocorrelation, we derive a diffusion approximation for evolution of the reproductive value weighted allele frequency. The expected evolution obeys an adaptive topography defined by the long-run growth rate of the population. The expected fitness of a genotype is its Malthusian fitness in the average environment minus the covariance of its growth rate with that of the population. Simulations of the age-structured model verify the accuracy of the diffusion approximation. We develop statistical methods for measuring the expected selection on the reproductive value weighted allele frequency in a fluctuating age-structured population.

Additive genetic variability and the Bayesian alphabet

The use of all available molecular markers in statistical models for prediction of quantitative traits has led to what could be termed a genomic-assisted selection paradigm in animal and plant breeding. This article provides a critical review of some theoretical and statistical concepts in the context of genomic-assisted genetic evaluation of animals and crops. First, relationships between the (Bayesian) variance of marker effects in some regression models and additive genetic variance are examined under standard assumptions. Second, the connection between marker genotypes and resemblance between relatives is explored, and linkages between a marker-based model and the infinitesimal model are reviewed. Third, issues associated with the use of Bayesian models for marker-assisted selection, with a focus on the role of the priors, are examined from a theoretical angle. The sensitivity of a Bayesian specification that has been proposed (called "Bayes A") with respect to priors is illustrated with a simulation. Methods that can solve potential shortcomings of some of these Bayesian regression procedures are discussed briefly.

Genetic diversification, vicariance, and selection in a polytypic frog

Spatial patterns of heritable phenotypic diversity reflect the relative roles of gene flow and selection in determining geographic variation within a species. We quantified color differentiation and genetic divergence among 20 populations of the red-eyed tree frog (Agalychnis callidryas) in lower Central America. Phylogenetic analyses revealed 5 well-supported mitochondrial DNA clades, and we infer from our phylogeny that geographic barriers have played a large role in structuring populations. Two phenotypic characters varied independently among isolated population groups: Flank coloration distinguished Caribbean from Pacific individuals, whereas leg coloration exhibited a more complex geographic pattern. We detected 3 generalized spatial patterns of genetic and phenotypic diversity: 1) phenotypic differentiation in the presence of historical connectivity, 2) phenotypic uniformity across genetically differentiated regions, and 3) codistribution of genetic and phenotypic characters. These patterns indicate that phenotypic diversification is highly regionalized and can result from spatial variation in localized adaptations, geographic isolation, genetic drift, and/or evolutionary stasis. Although the mode of selection underlying color variation was not the focal objective of this study, we discuss the possible roles of natural and sexual selection in mediating population differentiation. Our study underscores the fact that selection gradients vary across relatively small spatial scales, even in species that occupy relatively homogeneous environments.

On the distribution of recessive embryonic lethals in a natural population ofCoelopa frigida(Fab.)

An account is given of the habitat and ecology of a wrackbed population ofCoelopa frigida(Fab.). The spatial distribution of the third-instar larvae was found to be patchy. This is due to a preference of adult flies for oviposition sites in zones of high temperature within the wrackbed. The relationship between larval density and temperature was found to account only in part for the patchy distribution, a second factor being the formation of family aggregates within each temperature zone. The effect of this type of spatial distribution on the interpretation of genetic sampling methods for the population is discussed.

Samples of third-instar larvae from the wrackbed population have been analysed for the presence of recessive embryonic lethals in three consecutive years from 1957 to 1959. From a total of 528 gametes tested, 44 recessive embryonic lethals were isolated. Cross tests for allelism showed that certain lethals were repeated within samples taken in the same year.

The gross frequency of embryonic lethals is shown to be independent of seasonal changes in population density. Estimates of gene frequency are made for certain individual lethals and these are shown to be greater than expected on the basis of the census size of the population. Possible causes of this discrepancy are examined.

Genetic differentiation of quantitative characters between populations or species: I. Mutation and random genetic drift

Introducing a new genetic model called the discrete allelic-state model, the evolutionary change of genetic variation of quantitative characters within and between populations is studied under the assumption of no selection. This model allows us to study the effects of mutation and random genetic drift in detail. It is shown that when the allelic effects on phenotype are additive, the rate of approach of the genetic variance within populations to the equilibrium value depends only on the effective population size. It is also shown that the distribution of genotypic value often deviates from normality particularly when the effective population size and the number of loci concerned are small. On the other hand, the interpopulational variance increases linearly with time, if the intrapopu-lational variance remains constant. Therefore, the ratio of interpopulational variance to intrapopulational variance can be used for testing the hypothesis of neutral evolution of quantitative characters.

