The Sampling Distribution of Linkage Disequilibrium under an Infinite Allele Model without Selection

The sampling distributions of several statistics that measure the association of alleles on gametes (linkage disequilibrium) are estimated under a two-locus neutral infinite allele model using an efficient Monte Carlo method. An often used approximation for the mean squared linkage disequilibrium is shown to be inaccurate unless the proper statistical conditioning is used. The joint distribution of linkage disequilibrium and the allele frequencies in the sample is studied. This estimated joint distribution is sufficient for obtaining an approximate maximum likelihood estimate of C = 4Nc, where N is the population size and c is the recombination rate. It has been suggested that observations of high linkage disequilibrium might be a good basis for rejecting a neutral model in favor of a model in which natural selection maintains genetic variation. It is found that a single sample of chromosomes, examined at two loci cannot provide sufficient information for such a test if C less than 10, because with C this small, very high levels of linkage disequilibrium are not unexpected under the neutral model. In samples of size 50, it is found that, even when C is as large as 50, the distribution of linkage disequilibrium conditional on the allele frequencies is substantially different from the distribution when there is no linkage between the loci. When conditioned on the number of alleles at each locus in the sample, all of the sample statistics examined are nearly independent of theta = 4N mu, where mu is the neutral mutation rate.     

Maximum likelihood estimation of recombination rates from population data

We describe a method for co-estimating r = C/mu (where C is the per-site recombination rate and mu is the per-site neutral mutation rate) and Theta = 4N(e)mu (where N(e) is the effective population size) from a population sample of molecular data. The technique is Metropolis-Hastings sampling: we explore a large number of possible reconstructions of the recombinant genealogy, weighting according to their posterior probability with regard to the data and working values of the parameters. Different relative rates of recombination at different locations can be accommodated if they are known from external evidence, but the algorithm cannot itself estimate rate differences. The estimates of Theta are accurate and apparently unbiased for a wide range of parameter values. However, when both Theta and r are relatively low, very long sequences are needed to estimate r accurately, and the estimates tend to be biased upward. We apply this method to data from the human lipoprotein lipase locus.     

Estimating effective population size from samples of sequences: a bootstrap Monte Carlo integration method.

We would like to use maximum likelihood to estimate parameters such as the effective population size N(e) or, if we do not know mutation rates, the product 4N(e) mu of mutation rate per site and effective population size. To compute the likelihood for a sample of unrecombined nucleotide sequences taken from a random-mating population it is necessary to sum over all genealogies that could have led to the sequences, computing for each one the probability that it would have yielded the sequences, and weighting each one by its prior probability. The genealogies vary in tree topology and in branch lengths. Although the likelihood and the prior are straightforward to compute, the summation over all genealogies seems at first sight hopelessly difficult. This paper reports that it is possible to carry out a Monte Carlo integration to evaluate the likelihoods approximately. The method uses bootstrap sampling of sites to create data sets for each of which a maximum likelihood tree is estimated. The resulting trees are assumed to be sampled from a distribution whose height is proportional to the likelihood surface for the full data. That it will be so is dependent on a theorem which is not proven, but seems likely to be true if the sequences are not short. One can use the resulting estimated likelihood curve to make a maximum likelihood estimate of the parameter of interest, N(e) or of 4N(e) mu. The method requires at least 100 times the computational effort required for estimation of a phylogeny by maximum likelihood, but is practical on today's work stations. The method does not at present have any way of dealing with recombination.     

