Interchromosomal Biased Gene Conversion, Mutation and Selection in a Multigene Family

A mathematical model of the effects of interchromosomal biased gene conversion, mutation and natural selection on a multigene family is developed and analyzed. The model assumes two allelic states at each of n loci. The effects of genetic drift are ignored. The model is developed under the assumption of no recombination, but the analysis shows that, at equilibrium, there is no linkage disequilibrium, which implies that the conclusions are valid for arbitrary recombination among loci. At equilibrium, the balance between mutation, gene conversion and selection depends on the ratio of the mutation rates to the quantity [s + g(2α - 1)/ n], where s is the increment or decrement in relative fitness with each additional copy of one of the alleles, g is the conversion rate, and α is a measure of the bias in favor of one of the alleles. When this quantity is large relative to the mutation rates, the allele that has the net advantage, combining the effects of selection and conversion, will be nearly fixed in the multigene family. A comparison of these results with those from a comparable model of intrachromosomal biased conversion shows that biased interchromosomal conversion leads to approximately the same equilibrium copy number as does intrachromosomal conversion of the same strength. Interchromosomal conversion is much more effective in causing the substitution of one allele by another. The relative frequencies of interchromosomal and intrachromosomal conversion is indicated by the extent of the linkage disequilibrium among the loci in a multigene family.     

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.     

A simple model of linkage disequilibrium and genetic drift in human genomic SNPs: importance of demography and SNP age

We propose a simple model of evolution at a pair of SNP loci, under mutation, genetic drift and recombination. The developed model allows to consider evolution of SNPs under different demographic scenarios. We applied it to SNP data containing polymorphisms spanning 19 gene regions. We initially matched the linkage disequilibrium (LD) data only, and then we reconciled both LD and heterozygosity data. The imbalance between LD and heterozygosity data, observed for some of the analyzed genomic regions, may be a signature of selection acting in these regions. However, assuming neutrality, we obtain estimates of the age of population expansion of modern humans, which are consistent with the consensus estimates. In addition, we are able to estimate the ages of the polymorphisms observed in different genomic regions and we find that they vary widely with respect to their age. Polymorphisms at loci implicated in human disease, seem to be younger than average. Our results supplement the conclusions originally obtained by Reich and co-workers for the same set of data.     

Some additional results about polymorphisms in models of an additive quantitative trait under stabilizing selection

 The existence of two stable, symmetric (allelic frequency 0.5 in each locus) polymorphic states is demonstrated for a two-locus model of an additive quantitative trait under strong Gaussian selection. Linkage disequilibrium at one of the states is negative whereas it is positive at the other state. For a three-locus model, it is shown that in order to maintain a stable polymorphism in all three loci, selection must be sufficiently but not exces- sively strong relative to recombination. Also, positive linkage disequilibrium can be maintained in a three-locus model under stabilizing selection that is not very strong. Received 15 July 1995     

The coalescent process in models with selection, recombination and geographic subdivision

A population genetic model with a single locus at which balancing selection acts and many linked loci at which neutral mutations can occur is analysed using the coalescent approach. The model incorporates geographic subdivision with migration, as well as mutation, recombination, and genetic drift of neutral variation. It is found that geographic subdivision can affect genetic variation even with high rates of migration, providing that selection is strong enough to maintain different allele frequencies at the selected locus. Published sequence data from the alcohol dehydrogenase locus of Drosophila melanogaster are found to fit the proposed model slightly better than a similar model without subdivision.     

The impact of homologous recombination on the generation of diversity in bacteria

The imprint of demographic and selective processes on bacterial population structure needs to be evaluated as deviation from the expectations of an appropriate null neutral model. We explore the impact of varying the population mutation and recombination rates theta and rho on ideal populations, using a recently developed model of neutral drift at multiple loci. This model may be fitted to experimental data to provide estimates of these parameters, and we do so for seven bacterial species (Neisseria meningitidis, Streptococcus pneumoniae, Streptococcus pyogenes, Staphylococcus aureus, Helicobacter pylori, Burkholderia pseudomallei and Bacillus cereus), illustrating that bacterial species vary extensively in these fundamental parameters. Historically, the influence of recombination has often been estimated through its influence on the Index of Association I(A). We show that this may be relatively insensitive to changes in either mutation or recombination rates. It is known that biased sampling can lead to artificially high estimates of I(A). We therefore provide a method of precisely separating the effects of such bias and true linkage between alleles. We also demonstrate that by fitting the neutral model to experimental data, more informative and precise estimates of the relative roles of recombination and mutation may be obtained.     