The maintenance of the genetic variability of polygenic characters by heterozygous advantage

The results of a previous paper on the effect of optimizing selection, mutation and drift on a metric character determined by a large number of loci have been extended to include the possibility that, in addition to selection for an optimal value, there may be independent selection in favour of heterozygotes; it is assumed for simplicity that at each locus the heterozygote has the same advantage,s, over each of the homozygotes. Under selection alone there is a stable equilibrium ifs>ca2, wherecis a measure of the intensity of the optimizing selection andais the effect of a gene substitution. Under the additional forces exerted by mutation and by drift due to finite population size each locus behaves independently of the other loci as if it had a heterozygous advantage equal to (s−ca2).

Statistical mechanics and the evolution of polygenic quantitative traits

The evolution of quantitative characters depends on the frequencies of the alleles involved, yet these frequencies cannot usually be measured. Previous groups have proposed an approximation to the dynamics of quantitative traits, based on an analogy with statistical mechanics. We present a modified version of that approach, which makes the analogy more precise and applies quite generally to describe the evolution of allele frequencies. We calculate explicitly how the macroscopic quantities (i.e., quantities that depend on the quantitative trait) depend on evolutionary forces, in a way that is independent of the microscopic details. We first show that the stationary distribution of allele frequencies under drift, selection, and mutation maximizes a certain measure of entropy, subject to constraints on the expectation of observable quantities. We then approximate the dynamical changes in these expectations, assuming that the distribution of allele frequencies always maximizes entropy, conditional on the expected values. When applied to directional selection on an additive trait, this gives a very good approximation to the evolution of the trait mean and the genetic variance, when the number of mutations per generation is sufficiently high (4Nmicro > 1). We show how the method can be modified for small mutation rates (4Nmicro --> 0). We outline how this method describes epistatic interactions as, for example, with stabilizing selection.

Impact of amplified fragment length polymorphism size homoplasy on the estimation of population genetic diversity and the detection of selective loci

AFLP markers are becoming one of the most popular tools for genetic analysis in the fields of evolutionary genetics and ecology and conservation of genetic resources. The technique combines a high-information content and fidelity with the possibility of carrying out genomewide scans. However, a potential problem with this technique is the lack of homology of bands with the same electrophoretic mobility, what is known as fragment-size homoplasy. We carried out a theoretical analysis aimed at quantifying the impact of AFLP homoplasy on the estimation of within- and between-neutral population genetic diversity in a model of a structured finite population with migration among subpopulations. We also investigated the performance of a currently used method (DFDIST software) to detect selective loci from the comparison between genetic differentiation and heterozygosis of dominant molecular markers, as well as the impact of AFLP homoplasy on its effectiveness. The results indicate that the biases produced by homoplasy are: (1) an overestimation of the frequency of the allele determining the presence of the band, (2) an underestimation of the degree of differentiation between subpopulations, and (3) an overestimation or underestimation of the heterozygosis, depending on the allele frequency of the markers. The impact of homoplasy is quickly diminished by reducing the number of fragments analyzed per primer combination. However, substantial biases on the expected heterozygosity (up to 15-25%) may occur with approximately 50-100 fragments per primer combination. The performance of the DFDIST software to detect selective loci from dominant markers is highly dependent on the number of selective loci in the genome and their average effects, the estimate of genetic differentiation chosen to be used in the analysis, and the critical bound probability used to detect outliers. Overall, the results indicate that the software should be used with caution. AFLP homoplasy can produce a reduction of up to 15% in the power to detect selective loci.

The different sources of variation in inbreeding depression, heterosis and outbreeding depression in a metapopulation of Physa acuta

Understanding how parental distance affects offspring fitness, i.e., the effects of inbreeding and outbreeding in natural populations, is a major goal in evolutionary biology. While inbreeding is often associated with fitness reduction (inbreeding depression), interpopulation outcrossing may have either positive (heterosis) or negative (outbreeding depression) effects. Within a metapopulation, all phenomena may occur with various intensities depending on the focal population (especially its effective size) and the trait studied. However, little is known about interpopulation variation at this scale. We here examine variation in inbreeding depression, heterosis, and outbreeding depression on life-history traits across a full-life cycle, within a metapopulation of the hermaphroditic snail Physa acuta. We show that all three phenomena can co-occur at this scale, although they are not always expressed on the same traits. A large variation in inbreeding depression, heterosis, and outbreeding depression is observed among local populations. We provide evidence that, as expected from theory, small and isolated populations enjoy higher heterosis upon outcrossing than do large, open populations. These results emphasize the need for an integrated theory accounting for the effects of both deleterious mutations and genetic incompatibilities within metapopulations and to take into account the variability of the focal population to understand the genetic consequences of inbreeding and outbreeding at this scale.