Using molecular markers with high mutation rates to obtain estimates of relative population size and to distinguish the effects of gene flow and mutation: a demonstration using data from endemic Mauritian skinks

We propose a method of analysing genetic data to obtain separate estimates of the size (N(p)) and migration rate (m(p)) for the sampled populations, without precise prior knowledge of mutation rates at each locus ( micro(L)). The effects of migration and mutation can be distinguished because high migration has the effect of reducing genetic differentiation across all loci, whereas a high mutation rate will only affect the locus in question. The method also takes account of any differences between the spectra of immigrant alleles and of new mutant alleles. If the genetic data come from a range of population sizes, and the loci have a range of mutation rates, it is possible to estimate the relative sizes of the different N(p) values, and likewise the m(p) and the micro(L). Microsatellite loci may also be particularly appropriate because loci with a high mutation rate can reach mutation-drift-migration equilibrium more quickly, and because the spectra of mutants arriving in a population can be particularly distinct from the immigrants. We demonstrate this principle using a microsatellite data set from Mauritian skinks. The method identifies low gene flow between a putative new species and populations of its sister species, whereas the differentiation of two other populations is attributed to small population size. These distinct interpretations were not readily apparent from conventional measures of genetic differentiation and gene diversity. When the method is evaluated using simulated data sets, it correctly distinguishes low gene flow from small population size. Loci that are not at mutation-migration-drift equilibrium can distort the parameter estimates slightly. We discuss strategies for detecting and overcoming this effect.     

Simple method for analyzing the pattern of DNA polymorphism and its application to SNP data of human

In order to analyze the pattern of DNA polymorphism in detail, we have developed a simple method using a new statistic theta(i) which estimates 4Nmu from the number of segregating sites whose allelic nucleotide frequency is i/n among n DNA sequences, where N is the effective population size and mu is the mutation rate per generation per nucleotide site. Under the assumption that mutations are selectively neutral and a population size is constant, the expectation of theta(i) is equal to that of theta, which estimates 4Nmu from the number of segregating sites, so that the distribution of theta(i) is flat. Therefore, the departure of the distribution of theta(i) from the horizontal line, which represents the value of theta, reflects change in population size and natural selection. Results of the coalescent simulation show that the distributions of theta(i) in the populations which experienced expansion and reduction are U-shaped and upside-down U-shaped, respectively. And the distributions of theta(i) in some populations that experienced bottleneck are W-shaped. Furthermore, we have applied this method to the SNP data in the International HapMap Project. Results of data analyses show that the distributions of theta(i) in the CEU (European), CHB and JPT (Asian) populations are different from that in the YRI population (African). From these results of data analyses in nuclear DNA and the pattern of polymorphism in human mitochondrial DNA already known, we infer that the CEU, CHB and JPT populations experienced the bottleneck.     

Heteroplasmy of Short Tandem Repeats in Mitochondrial DNA of Atlantic Cod, Gadus Morhua

The mitochondrial DNA of the Atlantic cod (Gadus morhua) contains a tandem array of 40-bp repeats in the D-loop region of the molecule. Variation among molecules in the copy number of these repeats results in mtDNA length variation and heteroplasmy (the presence of more than one form of mtDNA in an individual). In a sample of fish collected from different localities around Iceland and off George's Bank, each individual was heteroplasmic for two or more mtDNAs ranging in repeat copy number from two (common) to six (rare). An earlier report on mtDNA heteroplasmy in sturgeon (Acipenser transmontanus) presented a competitive displacement model for length mutations in mtDNAs containing tandem arrays and the cod data deviate from this model. Depending on the nature of putative secondary structures and the location of D-loop strand termination, additional mechanisms of length mutation may be needed to explain the range of mtDNA length variants maintained in these populations. The balance between genetic drift and mutation in maintaining this length polymorphism is estimated through a hierarchical analysis of diversity of mtDNA length variation in the Iceland samples. Eighty percent of the diversity lies within individuals, 8% among individuals and 12% among localities. An estimate of theta = 2N(eo) mu greater than 1 indicates that this system is characterized by a high mutation rate and is governed primarily by deterministic dynamics. The sequences of repeat arrays from fish collected in Norway, Iceland and George's Bank show no nucleotide variation suggesting that there is very little substructuring to the North Atlantic cod population.     

DNA sequence variation and the recombinational landscape in Drosophila pseudoobscura: a study of the second chromosome.