A Maximum-Likelihood Method to Correct for Allelic Dropout in Microsatellite Data with No Replicate Genotypes

Allelic dropout is a commonly observed source of missing data in microsatellite genotypes, in which one or both allelic copies at a locus fail to be amplified by the polymerase chain reaction. Especially for samples with poor DNA quality, this problem causes a downward bias in estimates of observed heterozygosity and an upward bias in estimates of inbreeding, owing to mistaken classifications of heterozygotes as homozygotes when one of the two copies drops out. One general approach for avoiding allelic dropout involves repeated genotyping of homozygous loci to minimize the effects of experimental error. Existing computational alternatives often require replicate genotyping as well. These approaches, however, are costly and are suitable only when enough DNA is available for repeated genotyping. In this study, we propose a maximum-likelihood approach together with an expectation-maximization algorithm to jointly estimate allelic dropout rates and allele frequencies when only one set of nonreplicated genotypes is available. Our method considers estimates of allelic dropout caused by both sample-specific factors and locus-specific factors, and it allows for deviation from Hardy–Weinberg equilibrium owing to inbreeding. Using the estimated parameters, we correct the bias in the estimation of observed heterozygosity through the use of multiple imputations of alleles in cases where dropout might have occurred. With simulated data, we show that our method can (1) effectively reproduce patterns of missing data and heterozygosity observed in real data; (2) correctly estimate model parameters, including sample-specific dropout rates, locus-specific dropout rates, and the inbreeding coefficient; and (3) successfully correct the downward bias in estimating the observed heterozygosity. We find that our method is fairly robust to violations of model assumptions caused by population structure and by genotyping errors from sources other than allelic dropout. Because the data sets imputed under our model can be investigated in additional subsequent analyses, our method will be useful for preparing data for applications in diverse contexts in population genetics and molecular ecology.     

The variance of sample heterozygosity

The variance of sample heterozygosity, averaged over several loci, is studied in a variety of situations. The variance depends on the sampling implicit in the mating system as well as on that explicit in the loci scored and individuals sampled. There are also effects of allelic distributions over loci and of linkage or linkage disequilibrium between pairs of loci. Results are obtained for populations in drift and mutation balance, for infinite populations undergoing mixed self and random mating, and for finite monoecious populations with or without selfing. For unlinked loci in drift/mutation balance, variances appear to be lessened more by increasing the number of loci scored than by increasing the number of individuals sampled. For infinite populations under the mixed self and random mating system, however, the reverse is true. Methods for estimating the variance of sample heterozygosity are discussed, with attention being paid to unbalanced data where not all loci are scored in all individuals.     

Statistics for Microsatellite Variation Based on Coalescence

The stepwise mutation model, which was at one time chiefly of interest in studying the evolution of protein charge-states, has recently undergone a resurgence of interest with the new popularity of microsatellites as phylogenetic markers. In this paper we describe a method which makes it possible to transfer many population genetics results from the standard infinite sites model to the stepwise mutation model. We study in detail the properties of pairwise differences in microsatellite repeat number between randomly chosen alleles. We show that the problem of finding the expected squared distance between two individuals and finding the variance of the squared distance can be reduced for a wide range of population models to finding the mean and mean square coalescence times. In many cases the distributions of coalescence times have already been studied for infinite site problems. In this study we show how to calculate these quantities for several population models. We also calculate the variance in mean squared pairwise distance (an estimator of mutation rate × population size) for samples of arbitrary size and show that this variance does not approach zero as the sample size increases. We can also use our method to study alleles at linked microsatellite loci. We suggest a metric which quantifies the level of association between loci—effectively a measure of linkage disequilibrium. It is shown that there can be linkage disequilibrium between partially linked loci at mutation–drift equilibrium.     

Insight into the genetic bases of climatic adaptation in experimentally evolving wheat populations

Experimental populations evolving under natural selection represent an interesting tool to study genetic bases of adaptation. Evolution of genes possibly involved in adaptive response can be followed together with the corresponding phenotypic traits. Using experimental populations of hexaploid wheat, we studied the evolution of flowering time, a major adaptive trait that synchronizes the initiation of reproduction and the occurrence of favourable environmental conditions. During 12 generations, three populations were grown in contrasted environments (Vervins North France, Le Moulon near Paris, Toulouse South France) under the influence of natural selection, drift, mutation and recombination. Evolution of diversity at the major gene VRN-1 involved in wheat vernalization response has been analysed jointly with earliness estimated in controlled conditions. Whatever the population, rapid phenotypic changes as well as parallel genotypic variations were observed in the first seven generations, probably as the result of selection acting on this major gene which explains 80% of the trait variation overall. Different allelic combinations at physically unlinked copies of VRN-1 located on distinct genomes (A, B and D) were selected between populations. As theoretically expected, due to population differentiation, a high level of genetic diversity was maintained overall in generation 12. Surprisingly, in two populations out of three, the emergence of new alleles by mutation or migration, coupled with temporal variable selection or frequency-dependent selection, allowed to maintain within-population diversity despite local genetic drift and natural selection. This result may plead for an evolutionary approach of wheat genetic resource conservation.     

