Testing models of selection and demography in Drosophila simulans

We analyze patterns of nucleotide variability at 15 X-linked loci and 14 autosomal loci from a North American population of Drosophila simulans. We show that there is significantly more linkage disequilibrium on the X chromosome than on chromosome arm 3R and much more linkage disequilibrium on both chromosomes than expected from estimates of recombination rates, mutation rates, and levels of diversity. To explore what types of evolutionary models might explain this observation, we examine a model of recurrent, nonoverlapping selective sweeps and a model of a recent drastic bottleneck (e.g., founder event) in the demographic history of North American populations of D. simulans. The simple sweep model is not consistent with the observed patterns of linkage disequilibrium nor with the observed frequencies of segregating mutations. Under a restricted range of parameter values, a simple bottleneck model is consistent with multiple facets of the data. While our results do not exclude some influence of selection on X vs. autosome variability levels, they suggest that demography alone may account for patterns of linkage disequilibrium and the frequency spectrum of segregating mutations in this population of D. simulans.     

A Two-Locus Neutrality Test: Applications to Humans, E. COLI and Lodgepole Pine

The expected disequilibrium between two loci with k alleles at one locus and l alleles at the other is given for a sample of size n drawn from a population under neutrality equilibrium. Three different measures of disequilibrium with 95% intervals are tabulated for combinations of n, k, l and 4Nc, where N is the effective population size and c is the amount of recombination between the loci. The extent and pattern of disequilibrium are strongly dependent upon 4Nc and are somewhat dependent on n, k and l. The 95% intervals are large, particularly for low numbers of alleles and low values of 4Nc. As examples, observed disequilibrium from histocompatibility loci in humans (HLA) and electrophoretic data in E. coli and lodgepole pine were compared to these theoretical values. Using information about recombination rates, the HLA data showed more disequilibrium than neutrality expectations, whereas electrophoretic data from E. coli and lodgepole pine had somewhat less disequilibrium than neutrality expectations.     

Analytical results concerning linkage disequilibrium in models with genetic transformation and conjugation

Expressions are obtained for the expected levels of linkage disequilibrium under three different equilibrium neutral models that make different assumptions about how recombination takes place. A transformation model is considered in which exchange events involve only one locus at a time. Two conjugation models are considered one with a linear genome and one with a circular genome. In the conjugation models large blocks of genes can be transferred with each conjugation. Consistent with published simulation results, it is found that if the transformation rate per locus is more than twenty times the mutation rate per locus, then the levels of linkage disequilibrium are quite low. If the number of loci being sampled is greater than 10, conjugation with a circular genome can be considerably more effective than transformation in reducing linkage disequilibrium. When recombination rates are high, expected linkage disequilibrium is shown to be proportional to the inverse of the transformation rate (or conjugation rate.)     

Hitchhiking and recombination in birds: evidence from Mhc-linked and unlinked loci in Red-winged Blackbirds (Agelaius phoeniceus)

Hitchhiking phenomena and genetic recombination have important consequences for a variety of fields for which birds are model species, yet we know virtually nothing about naturally occurring rates of recombination or the extent of linkage disequilibrium in birds. We took advantage of a previously sequenced cosmid clone from Red-winged Blackbirds (Agelaius phoeniceus) bearing a highly polymorphic Mhc class II gene, Agph-DABI, to measure the extent of linkage disequilibrium across approximately 40 kb of genomic DNA and to determine whether non-coding nucleotide diversity was elevated as a result of physical proximity to a target of balancing selection. Application of coalescent theory predicts that the hitchhiking effect is enhanced by the larger effective population size of blackbirds compared with humans, despite the presumably higher rates of recombination in birds. We surveyed sequence polymorphism at three Mhc-linked loci occurring 1.5-40 kb away from Agph-DAB1 and found that nucleotide diversity was indistinguishable from that found at three presumably unlinked, non-coding introns (beta-actin intron 2, beta-fibrinogen intron 7 and rhodopsin intron 2). Linkage disequilibrium as measured by Lewontin's D' was found only across a few hundred base pairs within any given locus, and was not detectable among any Mhc-linked loci. Estimated rates of the per site recombination rate p derived from three different analytical methods suggest that the amounts of recombination in blackbirds are up to two orders of magnitude higher than in humans, a discrepancy that cannot be explained entirely by the higher effective population size of blackbirds relative to humans. In addition, the ratio of the number of estimated recombination events per mutation frequently exceeds 1, as in Drosophila, again much higher than estimates in humans. Although the confidence limits of the blackbird estimates themselves span an order of magnitude, these data suggest that in blackbirds the hitchhiking effect for this region is negligible and may imply that the per site per individual recombination rate is high, resembling those of Drosophila more than those of humans.     