The relationship between rates of recombination and DNA sequence polymorphism was analyzed for the second chromosome of Drosophila pseudoobscura. We constructed integrated genetic and physical maps of this chromosome using molecular markers at 10 loci spanning most of its physical length. The total length of the map was 128.2 cM, almost twice that of the homologous chromosome arm (3R) in D. melanogaster. There appears to be very little centromeric suppression of recombination, and rates of recombination are quite uniform across most of the chromosome. Levels of sequence variation (theta(W), based on the number of segregating sites) at seven loci (tropomyosin 1, Rhodopsin 3, Rhodopsin 1, bicoid, Xanthine dehydrogenase, Myosin light chain 1, and ribosomal protein 49) varied from 0.0036 to 0.0167. Generally consistent with earlier studies, the average estimate of theta(W) at total sites is 1.5-fold higher than that in D. melanogaster, while average theta(W) at silent sites is almost 3-fold higher. These estimates of variation were analyzed in the context of a background selection model under the same parameters of mutation rate and selection as have been proposed for D. melanogaster. It is likely that a significant fraction of the higher level of sequence variation in D. pseudoobscura can be explained by differences in regional rates of recombination rather than a larger species-level effective population size. However, the distribution of variation among synonymous, nonsynonymous, and noncoding sites appears to be quite different between the species, making direct comparisons of neutral variation, and hence inferences about effective population size, difficult. Tajima's D statistics for 6 out of the 7 loci surveyed are negative, suggesting that D. pseudoobscura may have experienced a rapid population expansion in the recent past or, alternatively, that slightly deleterious mutations constitute an important component of standing variation in this species.     

Estimating effective population size or mutation rate with microsatellites

Microsatellites are short tandem repeats that are widely dispersed among eukaryotic genomes. Many of them are highly polymorphic; they have been used widely in genetic studies. Statistical properties of all measures of genetic variation at microsatellites critically depend upon the composite parameter theta = 4Nmicro, where N is the effective population size and micro is mutation rate per locus per generation. Since mutation leads to expansion or contraction of a repeat number in a stepwise fashion, the stepwise mutation model has been widely used to study the dynamics of these loci. We developed an estimator of theta, theta; (F), on the basis of sample homozygosity under the single-step stepwise mutation model. The estimator is unbiased and is much more efficient than the variance-based estimator under the single-step stepwise mutation model. It also has smaller bias and mean square error (MSE) than the variance-based estimator when the mutation follows the multistep generalized stepwise mutation model. Compared with the maximum-likelihood estimator theta; (L) by, theta; (F) has less bias and smaller MSE in general. theta; (L) has a slight advantage when theta is small, but in such a situation the bias in theta; (L) may be more of a concern.     

Bayesian estimation of range for microsatellite loci

Microsatellite loci have become important in population genetics because of their high level of polymorphism in natural populations, very frequent occurrence throughout the genome, and apparently high mutation rate. Observed repeat numbers (alleles size) in natural populations and expectations based on computer simulations suggest that the range of repeat numbers at a microsatellite locus is restricted. This range is a key parameter that should be properly estimated in order to proceed with calculations of divergence times in phylogenetic studies and to better investigate the within- and between-population variability. The 'plug-in' estimate of range based on the minimum and maximum value observed in a sample is not satisfactory because of the relatively large number of alleles in comparison with typical sample sizes. In this paper, a set of data from 30 dinucleotide microsatellite loci is analysed under the assumption of independence among loci. Bayesian inference on range for one locus is obtained by assuming that constraints on range values exist as sharp bounds. Closed-form calculations and robustness revealed by our analysis suggest that the proposed Bayesian approach might be routinely used by researchers to classify microsatellite loci according to the estimated value of their allelic range.     