Adaptive topography of fluctuating selection in a Mendelian population

An adaptive topography is derived for a large randomly mating diploid population under weak density-independent selection in a fluctuating environment. Assuming a stationary distribution of environmental states with no temporal autocorrelation, a diffusion approximation for population size and allele frequency, p, reveals that the expected change in p involves the gradient with respect to p of the stochastic intrinsic rate of increase (the density-independent long-run growth rate), r = r - sigma 2 e/2, where r is the mean Malthusian fitness in the average environment and is the environmental variance in population growth rate. The expected relative fitness of a genotype is its Malthusian fitness in the average environment minus the covariance of its fitness with population growth rate. The influence of fitness correlation between genotypes is illustrated by an analysis of the Haldane-Jayakar model of fluctuating selection on a single diallelic locus, and on two loci with additive effects on a quantitative character.

Comparison of genomic and traditional BLUP-estimated breeding value accuracy and selection response under alternative trait and genomic parameters

Accuracy of prediction of estimated breeding values based on genome-wide markers (GEBV) and selection based on GEBV as compared with traditional Best Linear Unbiased Prediction (BLUP) was examined for a number of alternatives, including low heritability, number of generations of training, marker density, initial distributions, and effective population size (Ne). Results show that the more the generations of data in which both genotypes and phenotypes were collected, termed training generations (TG), the better the accuracy and persistency of accuracy based on GEBV. GEBV excelled for traits of low heritability regardless of initial equilibrium conditions, as opposed to traditional marker-assisted selection, which is not useful for traits of low heritability. Effective population size is critical for populations starting in Hardy-Weinberg equilibrium but not for populations started from mutation-drift equilibrium. In comparison with traditional BLUP, GEBV can exceed the accuracy of BLUP provided enough TG are included. Unfortunately selection rapidly reduces the accuracy of GEBV. In all cases examined, classic BLUP selection exceeds what was possible for GEBV selection. Even still, GEBV could have an advantage over traditional BLUP in cases such as sex-limited traits, traits that are expensive to measure, or can only be measured on relatives. A combined approach, utilizing a mixed model with a second random effect to account for quantitative trait loci in linkage equilibrium (the polygenic effect) was suggested as a way to capitalize on both methodologies.

Distinguishing drift and selection empirically: "the great snail debate" of the 1950s

Biologists and philosophers have been extremely pessimistic about the possibility of demonstrating random drift in nature, particularly when it comes to distinguishing random drift from natural selection. However, examination of a historical case--Maxime Lamotte's study of natural populations of the land snail, Cepaea nemoralis in the 1950s--shows that while some pessimism is warranted, it has been overstated. Indeed, by describing a unique signature for drift and showing that this signature obtained in the populations under study, Lamotte was able to make a good case for a significant role for drift. It may be difficult to disentangle the causes of drift and selection acting in a population, but it is not (always) impossible.

Estimation of the number of individuals founding colonized populations

A method for estimating the number of founding chromosomes in an isolated population is introduced. The method assumes that n/2 diploid individuals are sampled from a population and that alleles are identified at L unlinked loci. The population is assumed to have been founded T generations in the past by individuals carrying c chromosomes drawn randomly from a known source population, which has also been sampled. If c is small and the population grew rapidly after it was founded, accurate estimates of c can be obtained and those estimates are not sensitive to details of the history of population sizes. If c is larger or the population remained small after it was founded, then estimates of c depend on the history of population sizes. We test the performance of our method on simulated data and demonstrate its use on data from a rainbow trout (Oncorhynchus mykiss) population.