Multilocus patterns of nucleotide polymorphism and the demographic history of Populus tremula

I have studied nucleotide polymorphism and linkage disequilibrium using multilocus data from 77 fragments, with an average length of fragments of 550 bp, in the deciduous tree Populus tremula (Salicaceae). The frequency spectrum across loci showed a modest excess of mutations segregating at low frequency and a marked excess of high-frequency derived mutations at silent sites, relative to neutral expectations. These excesses were also seen at replacement sites, but were not so pronounced for high-frequency derived mutations. There was a marked excess of low-frequency mutations at replacement sites, likely indicating deleterious amino acid-changing mutations that segregate at low frequencies in P. tremula. I used approximate Bayesian computation (ABC) to evaluate a number of different demographic scenarios and to estimate parameters for the best-fitting model. The data were found to be consistent with a historical reduction in the effective population size of P. tremula through a bottleneck. The timing inferred for this bottleneck is largely consistent with geological data and with data from several other long-lived plant species. The results show that P. tremula harbors substantial levels of nucleotide polymorphism with the posterior mode of the scaled mutation rate, = 0.0177 across loci. The ABC analyses also provided an estimate of the scaled recombination rate that indicates that recombination rates in P. tremula are likely to be 2-10 times higher than the mutation rate. This study reinforces the notion that linkage disequilibrium is low and decays to negligible levels within a few hundred base pairs in P. tremula.     

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.     

Estimates of Linkage Disequilibrium and the Recombination Parameter Determined from Segregating Nucleotide Sites in the Alcohol Dehydrogenase Region of Drosophila Pseudoobscura

The alcohol dehydrogenase (Adh) region of Drosophila pseudoobscura, which includes the two genes Adh and Adh-Dup, was used to examine the pattern and organization of linkage disequilibrium among pairs of segregating nucleotide sites. A collection of 99 strains from the geographic range of D. pseudoobscura were nucleotide-sequenced with polymerase chain reaction-mediated techniques. All pairs of the 359 polymorphic sites in the 3.5-kb Adh region were tested for significant linkage disequilibrium with Fisher's exact test. Of the 74,278 pairwise comparisons of segregating sites, 127 were in significant linkage disequilibrium at the 5% level. The distribution of five linkage disequilibrium estimators D(ij), D(2), r(ij), r(2) and Dij were compared to theoretical distributions. The observed distributions of D(ij), D(2), r(ij) and r(2) were consistent with the theoretical distribution given an infinite sites model. The observed distribution of Dij differed from the theoretical distribution because of an excess of values at -1 and 1. No spatial pattern was observed in the linkage disequilibrium pattern in the Adh region except for two clusters of sites nonrandomly associated in the adult intron and intron 2 of Adh. The magnitude of linkage disequilibrium decreases significantly as nucleotide distance increases, or a distance effect. Adh-Dup had a larger estimate of the recombination parameter, 4Nc, than Adh, where N is the effective population size and c is the recombination rate. A comparison of the mutation and recombination parameters shows that 7-17 recombination events occur for each mutation event. The heterogeneous estimates of the recombination parameter and the inverse relationship between linkage disequilibrium and nucleotide distance are no longer significant when the two clusters of Adh intron sites are excluded from analyses. The most likely explanation for the two clusters of linkage disequilibria is epistatic selection between sites in the cluster to maintain pre-mRNA secondary structure.     