Microsatellite variation and recombination rate in the human genome

Background (purifying) selection on deleterious mutations is expected to remove linked neutral mutations from a population, resulting in a positive correlation between recombination rate and levels of neutral genetic variation, even for markers with high mutation rates. We tested this prediction of the background selection model by comparing recombination rate and levels of microsatellite polymorphism in humans. Published data for 28 unrelated Europeans were used to estimate microsatellite polymorphism (number of alleles, heterozygosity, and variance in allele size) for loci throughout the genome. Recombination rates were estimated from comparisons of genetic and physical maps. First, we analyzed 61 loci from chromosome 22, using the complete sequence of this chromosome to provide exact physical locations. These 61 microsatellites showed no correlation between levels of variation and recombination rate. We then used radiation-hybrid and cytogenetic maps to calculate recombination rates throughout the genome. Recombination rates varied by more than one order of magnitude, and most chromosomes showed significant suppression of recombination near the centromere. Genome-wide analyses provided no evidence for a strong positive correlation between recombination rate and polymorphism, although analyses of loci with at least 20 repeats suggested a weak positive correlation. Comparisons of microsatellites in lowest-recombination and highest-recombination regions also revealed no difference in levels of polymorphism. Together, these results indicate that background selection is not a major determinant of microsatellite variation in humans.     

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     

Genetic differentiation and estimation of effective population size and migration rates in two sympatric ecotypes of the marine snail Littorina saxatilis

On exposed rocky shores in Galicia (northwest Spain), a striking polymorphism exists between two ecotypes (RB and SU) of Littorina saxatilis that occupy different levels of the intertidal zone and exhibit an incomplete reproductive isolation. The setting has been suggested to represent ongoing sympatric speciation by ecological adaptation of the two ecotypes to their respective habitats. In this article we address whether or not the ecotypes have developed their own population structures in response to the rigors of their corresponding environments and life histories. We analyzed four to five allozymic loci from three surveys of the same sites, spanning a 14-year period. An experimental design including three localities with two transects per locality and three shore levels allowed studying temporal and spatial population structure and estimation of effective population sizes (N(e)), neighborhood sizes (N(n)), and migration rates (m). Genetic differentiation was significantly lower in RB populations (theta(ST) = 0.067) than in SU ones (theta(ST) = 0.124). Mean estimates of N(e), N(n), and m did not differ significantly between ecotypes, but local ecotype differences in migration between the two closest localities (larger migration rates in RB than in SU populations) could explain the pattern in population differentiation.     

Reduced variation on the chicken Z chromosome

Understanding the population genetic factors that shape genome variability is pivotal to the design and interpretation of studies using large-scale polymorphism data. We analyzed patterns of polymorphism and divergence at Z-linked and autosomal loci in the domestic chicken (Gallus gallus) to study the influence of mutation, effective population size, selection, and demography on levels of genetic diversity. A total of 14 autosomal introns (8316 bp) and 13 Z-linked introns (6856 bp) were sequenced in 50 chicken chromosomes from 10 highly divergent breeds. Genetic variation was significantly lower at Z-linked than at autosomal loci, with one segregating site every 39 bp at autosomal loci (theta(W) = 5.8 +/- 0.8 x 10(-3)) and one every 156 bp on the Z chromosome (theta(W) = 1.4 +/- 0.4 x 10(-3)). This difference may in part be due to a low male effective population size arising from skewed reproductive success among males, evident both in the wild ancestor-the red jungle fowl-and in poultry breeding. However, this effect cannot entirely explain the observed three- to fourfold reduction in Z chromosome diversity. Selection, in particular selective sweeps, may therefore have had an impact on reducing variation on the Z chromosome, a hypothesis supported by the observation of heterogeneity in diversity levels among loci on the Z chromosome and the lower recombination rate on Z than on autosomes. Selection on sex-linked genes may be particularly important in organisms with female heterogamety since the heritability of sex-linked sexually antagonistic alleles advantageous to males is improved when fathers pass a Z chromosome to their sons.     