Mating systems and the efficacy of selection at the molecular level

Mating systems are thought to play a key role in molecular evolution through their effects on effective population size (N(e)) and effective recombination rate. Because of reduced N(e), selection in self-fertilizing species is supposed to be less efficient, allowing fixation of weakly deleterious alleles or lowering adaptation, which may jeopardize their long-term evolution. Relaxed selection pressures in selfers should be detectable at the molecular level through the analyses of the ratio of nonsynonymous and synonymous divergence, D(n)/D(s), or the ratio of nonsynonymous and synonymous polymorphism, pi(n)/pi(s). On the other hand, selfing reveals recessive alleles to selection (homozygosity effect), which may counterbalance the reduction in N(e). Through population genetics models, this study investigates which process may prevail in natural populations and which conditions are necessary to detect evidence for relaxed selection signature at the molecular level in selfers. Under a wide range of plausible population and mutation parameters, relaxed selection against deleterious mutations should be detectable, but the differences between the two mating systems can be weak. At equilibrium, differences between outcrossers and selfers should be more pronounced using divergence measures (D(n)/D(s) ratio) than using polymorphism data (pi(n)/pi(s) ratio). The difference in adaptive substitution rates between outcrossers and selfers is much less predictable because it critically depends on the dominance levels of new advantageous mutations, which are poorly known. Different ways of testing these predictions are suggested, and implications of these results for the evolution of self-fertilizing species are also discussed.

EXPECTED RELATIVE FITNESS AND THE ADAPTIVE TOPOGRAPHY OF FLUCTUATING SELECTION

Wright's adaptive topography describes gene frequency evolution as a maximization of mean fitness in a constant environment. I extended this to a fluctuating environment by unifying theories of stochastic demography and fluctuating selection, assuming small or moderate fluctuations in demographic rates with a stationary distribution, and weak selection among the types. The demography of a large population, composed of haploid genotypes at a single locus or normally distributed phenotypes, can then be approximated as a diffusion process and transformed to produce the dynamics of population size, N, and gene frequency, p, or mean phenotype, . The expected evolution of p or is a product of genetic variability and the gradient of the long-run growth rate of the population, , with respect to p or . This shows that the expected evolution maximizes , the mean Malthusian fitness in the average environment minus half the environmental variance in population growth rate. Thus, as a function of p or represents an adaptive topography that, despite environmental fluctuations, does not change with time. The haploid model is dominated by environmental stochasticity, so the expected maximization is not realized. Different constraints on quantitative genetic variability, and stabilizing selection in the average environment, allow evolution of the mean phenotype to undergo a stochastic maximization of . Although the expected evolution maximizes the long-run growth rate of the population, for a genotype or phenotype the long-run growth rate is not a valid measure of fitness in a fluctuating environment. The haploid and quantitative character models both reveal that the expected relative fitness of a type is its Malthusian fitness in the average environment minus the environmental covariance between its growth rate and that of the population.

Genetic load in sexual and asexual diploids: segregation, dominance and genetic drift

In diploid organisms, sexual reproduction rearranges allelic combinations between loci (recombination) as well as within loci (segregation). Several studies have analyzed the effect of segregation on the genetic load due to recurrent deleterious mutations, but considered infinite populations, thus neglecting the effects of genetic drift. Here, we use single-locus models to explore the combined effects of segregation, selection, and drift. We find that, for partly recessive deleterious alleles, segregation affects both the deterministic component of the change in allele frequencies and the stochastic component due to drift. As a result, we find that the mutation load may be far greater in asexuals than in sexuals in finite and/or subdivided populations. In finite populations, this effect arises primarily because, in the absence of segregation, heterozygotes may reach high frequencies due to drift, while homozygotes are still efficiently selected against; this is not possible with segregation, as matings between heterozygotes constantly produce new homozygotes. If deleterious alleles are partly, but not fully recessive, this causes an excess load in asexuals at intermediate population sizes. In subdivided populations without extinction, drift mostly occurs locally, which reduces the efficiency of selection in both sexuals and asexuals, but does not lead to global fixation. Yet, local drift is stronger in asexuals than in sexuals, leading to a higher mutation load in asexuals. In metapopulations with turnover, global drift becomes again important, leading to similar results as in finite, unstructured populations. Overall, the mutation load that arises through the absence of segregation in asexuals may greatly exceed previous predictions that ignored genetic drift.

Geographical variation in selection, from phenotypes to molecules

Molecular technologies now allow researchers to isolate quantitative trait loci (QTLs) and measure patterns of gene sequence variation within chromosomal regions containing important polymorphisms. I develop a simulation model to investigate gene sequence evolution within genomic regions that harbor QTLs. The QTLs influence a trait experiencing geographical variation in selection, which is common in nature and produces obvious differentiation at the phenotypic level. Counter to expectations, the simulations suggest that selection can substantially affect quantitative genetic variation without altering the amount and pattern of molecular variation at sites closely linked to the QTLs. Even with large samples of gene sequences, the likelihood of rejecting neutrality is often low. The exception is situations where strong selection is combined with low migration among demes, conditions that may be common in many plant species. The results have implications for gene sequence surveys and, perhaps more generally, for interpreting the apparently weak connection between levels of molecular and quantitative trait variation within species.

