The Linkage-Disequilibrium and Recombinational Landscape in Daphnia pulex.

By revealing the influence of recombinational activity beyond what can be achieved with controlled crosses, measures of linkage disequilibrium (LD) in natural populations provide a powerful means of defining the recombinational landscape within which genes evolve. In one of the most comprehensive studies of this sort ever performed, involving whole-genome analyses on nearly 1,000 individuals of the cyclically parthenogenetic microcrustacean Daphnia pulex, the data suggest a relatively uniform pattern of recombination across the genome. Patterns of LD are quite consistent among populations; average rates of recombination are quite similar for all chromosomes; and although some chromosomal regions have elevated recombination rates, the degree of inflation is not large, and the overall spatial pattern of recombination is close to the random expectation. Contrary to expectations for models in which crossing-over is the primary mechanism of recombination, and consistent with data for other species, the distance-dependent pattern of LD indicates excessively high levels at both short and long distances and unexpectedly low levels of decay at long distances, suggesting significant roles for factors such as nonindependent mutation, population subdivision, and recombination mechanisms unassociated with crossing over. These observations raise issues regarding the classical LD equilibrium model widely applied in population genetics to infer recombination rates across various length scales on chromosomes.

Evolutionary Genomics of a Subdivided Species.

The ways in which genetic variation is distributed within and among populations is a key determinant of the evolutionary features of a species. However, most comprehensive studies of these features have been restricted to studies of subdivision in settings known to have been driven by local adaptation, leaving our understanding of the natural dispersion of allelic variation less than ideal. Here, we present a geographic population-genomic analysis of 10 populations of the freshwater microcrustacean Daphnia pulex, an emerging model system in evolutionary genomics. These populations exhibit a pattern of moderate isolation-by-distance, with an average migration rate of 0.6 individuals per generation, and average effective population sizes of ∼650,000 individuals. Most populations contain numerous private alleles, and genomic scans highlight the presence of islands of excessively high population subdivision for more common alleles. A large fraction of such islands of population divergence likely reflect historical neutral changes, including rare stochastic migration and hybridization events. The data do point to local adaptive divergence, although the precise nature of the relevant variation is diffuse and cannot be associated with particular loci, despite the very large sample sizes involved in this study. In contrast, an analysis of between-species divergence highlights positive selection operating on a large set of genes with functions nearly nonoverlapping with those involved in local adaptation, in particular ribosome structure, mitochondrial bioenergetics, light reception and response, detoxification, and gene regulation. These results set the stage for using D. pulex as a model for understanding the relationship between molecular and cellular evolution in the context of natural environments.

Inference of Historical Population-Size Changes with Allele-Frequency Data.

With up to millions of nearly neutral polymorphisms now being routinely sampled in population-genomic surveys, it is possible to estimate the site-frequency spectrum of such sites with high precision. Each frequency class reflects a mixture of potentially unique demographic histories, which can be revealed using theory for the probability distributions of the starting and ending points of branch segments over all possible coalescence trees. Such distributions are completely independent of past population history, which only influences the segment lengths, providing the basis for estimating average population sizes separating tree-wide coalescence events. The history of population-size change experienced by a sample of polymorphisms can then be dissected in a model-flexible fashion, and extension of this theory allows estimation of the mean and full distribution of long-term effective population sizes and ages of alleles of specific frequencies. Here, we outline the basic theory underlying the conceptual approach, develop and test an efficient statistical procedure for parameter estimation, and apply this to multiple population-genomic datasets for the microcrustacean Daphnia pulex.

Genotype Calling from Population-Genomic Sequencing Data.

Genotype calling plays important roles in population-genomic studies, which have been greatly accelerated by sequencing technologies. To take full advantage of the resultant information, we have developed maximum-likelihood (ML) methods for calling genotypes from high-throughput sequencing data. As the statistical uncertainties associated with sequencing data depend on depths of coverage, we have developed two types of genotype callers. One approach is appropriate for low-coverage sequencing data, and incorporates population-level information on genotype frequencies and error rates pre-estimated by an ML method. Performance evaluation using computer simulations and human data shows that the proposed framework yields less biased estimates of allele frequencies and more accurate genotype calls than current widely used methods. Another type of genotype caller applies to high-coverage sequencing data, requires no prior genotype-frequency estimates, and makes no assumption on the number of alleles at a polymorphic site. Using computer simulations, we determine the depth of coverage necessary to accurately characterize polymorphisms using this second method. We applied the proposed method to high-coverage (mean 18×) sequencing data of 83 clones from a population of Daphnia pulex The results show that the proposed method enables conservative and reasonably powerful detection of polymorphisms with arbitrary numbers of alleles. We have extended the proposed method to the analysis of genomic data for polyploid organisms, showing that calling accurate polyploid genotypes requires much higher coverage than diploid genotypes.

Population Genomics of Daphnia pulex.

Using data from 83 isolates from a single population, the population genomics of the microcrustacean Daphnia pulex are described and compared to current knowledge for the only other well-studied invertebrate, Drosophila melanogaster These two species are quite similar with respect to effective population sizes and mutation rates, although some features of recombination appear to be different, with linkage disequilibrium being elevated at short ([Formula: see text] bp) distances in D. melanogaster and at long distances in D. pulex The study population adheres closely to the expectations under Hardy-Weinberg equilibrium, and reflects a past population history of no more than a twofold range of variation in effective population size. Fourfold redundant silent sites and a restricted region of intronic sites appear to evolve in a nearly neutral fashion, providing a powerful tool for population genetic analyses. Amino acid replacement sites are predominantly under strong purifying selection, as are a large fraction of sites in UTRs and intergenic regions, but the majority of SNPs at such sites that rise to frequencies [Formula: see text] appear to evolve in a nearly neutral fashion. All forms of genomic sites (including replacement sites within codons, and intergenic and UTR regions) appear to be experiencing an [Formula: see text] higher level of selection scaled to the power of drift in D. melanogaster, but this may in part be a consequence of recent demographic changes. These results establish D. pulex as an excellent system for future work on the evolutionary genomics of natural populations.