Linkage Disequilibrium in Subdivided Populations

The linkage disequilibrium in a subdivided populaton is shown to be equal to the sum of the average linkage disequilibrium for all subpopulations and the covariance between gene frequencies of the loci concerned. Thus, in a subdivided population the linkage disequilibrium may not be 0 even if the linkage disequilibrium in each subpopulation is 0. If a population is divided into two subpopulations between which migration occurs, the asymptotic rate of approach to linkage equilibrium is equal to either r or 2(m(1) + m(2)) - (m(1) + m(2))(2), whichever is smaller, where r is the recombination value and m(1) and m(2) are the proportions of immigrants in subpopulations 1 and 2, respectively. Thus, if migration rate is high compared with recombination value, the change of linkage disequilibrium in subdivided populations is similar to that of a single random mating population. On the other hand, if migration rate is low, the approach to lnkage equilibrium may be retarded in subdivided populations. If isolated populations begin to exchange genes by migration, linkage disequilibrium may increase temporarily even for neutral loci. If overdominant selection operates and the equilibrium gene frequencies are different in the two subpopulations, a permanent linkage disequilibrium may be produced without epistasis in each subpopulation.     

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.     

Estimation of population parameters and recombination rates from single nucleotide polymorphisms

Some general likelihood and Bayesian methods for analyzing single nucleotide polymorphisms (SNPs) are presented. First, an efficient method for estimating demographic parameters from SNPs in linkage equilibrium is derived. The method is applied in the estimation of growth rates of a human population based on 37 SNP loci. It is demonstrated how ascertainment biases, due to biased sampling of loci, can be avoided, at least in some cases, by appropriate conditioning when calculating the likelihood function. Second, a Markov chain Monte Carlo (MCMC) method for analyzing linked SNPs is developed. This method can be used for Bayesian and likelihood inference on linked SNPs. The utility of the method is illustrated by estimating recombination rates in a human data set containing 17 SNPs and 60 individuals. Both methods are based on assumptions of low mutation rates.     

Maximum-likelihood estimation of gene location by linkage disequilibrium.

Linkage disequilibrium, D, between a polymorphic disease and mapped markers can, in principle, be used to help find the map position of the disease gene. Likelihoods are therefore derived for the value of D conditional on the observed number of haplotypes in the sample and on the population parameter Nc, where N is the effective population size and c the recombination fraction between the disease and marker loci. The likelihood is computed explicitly for the case of two loci with heterozygote superiority and, more generally, by computer simulations assuming a steady state of constant population size and selective pressures or neutrality. It is found that the likelihood is, in general, not very dependent on the degree of selection at the loci and is very flat. This suggests that precise information on map position will not be obtained from estimates of linkage disequilibrium.     

Recombination and nucleotide diversity in the sex chromosomal pseudoautosomal region of the emu, Dromaius novaehollandiae

Pseudoautosomal regions (PARs) shared by avian Z and W sex chromosomes are typically small homologous regions within which recombination still occurs and are hypothesized to share the properties of autosomes. We capitalized on the unusual structure of the sex chromosomes of emus, Dromaius novaehollandiae, which consist almost entirely of PAR shared by both sex chromosomes, to test this hypothesis. We compared recombination, linkage disequilibrium (LD), GC content, and nucleotide diversity between pseudoautosomal and autosomal loci derived from 11 emu bacterial artificial chromosome (BAC) clones that were mapped to chromosomes by fluorescent in situ hybridization. Nucleotide diversity (pi = 4N(e)mu) was not significantly lower in pseudoautosomal loci (14 loci, 1.9 +/- 2.4 x 10(-3)) than autosomal loci (8 loci, 4.2 +/- 6.1 x 10(-3)). By contrast, recombination per site within BAC-end sequences (rho = 4Nc) (pseudoautosomal, 3.9 +/- 6.9 x 10(-2); autosomal, 2.3 +/- 3.7 x 10(-2)) was higher and average LD (D') (pseudoautosomal, 4.2 +/- 0.2 x 10(-1); autosomal, 4.7 +/- 0.5 x 10(-1)) slightly lower in pseudoautosomal sequences. We also report evidence of deviation from a simple neutral model in the PAR and in autosomal loci, possibly caused by departures from demographic equilibrium, such as population growth. This study provides a snapshot of the population genetics of avian sex chromosomes at an early stage of differentiation.     