Joint effects of self-fertilization and population structure on mutation load, inbreeding depression and heterosis

Both the spatial distribution of organisms and their mode of reproduction have important effects on the change in allele frequencies within populations. In this article, we study the combined effect of population structure and the rate of partial selfing of organisms on the efficiency of selection against recurrent deleterious mutations. Assuming an island model of population structure and weak selection, we express the mutation load, the within- and between-deme inbreeding depression, and heterosis as functions of the frequency of deleterious mutants in the metapopulation; we then use a diffusion model to calculate an expression for the equilibrium probability distribution of this frequency of deleterious mutants. This allows us to derive approximations for the average mutant frequency, mutation load, inbreeding depression, and heterosis, the simplest ones being Equations 35-39 in the text. We find that population structure can help to purge recessive deleterious mutations and reduce the load for some parameter values (in particular when the dominance coefficient of these mutations is <0.2-0.3), but that this effect is reversed when the selfing rate is above a given value. Conversely, within-deme inbreeding depression always decreases, while heterosis always increases, with the degree of population subdivision, for all selfing rates.

An efficient Monte Carlo method for estimating Ne from temporally spaced samples using a coalescent-based likelihood

This article presents an efficient importance-sampling method for computing the likelihood of the effective size of a population under the coalescent model of Berthier et al. Previous computational approaches, using Markov chain Monte Carlo, required many minutes to several hours to analyze small data sets. The approach presented here is orders of magnitude faster and can provide an approximation to the likelihood curve, even for large data sets, in a matter of seconds. Additionally, confidence intervals on the estimated likelihood curve provide a useful estimate of the Monte Carlo error. Simulations show the importance sampling to be stable across a wide range of scenarios and show that the N(e) estimator itself performs well. Further simulations show that the 95% confidence intervals around the N(e) estimate are accurate. User-friendly software implementing the algorithm for Mac, Windows, and Unix/Linux is available for download. Applications of this computational framework to other problems are discussed.

A multilocus analysis of intraspecific competition and stabilizing selection on a quantitative trait

The equilibrium structure of an additive, diallelic multilocus model of a quantitative trait under frequency- and density-dependent selection is derived. The trait is under stabilizing selection and mediates intraspecific competition as induced, for instance, by differential resource utilization. It is assumed that stabilizing selection is weak, but the strength of competition may be arbitrary relative to it. Density dependence is caused by population regulation, which may be of a very general kind. The number and effects of loci are arbitrary, and stabilizing selection is not necessarily symmetric with respect to the range of phenotypic values. All previously studied models of intraspecific competition for a continuum of resources known to the author reduce to a special case of the present model if overall selection is weak. Therefore, in this case our results are applicable as approximations to all these models. Our central result is the (nearly) complete characterization of the equilibrium and stability structure in terms of all parameters. It is derived under the sole assumption that selection is weak enough relative to recombination to ignore linkage disequilibrium. In particular, necessary and sufficient conditions on the strength of competition relative to stabilizing selection are found that ensure the maintenance of multilocus polymorphism and the occurrence of disruptive selection. In this case, explicit formulas for the number of polymorphic loci at equilibrium, the allele frequencies, the genetic variance, and the strength of disruptive selection are obtained. For two loci, the effects of linkage are investigated analytically; for several loci, they are studied numerically.

Effect of breeding structure on population genetic parameters in Drosophila

The breeding structure of populations has been neglected in studies of Drosophila, even though Wright and Dobzhansky's pioneering work on the genetics of natural populations was an attempt to tackle what they regarded as an essential factor in evolution. We compared the breeding structure of sympatric populations of D. melanogaster and D. simulans, two sibling species that are widely used in evolutionary studies. We recorded changes in population density and microsatellite variation patterns for 3 years in a temperate environment of southwestern France. Results were distinctively different in the two species. Maximum population levels in summer and in autumn were similar and fluctuated greatly over years, each species being in turn the most abundant. However, genetic data showed that D. melanogaster made up a continuous breeding population in time and space of practically infinite effective size. D. simulans was fragmented into isolates with a local effective size of between 50 and 350 individuals. A consequence of this was that, while a local sample provided a reliable estimate of regional genetic variability in D. melanogaster, a sample from the same area provided an underestimate of this parameter in D. simulans. In practical terms, this means that variations in breeding structure should be accounted for in sampling schemes and in designing evolutionary genetic models. More generally, this suggests the existence of differential reactions to local environments that might contribute to several genomic differences observed between these species.