Estimating the contribution of mutation, recombination and gene conversion in the generation of haplotypic diversity

Recombination occurs through both homologous crossing over and homologous gene conversion during meiosis. The contribution of recombination relative to mutation is expected to be dramatically reduced in inbreeding organisms. We report coalescent-based estimates of the recombination parameter (rho) relative to estimates of the mutation parameter (theta) for 18 genes from the highly self-fertilizing grass, wild barley, Hordeum vulgare ssp. spontaneum. Estimates of rho/theta are much greater than expected, with a mean rho/theta approximately 1.5, similar to estimates from outcrossing species. We also estimate rho with and without the contribution of gene conversion. Genotyping errors can mimic the effect of gene conversion, upwardly biasing estimates of the role of conversion. Thus we report a novel method for identifying genotyping errors in nucleotide sequence data sets. We show that there is evidence for gene conversion in many large nucleotide sequence data sets including our data that have been purged of all detectable sequencing errors and in data sets from Drosophila melanogaster, D. simulans, and Zea mays. In total, 13 of 27 loci show evidence of gene conversion. For these loci, gene conversion is estimated to contribute an average of twice as much as crossing over to total recombination.     

Rates of DNA sequence evolution are not sex-biased in Drosophila melanogaster and D. simulans

To determine whether male- or female-biased mutation rates have affected the molecular evolution of Drosophila melanogaster and D. simulans, we calculated the male-to-female ratio of germline cell divisions ([symbol: see text]) from germline generation data and the male-to-female ratio of mutation rate ([symbol: see text]) by comparing chromosomal levels of nucleotide divergence. We found that the ratio of germline cell divisions changes from indicating a weak female bias to indicating a weak male bias as the age of reproduction increases. The range of [symbol: see text] values that we observed, however, does not lead us to expect much, if any, difference in mutation rate between the sexes. Silent and intron nucleotide divergence were compared between nine loci on the X chromosome and nine loci on the second and third chromosomes. The average levels of nucleotide divergence were not significantly different across the chromosomes, although both silent and intron sites show a trend toward slightly more divergence on the X. These results indicate a lack of sex- or chromosome-biased molecular evolution in D. melanogaster and D. simulans.      

Minisatellite mutational processes reduce Fst estimates

We have used a new method for binning minisatellite alleles (semi-automated allele aggregation) and report the extent of population diversity detectable by eleven minisatellite loci in 2,689 individuals from 19 human populations distributed widely throughout the world. Whereas population relationships are consistent with those found in other studies, our estimate of genetic differentiation (F(st)) between populations is less than 8%, which is lower than comparative estimates of between 10%-15% obtained by using other sources of polymorphism data. We infer that mutational processes are involved in reducing F(st) estimates from minisatellite data because, first, the lowest F(st) estimates are found at loci showing autocorrelated frequencies among alleles of similar size and, second, F(st) declines with heterozygosity but by more than predicted assuming simple models of mutation. These conclusions are consistent with the view that minisatellites are subject to selective or mutational constraints in addition to those expected under simple step-wise mutation models.     

Pairwise Comparisons of Mitochondrial DNA Sequences in Stable and Exponentially Growing Populations

We consider the distribution of pairwise sequence differences of mitochondrial DNA or of other nonrecombining portions of the genome in a population that has been of constant size and in a population that has been growing in size exponentially for a long time. We show that, in a population of constant size, the sample distribution of pairwise differences will typically deviate substantially from the geometric distribution expected, because the history of coalescent events in a single sample of genes imposes a substantial correlation on pairwise differences. Consequently, a goodness-of-fit test of observed pairwise differences to the geometric distribution, which assumes that each pairwise comparison is independent, is not a valid test of the hypothesis that the genes were sampled from a panmictic population of constant size. In an exponentially growing population in which the product of the current population size and the growth rate is substantially larger than one, our analytical and simulation results show that most coalescent events occur relatively early and in a restricted range of times. Hence, the "gene tree" will be nearly a "star phylogeny" and the distribution of pairwise differences will be nearly a Poisson distribution. In that case, it is possible to estimate r, the population growth rate, if the mutation rate, mu, and current population size, N0, are assumed known. The estimate of r is the solution to ri/mu = ln(N0r) - gamma, where i is the average pairwise difference and gamma approximately 0.577 is Euler's constant.     