Factors affecting polymorphism at microsatellite loci in bread wheat [<Emphasis Type="Italic">Triticum aestivum</Emphasis> (L.) Thell]: effects of mutation processes and physical distance from the centromere

The effects of factors known to influence the level of polymorphism at microsatellite loci were studied using 99 markers and seven lines of bread wheat. Mutational factors as well as indirect selective events shape diversity at these loci. Theory predicts that the selection of favorable alleles should reduce polymorphism at neutral neighboring loci in genomic areas with low recombination rates. In wheat, local recombination rate is positively correlated with physical distance from the centromere. Seventy four loci among the 99 used could be physically located on the chromosome. We studied how the following affected the diversity among a set of inbred lines: the length of the alleles, the motif (CA versus CT), the structure of the loci (perfect versus imperfect) and the chromosomal position of the loci. For each locus, we determined whether the polymorphism observed at a locus was compatible with the Stepwise Mutation Model (SMM) or the Two-Phase Model (TPM). Both the mutation rate and the compatibility with the SMM or the TPM were shown to be variable between loci. Wheat microsatellite loci were found to be more variable when segregating alleles were perfect and had long motifs (composed of many repetitions). Diversity observed at 19 loci was not compatible with the SMM. Loci located in distal regions, with presumably high recombination rates, had longer allele sizes and were more polymorphic than loci located in proximal regions. We conclude that both mutation factors and indirect selective events vary according to the local recombination rate and therefore jointly influence the level of polymorphism at microsatellite loci in wheat.Communicated by J. Dvorak     

Rapid evolutionary escape by large populations from local fitness peaks is likely in nature

Fitness interactions between loci in the genome, or epistasis, can result in mutations that are individually deleterious but jointly beneficial. Such epistasis gives rise to multiple peaks on the genotypic fitness landscape. The problem of evolutionary escape from such local peaks has been a central problem of evolutionary genetics for at least 75 years. Much attention has focused on models of small populations, in which the sequential fixation of valley genotypes carrying individually deleterious mutations operates most quickly owing to genetic drift. However, valley genotypes can also be subject to mutation while transiently segregating, giving rise to copies of the high fitness escape genotype carrying the jointly beneficial mutations. In the absence of genetic recombination, these mutations may then fix simultaneously. The time for this process declines sharply with increasing population size, and it eventually comes to dominate evolutionary behavior. Here we develop an analytic expression for N(crit), the critical population size that defines the boundary between these regimes, which shows that both are likely to operate in nature. Frequent recombination may disrupt high-fitness escape genotypes produced in populations larger than N(crit) before they reach fixation, defining a third regime whose rate again slows with increasing population size. We develop a novel expression for this critical recombination rate, which shows that in large populations the simultaneous fixation of mutations that are beneficial only jointly is unlikely to be disrupted by genetic recombination if their map distance is on the order of the size of single genes. Thus, counterintuitively, mass selection alone offers a biologically realistic resolution to the problem of evolutionary escape from local fitness peaks in natural populations.     

Microsatellites, transposable elements and the X chromosome

Variability at microsatellite (MS) loci is generally perceived as resulting from an interaction between mutation and genetic drift and, to a lesser extent, selection and recombination. Less investigated has been the reason for MS accumulation in genomes. We present here a simple model that could account for the variation in density of MS loci, assuming that they are created either through replication slippage or in association with transposable elements. Microsatellites then evolve under the forces cited above. We use this framework to revisit two results obtained from high-density genomic maps of the human and mouse genomes built with thousands of CA repeats: MS loci are (1) less variable and (2) less dense on the X chromosome than on autosomes. The first result is most likely explained by differential mutation on the X chromosome and the autosomes. The second result may be explained by differential mutation, provided the distributions of MS loci are still not at equilibrium. Selection, acting either directly on large allele size or indirectly on the transposable elements associated with MS, may explain the same result. The framework developed here is a first step toward more rigorous models, calling for additional data.      