Polygenic variation maintained by balancing selection: pleiotropy, sex-dependent allelic effects and G x E interactions

We investigate three alternative selection-based scenarios proposed to maintain polygenic variation: pleiotropic balancing selection, G x E interactions (with spatial or temporal variation in allelic effects), and sex-dependent allelic effects. Each analysis assumes an additive polygenic trait with n diallelic loci under stabilizing selection. We allow loci to have different effects and consider equilibria at which the population mean departs from the stabilizing-selection optimum. Under weak selection, each model produces essentially identical, approximate allele-frequency dynamics. Variation is maintained under pleiotropic balancing selection only at loci for which the strength of balancing selection exceeds the effective strength of stabilizing selection. In addition, for all models, polymorphism requires that the population mean be close enough to the optimum that directional selection does not overwhelm balancing selection. This balance allows many simultaneously stable equilibria, and we explore their properties numerically. Both spatial and temporal G x E can maintain variation at loci for which the coefficient of variation (across environments) of the effect of a substitution exceeds a critical value greater than one. The critical value depends on the correlation between substitution effects at different loci. For large positive correlations (e.g., rho(ij)2>3/4), even extreme fluctuations in allelic effects cannot maintain variation. Surprisingly, this constraint on correlations implies that sex-dependent allelic effects cannot maintain polygenic variation. We present numerical results that support our analytical approximations and discuss our results in connection to relevant data and alternative variance-maintaining mechanisms.

Effect of unsampled populations on the estimation of population sizes and migration rates between sampled populations

Current estimators of gene flow come in two methods; those that estimate parameters assuming that the populations investigated are a small random sample of a large number of populations and those that assume that all populations were sampled. Maximum likelihood or Bayesian approaches that estimate the migration rates and population sizes directly using coalescent theory can easily accommodate datasets that contain a population that has no data, a so-called 'ghost' population. This manipulation allows us to explore the effects of missing populations on the estimation of population sizes and migration rates between two specific populations. The biases of the inferred population parameters depend on the magnitude of the migration rate from the unknown populations. The effects on the population sizes are larger than the effects on the migration rates. The more immigrants from the unknown populations that are arriving in the sample populations the larger the estimated population sizes. Taking into account a ghost population improves or at least does not harm the estimation of population sizes. Estimates of the scaled migration rate M (migration rate per generation divided by the mutation rate per generation) are fairly robust as long as migration rates from the unknown populations are not huge. The inclusion of a ghost population does not improve the estimation of the migration rate M; when the migration rates are estimated as the number of immigrants Nm then a ghost population improves the estimates because of its effect on population size estimation. It seems that for 'real world' analyses one should carefully choose which populations to sample, but there is no need to sample every population in the neighbourhood of a population of interest.

Polygenic Variation Maintained by Balancing Selection: Pleiotropy, Sex-Dependent Allelic Effects and G × E Interactions

We investigate three alternative selection-based scenarios proposed to maintain polygenic variation: pleiotropic balancing selection, G × E interactions (with spatial or temporal variation in allelic effects), and sex-dependent allelic effects. Each analysis assumes an additive polygenic trait with n diallelic loci under stabilizing selection. We allow loci to have different effects and consider equilibria at which the population mean departs from the stabilizing-selection optimum. Under weak selection, each model produces essentially identical, approximate allele-frequency dynamics. Variation is maintained under pleiotropic balancing selection only at loci for which the strength of balancing selection exceeds the effective strength of stabilizing selection. In addition, for all models, polymorphism requires that the population mean be close enough to the optimum that directional selection does not overwhelm balancing selection. This balance allows many simultaneously stable equilibria, and we explore their properties numerically. Both spatial and temporal G × E can maintain variation at loci for which the coefficient of variation (across environments) of the effect of a substitution exceeds a critical value greater than one. The critical value depends on the correlation between substitution effects at different loci. For large positive correlations (e.g., ρij2&gt;3∕4), even extreme fluctuations in allelic effects cannot maintain variation. Surprisingly, this constraint on correlations implies that sex-dependent allelic effects cannot maintain polygenic variation. We present numerical results that support our analytical approximations and discuss our results in connection to relevant data and alternative variance-maintaining mechanisms.