High intraspecific recombination rate in a native population of Candidatus pelagibacter ubique (SAR11)

Recombination is an important process in microbial evolution. Rates of recombination with extracellular DNA matter because models of microbial population structure are profoundly influenced by the degree to which recombination is occurring within the population. Low rates of recombination may be sufficient to ensure the lateral propagation of genes that have a high selective advantage without disrupting the clonal pattern of inheritance for other genes. High rates of recombination potentially can obscure clonal patterns, leading to linkage equilibrium, and give microbial populations a population genetic structure more akin to sexually interbreeding eukaryotic populations. We examined eight loci from nine strains of candidatus Pelagibacter ubique (SAR11), isolated from a single 2L niskin sample of natural seawater, for evidence of genetic recombination between strains. The Shimodaira-Hasegawa test revealed significant phylogenetic incongruence in seven of the genes, indicating that frequent recombination obscures phylogenetic signals from the linear inheritance of genes in this population. Statistical evidence for intragenic recombination was found for six loci. An informative sites matrix showed extensive evidence for a widespread breakdown of linkage disequilibrium. Although the mechanisms of genetic transfer in native SAR11 populations are unknown, we measured recombination rates, rho, that are much higher than point mutation rates, theta, as a source of genetic diversity in this clade. The eukaryotic model of species sharing a common pool of alleles is more apt for this SAR11 population than a strictly clonal model of inheritance in which allelic diversity is controlled by periodic selection.     

Linkage disequilibrium under skewed offspring distribution among individuals in a population

Correlations in coalescence times between two loci are derived under selectively neutral population models in which the offspring of an individual can number on the order of the population size. The correlations depend on the rates of recombination and random drift and are shown to be functions of the parameters controlling the size and frequency of these large reproduction events. Since a prediction of linkage disequilibrium can be written in terms of correlations in coalescence times, it follows that the prediction of linkage disequilibrium is a function not only of the rate of recombination but also of the reproduction parameters. Low linkage disequilibrium is predicted if the offspring of a single individual frequently replace almost the entire population. However, high linkage disequilibrium can be predicted if the offspring of a single individual replace an intermediate fraction of the population. In some cases the model reproduces the standard Wright-Fisher predictions. Contrary to common intuition, high linkage disequilibrium can be predicted despite frequent recombination, and low linkage disequilibrium under infrequent recombination. Simulations support the analytical results but show that the variance of linkage disequilibrium is very large.     

Evolution at the tip and base of the X chromosome in an African population of Drosophila melanogaster

Hitchhiking effects of advantageous mutations have been invoked to explain reduced polymorphism in regions of low crossing-over in Drosophila. Besides reducing DNA heterozygosity, hitchhiking effects should produce strong linkage disequilibrium and a frequency spectrum skewed toward an excess of rare polymorphisms (compared to the neutral expectation). We measured DNA polymorphism in a Zimbabwe population of D. melanogaster at three loci, yellow, achaete, and suppressor of forked, located in regions of reduced crossing-over. Similar to previously published surveys of these genomic regions in other populations, we observed low levels of nucleotide variability. However, the frequency spectrum was compatible with a neutral model, and there was abundant evidence for recombination in the history of the yellow and ac genes. Thus, some aspects of the data cannot be accounted for by a simple hitchhiking model. An alternative hypothesis, background selection, might be compatible with the observed patterns of linkage disequilibrium and the frequency spectrum. However, this model cannot account for the observed reduction in nucleotide heterozygosity. Thus, there is currently no satisfactory theoretical model for the data from the tip and base of the X chromosome in D. melanogaster.      

Linkage disequilibrium patterns across a recombination gradient in African Drosophila melanogaster

Previous multilocus surveys of nucleotide polymorphism have documented a genome-wide excess of intralocus linkage disequilibrium (LD) in Drosophila melanogaster and D. simulans relative to expectations based on estimated mutation and recombination rates and observed levels of diversity. These studies examined patterns of variation from predominantly non-African populations that are thought to have recently expanded their ranges from central Africa. Here, we analyze polymorphism data from a Zimbabwean population of D. melanogaster, which is likely to be closer to the standard population model assumptions of a large population with constant size. Unlike previous studies, we find that levels of LD are roughly compatible with expectations based on estimated rates of crossing over. Further, a detailed examination of genes in different recombination environments suggests that markers near the telomere of the X chromosome show considerably less linkage disequilibrium than predicted by rates of crossing over, suggesting appreciable levels of exchange due to gene conversion. Assuming that these populations are near mutation-drift equilibrium, our results are most consistent with a model that posits heterogeneity in levels of exchange due to gene conversion across the X chromosome, with gene conversion being a minor determinant of LD levels in regions of high crossing over. Alternatively, if levels of exchange due to gene conversion are not negligible in regions of high crossing over, our results suggest a marked departure from mutation-drift equilibrium (i.e., toward an excess of LD) in this Zimbabwean population. Our results also have implications for the dynamics of weakly selected mutations in regions of reduced crossing over.     