Relative roles of mutation and recombination in generating allelic polymorphism at an MHC class II locus in Peromyscus maniculatus

The MHC class II loci encoding cell surface antigens exhibit extremely high allelic polymorphism. There is considerable uncertainty in the literature over the relative roles of recombination and de novo mutation in generating this diversity. We studied class II sequence diversity and allelic polymorphism in two populations of Peromyscus maniculatus, which are among the most widespread and abundant mammals of North America. We find that intragenic recombination (or gene conversion) has been the predominant mode for the generation of allelic polymorphism in this species, with the amount of population recombination per base pair exceeding mutation by at least an order of magnitude during the history of the sample. Despite this, patchwork motifs of sites with high linkage disequilibrium are observed. This does not appear to be consistent with the much larger amount of recombination versus mutation in the history of the sample, unless the recombination rate is highly non-uniform over the sequence or selection maintains certain sites in linkage disequilibrium. We conclude that selection is most likely to be responsible for preserving sequence motifs in the presence of abundant recombination.     

The distribution of allelic effects under mutation and selection

The Price (1970, 1972) equation is applied to the problem of describing the changes in the moments of allelic effects caused by selection, mutation and recombination at loci governing a quantitative genetic character. For comparable assumptions the resulting equations are the same as those obtained by different means by Barton & Turelli (1987; Turelli & Barton, 1989). The Price equation provides a natural framework within which to examine certain kinds of non-additive allelic effects, recombination and assortative mating. The use of the Price equation is illustrated by finding the equilibrium genetic variance under multiplicative dominance and epistasis and under assortative mating at an additive locus. The limitations of the use of recursion equations for the moments of allelic effects are also discussed.     

Effect of gene conversion on variances of digenic identity measures

The variances and covariances of digenic descent measures are studied for a two-locus model incorporating mutation, gene conversion, recombination, drift, and finite sampling. Gene conversion can occur between allelic pairs of genes or between non-allelic pairs on the same or different gametes within individuals. Most interest therefore centers on pairs of genes, and five digenic identity measures are required. The behavior over time of these measures is studied, with an emphasis on the effects of gene conversion. Because of the stochastic nature of the forces of drift, recombination, mutation, and conversion, the actual identity status of gene pairs can vary from expectation among replicate populations. To study this variation we compute the expected variances and covariances of the measures, and show that this requires the introduction of trigenic and quadrigenic measures. Allowing for conversion between genes on different gametes requires a large number of these higher-order measures.     

Linkage disequilibrium between the fragile X mutation and two closely linked CA repeats suggests that fragile X chromosomes are derived from a small number of founder chromosomes

In order to investigate the origin of mutations responsible for the fragile X syndrome, two polymorphic CA repeats, one at 10 kb (FRAXAC2) and the other at 150 kb (DXS548) from the mutation target, were analyzed in normal and fragile X chromosomes. Contrary to observations made in myotonic dystrophy, fragile X mutations were not strongly associated with a single allele at the marker loci. However, significant differences in allelic and haplotypic distributions were observed between normal and fragile X chromosomes, indicating that a limited number of primary events may have been at the origin of most present-day fragile X chromosomes in Caucasian populations. We propose a putative scheme with six founder chromosomes from which most of the observed fragile X–linked haplotypes can be derived directly or by a single event at one of the marker loci, either a change of one repeat unit or a recombination between DXS548 and the mutation target. Such founder chromosomes may have carried a number of CGG repeats in an upper-normal range, from which recurrent multistep expansion mutations have arisen.     

Model-Based Inference of Recombination Hotspots in a Highly,Variable Oncogene

An emergent problem in the study of pathogen evolution is our ability to determine the extent to which their rapidly evolving genomes recombine. Such information is necessary and essential for locating pathogenicity loci using association studies, and it also directs future screening, therapeutic and vaccination strategies. Recombination also complicates the use of phylogenetic approaches to infer evolutionary parameters including selection pressures. Reliable methods that identify the presence of regions of recombination are therefore vital. We illustrate the use of an integrated model-based approach to inferring recombination structure using all available sequences of the highly variable, transforming Kaposis sarcoma-associated herpesviral gene, ORF-K1. This technique learns the parameters of a statistical model that takes recombination hotspots, population genetic effects, and variable rates of mutation into account. As there are no known mechanisms to explain the high mutation rate in this DNA viral gene, recombination may account for some of the variability observed. We infer recombination hotspots in conserved sites such as the tyrosine kinase signaling motif, referred to here as recombination drift, as well as in nonconserved sites, a process described as recombination shift.This article contains online supplementary material.