Molecular evidence for selection on female color polymorphism in the damselfly Ischnura graellsii

The significance of female color polymorphism in Odonata remains controversial despite many field studies. The importance of random factors (founder effects, genetic drift and migration) versus selective forces for the maintenance of this polymorphism is still discussed. In this study, we specifically test whether the female color polymorphism of Ischnura graellsii (Odonata, Coenagrionidae) is under selection in the wild. We compared the degree of genetic differentiation based on RAPD markers (assumed to be neutral) with the degree of differentiation based on color alleles. Weir and Cockerham's theta values showed a significant degree of population differentiation for both sets of loci (RAPD and color alleles) but the estimated degree of population differentiation (theta) was significantly greater for the set of RAPD loci. This result shows that some sort of selection contributes to the maintenance of similar color morph frequencies across the studied populations. Our results combined with those of previous field studies suggest that at least in some I. graellsii populations, density-dependent mechanisms might help to prevent the loss of this polymorphism but cannot explain the similarity in morph frequencies among populations.     

Combined effects of bottlenecks and selfing in populations of Corella eumyota, a recently introduced sea squirt in the English Channel

The success of an exotic species depends notably on its capacity to initiate a new population from a few individuals, to survive genetic bottlenecks and to adapt locally. Species with multiple reproductive strategies (e.g. mixed-mating system with both self- and cross-fertilization) can be efficient colonizers. Herein we focus on Corella eumyota , an exotic ascidian that has rapidly invaded English Channel coasts in recent years. Interestingly, this brooding hermaphroditic ascidian is capable of self-fertilization in the laboratory. We developed 12 microsatellite markers from an enriched library of genomic DNA to investigate the level of inbreeding and selfing in two putatively native populations (South Africa, N  = 34, and New Zealand, N  = 28) and to examine if founder effects were possibly associated with its recent introduction in two French populations (Perros-Guirec, N  = 22 and Brest; N  = 25). Genetic polymorphism was very low in both native populations (i.e. less than 60% of the loci were polymorphic) and even lower in the introduced populations, one of which was monomorphic at all loci, suggesting a recent bottleneck. F _is and a new method based on multi-locus heterozygosity were used to provide estimates of inbreeding. A high selfing rate was inferred in the South Africa population with both methods ( s  = 0.90), whereas in the other native population (New Zealand) a lower but significant estimate of selfing rate ( s  = 0.29) was obtained with the multi-locus method. This variability of population selfing rate might be explained by a mixed-mating system, allowing C. eumyota to reproduce through inbreeding and outbreeding according to mating possibilities; this trait may have favoured the rapid establishment of new populations in Europe.     

Grinding up wheat: a massive loss of nucleotide diversity since domestication

Several demographic and selective events occurred during the domestication of wheat from the allotetraploid wild emmer (Triticum turgidum ssp. dicoccoides). Cultivated wheat has since been affected by other historical events. We analyzed nucleotide diversity at 21 loci in a sample of 101 individuals representing 4 taxa corresponding to representative steps in the recent evolution of wheat (wild, domesticated, cultivated durum, and bread wheats) to unravel the evolutionary history of cultivated wheats and to quantify its impact on genetic diversity. Sequence relationships are consistent with a single domestication event and identify 2 genetically different groups of bread wheat. The wild group is not highly polymorphic, with only 212 polymorphic sites among the 21,720 bp sequenced, and, during domestication, diversity was further reduced in cultivated forms--by 69% in bread wheat and 84% in durum wheat--with considerable differences between loci, some retaining no polymorphism at all. Coalescent simulations were performed and compared with our data to estimate the intensity of the bottlenecks associated with domestication and subsequent selection. Based on our 21-locus analysis, the average intensity of domestication bottleneck was estimated at about 3--giving a population size for the domesticated form about one third that of wild dicoccoides. The most severe bottleneck, with an intensity of about 6, occurred in the evolution of durum wheat. We investigated whether some of the genes departed from the empirical distribution of most loci, suggesting that they might have been selected during domestication or breeding. We detected a departure from the null model of demographic bottleneck for the hypothetical gene HgA. However, the atypical pattern of polymorphism at this locus might reveal selection on the linked locus Gsp1A, which may affect grain softness--an important trait for end-use quality in wheat.