Meiosis and the evolution of recombination at low mutation rates

The classical understanding of recombination is that in large asexual populations with multiplicative fitness, linkage disequilibrium is negligible, and thus there is no selective agent driving an allele for recombination. This has led researchers to recognize the importance of synergistic epistatic selection in generating negative linkage disequilibrium that thereby renders an advantage to recombination. Yet data on such selection is equivocal, and various works have shown that synergistic epistasis per se, when left unquantified in its magnitude or operation, is not sufficient to drive the evolution of recombination. Here we show that neither it, nor any mechanism generating negative linkage disequilibrium among fitness-related loci, is necessary. We demonstrate that a neutral gene for recombination can increase in frequency in a large population under a low mutation rate and strict multiplicative fitness. We work in a parameter range where individuals have, on average, less than one mutation each, yet recombination can still evolve. We demonstrate this in two ways: first, by examining the consequences of recombination correlated with misrepaired DNA damage and, second, by increasing the probability of recombination with declining fitness. Interestingly, the allele spreads without repairing even a single DNA mutation.     

The relative contributions of recombination and point mutation to the diversification of bacterial clones

Low levels of recombination in bacterial species have often been inferred from the presence of linkage disequilibrium between the alleles at different loci in the population. However, significant linkage disequilibrium is inevitable in organisms that divide by binary fission, and recombinational replacements must be very frequent, compared to point mutation, to dissipate disequilibrium. Recent studies using data from multilocus sequence typing indicate that, in many species, recombinational replacements contribute more greatly to clonal diversification than do point mutations and, in some species, recombination has been sufficient to eliminate any phylogenetic signal from gene trees. Recent efforts to improve understanding of the extent and impact of homologous recombination in the diversification of bacterial clones are discussed.     

Equilibrium processes cannot explain high levels of short- and medium-range linkage disequilibrium in the domesticated grass Sorghum bicolor

Patterns of linkage disequilibrium (LD) are of interest because they provide evidence of both equilibrium (e.g., mating system or long-term population structure) and nonequilibrium (e.g., demographic or selective) processes, as well as because of their importance in strategies for identifying the genetic basis of complex phenotypes. We report patterns of short and medium range (up to 100 kb) LD in six unlinked genomic regions in the partially selfing domesticated grass, Sorghum bicolor. The extent of allelic associations in S. bicolor, as assessed by pairwise measures of LD, is higher than in maize but lower than in Arabidopsis, in qualitative agreement with expectations based on mating system. Quantitative analyses of the population recombination parameter, rho, however, based on empirical estimates of rates of recombination, mutation, and self-pollination, show that LD is more extensive than expected under a neutral equilibrium model. The disparity between rho and the population mutation parameter, , is similar to that observed in other species whose population history appears to be complex. From a practical standpoint, these results suggest that S. bicolor is well suited for association studies using reasonable numbers of markers, since LD typically extends at least several kilobases but has largely decayed by 15 kb.     

Linkage and the Maintenance of Heritable Variation by Mutation-Selection Balance

The role of linkage in influencing heritable variation maintained through a balance between mutation and stabilizing selection is investigated for two different models. In both cases one trait is considered and the interactions within and between loci are assumed to be additive. Contrary to most earlier investigations of this problem no a priori assumptions on the distribution of genotypic values are imposed. For a deterministic two-locus two-allele model with recombination and mutation, related to the symmetric viability model, a complete nonlinear analysis is performed. It is shown that, depending on the recombination rate, multiple stable equilibria may coexist. The equilibrium genetic and genic variances are calculated. For a polygenic trait in a finite population with a possible continuum of allelic effects a simulation study is performed. In both models the equilibrium genetic and genic variances are roughly equal to the house-of-cards prediction or its finite population counterpart as long as the recombination rate is not extremely low. However, negative linkage disequilibrium builds up. If the loci are very closely linked the equilibrium additive genetic variance is slightly lower than the house-of-cards prediction, but the genic variance is much higher. Depending on whether the parameters are in favor of the house-of-cards or the Gaussian approximation, different behavior of the genetic system occurs with respect to linkage.