Origin and spread of the 1278insTATC mutation causing Tay-Sachs disease in Ashkenazi Jews: genetic drift as a robust and parsimonious hypothesis

The 1278insTATC is the most prevalent beta-hexosaminidase A ( HEXA) gene mutation causing Tay-Sachs disease (TSD), one of the four lysosomal storage diseases (LSDs) occurring at elevated frequencies among Ashkenazi Jews (AJs). To investigate the genetic history of this mutation in the AJ population, a conserved haplotype (D15S981:175-D15S131:240-D15S1050:284-D15S197:144-D15S188:418) was identified in 1278insTATC chromosomes from 55 unrelated AJ individuals (15 homozygotes and 40 heterozygotes for the TSD mutation), suggesting the occurrence of a common founder. When two methods were used for analysis of linkage disequilibrium (LD) between flanking polymorphic markers and the disease locus and for the study of the decay of LD over time, the estimated age of the insertion was found to be 40+/-12 generations (95% confidence interval: 30-50 generations), so that the most recent common ancestor of the mutation-bearing chromosomes would date to the 8th-9th century. This corresponds with the demographic expansion of AJs in central Europe, following the founding of the Ashkenaz settlement in the early Middle Ages. The results are consistent with the geographic distribution of the main TSD mutation, 1278insTATC being more common in central Europe, and with the coalescent times of mutations causing two other LSDs, Gaucher disease and mucolipidosis type IV. Evidence for the absence of a determinant positive selection (heterozygote advantage) over the mutation is provided by a comparison between the estimated age of 1278insTATC and the probability of the current AJ frequency of the mutant allele as a function of its age, calculated by use of a branching-process model. Therefore, the founder effect in a rapidly expanding population arising from a bottleneck provides a robust parsimonious hypothesis explaining the spread of 1278insTATC-linked TSD in AJ individuals.

A test for deviation from island-model population structure

The neutral island model forms the basis for several estimation models that relate patterns of genetic structure to microevolutionary processes. Estimates of gene flow are often based on this model and may be biased when the model's assumptions are violated. An appropriate test for violations is to compare FST scores for individual loci to a null distribution based on the average FST taken over multiple loci. A parametric bootstrap method is described here based on Wright's beta-distribution to generate null distributions of FST for each locus. These null distributions account for error introduced by sampling populations, individuals and loci, and also biological sources of error, including variable alleles/locus and inbreeding. Confidence limits can be obtained directly from these distributions. Significant deviations from the island model may be the result of selection, deviations from the island model's migration pattern, nonequilibrium conditions, or other deviations from island-model assumptions. Only strong biases are likely to be detected because of the inherently large sampling variation of FST. Nevertheless, a coefficient, Nb, describing bias in the spread of the beta-distribution in units comparable to the gene flow parameter, Nm, can be obtained for each locus. In samples from populations of the butterfly Coenonympha tullia, the loci Idh-1, Mdh-1, Pgi and Pgm showed significantly lower FST than expected.

The evolution of isochores: evidence from SNP frequency distributions

The large-scale systematic variation in nucleotide composition along mammalian and avian genomes has been a focus of the debate between neutralist and selectionist views of molecular evolution. Here we test whether the compositional variation is due to mutation bias using two new tests, which do not assume compositional equilibrium. In the first test we assume a standard population genetics model, but in the second we make no assumptions about the underlying population genetics. We apply the tests to single-nucleotide polymorphism data from noncoding regions of the human genome. Both models of neutral mutation bias fit the frequency distributions of SNPs segregating in low- and medium-GC-content regions of the genome adequately, although both suggest compositional nonequilibrium. However, neither model fits the frequency distribution of SNPs from the high-GC-content regions. In contrast, a simple population genetics model that incorporates selection or biased gene conversion cannot be rejected. The results suggest that mutation biases are not solely responsible for the compositional biases found in noncoding regions.

A 9.1-kb gap in the genome reference map is shown to be a stable deletion/insertion polymorphism of ancestral origin

We show a mute 9.1-kb gap in the human genome reference map, unraveled by RDA studies, to be a worldwide deletion/insertion polymorphism of stable type. The molecular and population data presented suggest its origin from a unique ancestral transposition event in chromosomal region 22q11.2, overlapping the IglambdaV genes at about 450 kb from the cluster of the IglambdaJ-C genes. These findings are not meant to be just another report of a polymorphic marker suitable for population studies. Rather, we wish to stress that a large number of inborn mute gaps may be spread all over the genome and that the many RDA-detected microdeletions already available are efficient tools for the discovery of this otherwise hidden category of genetic variation. Apart from their possible impact on expression of structural genes, mute gaps must be filled for the reference map of our genome to be truly completed.

Evolution of microbial genomes: sequence acquisition and loss

We present models describing the acquisition and deletion of novel sequences in populations of microorganisms. We infer that most novel sequences are neutral. Thus, sequence duplications and gene transfer between organisms sharing the same environment are rarely expected to generate adaptive functions. Two classes of models are considered: (1) a homogeneous population with constant size, and (2) an island model in which the population is subdivided into patches that are in contact through slow migration. Distributions of gene frequencies are derived in a Moran model with overlapping generations. We find that novel, neutral or near-neutral coding sequences in microorganisms will not be fixed globally because they offer large target sizes for mutations and because the populations are so large. At most, such genes may have a transient presence in only a small fraction of the population. Consequently, a microbial population is expected to have a very large diversity of transient neutral gene content. Only sequences that are under strong selection, globally or in individual patches, can be expected to persist. We suggest that genome size is maintained in microorganisms by a quasi-steady state mechanism in which random fluctuations in the effective acquisition and deletion rates result in genome sizes that vary from patch to patch. We assign the genomic identity of a global population to those genes that are required for the participation of patches in the genetic sweeps that maintain the genomic coherence of the population. In contrast, we stress the influence of sequence loss on the isolation and the divergence (speciation) of novel patches from a global population.

Can mutation or fixation biases explain the allele frequency distribution of human single nucleotide polymorphisms (SNPs)?

One of the most abiding controversies in evolutionary biology concerns the role of neutral processes in molecular evolution. A main focus of the debate has been the evolution of isochores, the strong and systematic variation of base composition in mammalian genomes. One set of hypotheses argue that regions of similar GC are owing to localised mutational biases coupled with neutral evolution. The alternatives point to either selection or biased gene conversion as mechanisms to preferentially remove A or T bases, favouring G and C instead. Using a novel method, we compare models including such fixation biases to models based on mutation bias alone, under the assumption that non-coding, non-repetitive human DNA is at compositional equilibrium. While failing to fully explain the allele frequency distributions of recent single nucleotide polymorphism data, we show that the data are best fitted if the mutation bias is assumed to be constant across the genome, while fixation bias varies with GC content. We also attempt to estimate the strength of fixation bias, which increases linearly with increasing GC. Our approximation suggests that this force exists within the necessary parameter range: it is not so weak as to be drowned by random drift, but not so strong as to lead to exclusive use of G and C alone. Together these results demonstrate that mutation bias fails to explain the evolution of isochores, and suggest that either selection or biased gene conversion are involved.

Lethals in finite populations

It has been assumed, based on theoretical studies, that lethals with the level of dominance estimated from experimental studies would have an allele frequency that is virtually independent of effective population size. However, here it is shown numerically that the expected frequency of lethals with low levels of dominance is also dependent on finite population size, although not as much as completely recessive lethals. This finding is significant in determining the standing level of inbreeding depression and the consequent potential for the evolution of self-fertilization. In addition, the architecture of genetic variation influencing inbreeding depression in populations with a history of small size may be of important consequence in endangered species. Finally, it is shown that the loss of lethal genetic variation often occurs much more quickly than the regeneration of lethal variation by mutation. This asymmetry may result in a lower standing genetic variation for inbreeding depression than expected from mutation rates and contemporary population size data.

Selection, load and inbreeding depression in a large metapopulation

The subdivision of a species into local populations causes its response to selection to change, even if selection is uniform across space. Population structure increases the frequency of homozygotes and therefore makes selection on homozygous effects more effective. However, population subdivision can increase the probability of competition among relatives, which may reduce the efficacy of selection. As a result, the response to selection can be either increased or decreased in a subdivided population relative to an undivided one, depending on the dominance coefficient F(ST) and whether selection is hard or soft. Realistic levels of population structure tend to reduce the mean frequency of deleterious alleles. The mutation load tends to be decreased in a subdivided population for recessive alleles, as does the expected inbreeding depression. The magnitude of the effects of population subdivision tends to be greatest in species with hard selection rather than soft selection. Population structure can play an important role in determining the mean fitness of populations at equilibrium between mutation and selection.