Genotype-Frequency Estimation from High-Throughput Sequencing Data.

Rapidly improving high-throughput sequencing technologies provide unprecedented opportunities for carrying out population-genomic studies with various organisms. To take full advantage of these methods, it is essential to correctly estimate allele and genotype frequencies, and here we present a maximum-likelihood method that accomplishes these tasks. The proposed method fully accounts for uncertainties resulting from sequencing errors and biparental chromosome sampling and yields essentially unbiased estimates with minimal sampling variances with moderately high depths of coverage regardless of a mating system and structure of the population. Moreover, we have developed statistical tests for examining the significance of polymorphisms and their genotypic deviations from Hardy-Weinberg equilibrium. We examine the performance of the proposed method by computer simulations and apply it to low-coverage human data generated by high-throughput sequencing. The results show that the proposed method improves our ability to carry out population-genomic analyses in important ways. The software package of the proposed method is freely available from https://github.com/Takahiro-Maruki/Package-GFE.

Genome-wide linkage-disequilibrium profiles from single individuals.

Although the analysis of linkage disequilibrium (LD) plays a central role in many areas of population genetics, the sampling variance of LD is known to be very large with high sensitivity to numbers of nucleotide sites and individuals sampled. Here we show that a genome-wide analysis of the distribution of heterozygous sites within a single diploid genome can yield highly informative patterns of LD as a function of physical distance. The proposed statistic, the correlation of zygosity, is closely related to the conventional population-level measure of LD, but is agnostic with respect to allele frequencies and hence likely less prone to outlier artifacts. Application of the method to several vertebrate species leads to the conclusion that >80% of recombination events are typically resolved by gene-conversion-like processes unaccompanied by crossovers, with the average lengths of conversion patches being on the order of one to several kilobases in length. Thus, contrary to common assumptions, the recombination rate between sites does not scale linearly with distance, often even up to distances of 100 kb. In addition, the amount of LD between sites separated by <200 bp is uniformly much greater than can be explained by the conventional neutral model, possibly because of the nonindependent origin of mutations within this spatial scale. These results raise questions about the application of conventional population-genetic interpretations to LD on short spatial scales and also about the use of spatial patterns of LD to infer demographic histories.

Genome-wide estimation of linkage disequilibrium from population-level high-throughput sequencing data.

Rapidly improving sequencing technologies provide unprecedented opportunities for analyzing genome-wide patterns of polymorphisms. In particular, they have great potential for linkage-disequilibrium analyses on both global and local genetic scales, which will substantially improve our ability to derive evolutionary inferences. However, there are some difficulties with analyzing high-throughput sequencing data, including high error rates associated with base reads and complications from the random sampling of sequenced chromosomes in diploid organisms. To overcome these difficulties, we developed a maximum-likelihood estimator of linkage disequilibrium for use with error-prone sampling data. Computer simulations indicate that the estimator is nearly unbiased with a sampling variance at high coverage asymptotically approaching the value expected when all relevant information is accurately estimated. The estimator does not require phasing of haplotypes and enables the estimation of linkage disequilibrium even when all individual reads cover just single polymorphic sites.

Population-genetic inference from pooled-sequencing data.

Although pooled-population sequencing has become a widely used approach for estimating allele frequencies, most work has proceeded in the absence of a proper statistical framework. We introduce a self-sufficient, closed-form, maximum-likelihood estimator for allele frequencies that accounts for errors associated with sequencing, and a likelihood-ratio test statistic that provides a simple means for evaluating the null hypothesis of monomorphism. Unbiased estimates of allele frequencies [Formula: see text] (where N is the number of individuals sampled) appear to be unachievable, and near-certain identification of a polymorphism requires a minor-allele frequency [Formula: see text]. A framework is provided for testing for significant differences in allele frequencies between populations, taking into account sampling at the levels of individuals within populations and sequences within pooled samples. Analyses that fail to account for the two tiers of sampling suffer from very large false-positive rates and can become increasingly misleading with increasing depths of sequence coverage. The power to detect significant allele-frequency differences between two populations is very limited unless both the number of sampled individuals and depth of sequencing coverage exceed 100.

Purifying selection modulates the estimates of population differentiation and confounds genome-wide comparisons across single-nucleotide polymorphisms.

An improved understanding of the biological and numerical properties of measures of population differentiation across loci is becoming increasingly more important because of their growing use in analyzing genome-wide polymorphism data for detecting population structures, inferring the rates of migration, and identifying local adaptations. In a genome-wide analysis, we discovered that the estimates of population differentiation (e.g., F(ST), θ, and Jost's D) calculated for human single-nucleotide polymorphisms (SNPs) are strongly and positively correlated to the position-specific evolutionary rates measured from multispecies alignments. That is, genomic positions (loci) experiencing higher purifying selection (lower evolutionary rates) produce lower values for the degree of population differentiation than those evolving with faster rates. We show that this pattern is completely mediated by the negative effects of purifying selection on the minor allele frequency (MAF) at individual loci. Our results suggest that inferences and methods relying on the comparison of population differentiation estimates (F(ST), θ, and Jost's D) based on SNPs across genomic positions should be restricted to loci with similar MAFs and/or the rates of evolution in genome scale surveys.

Hitchhiking effect of a beneficial mutation spreading in a subdivided population.

A central problem in population genetics is to detect and analyze positive natural selection by which beneficial mutations are driven to fixation. The hitchhiking effect of a rapidly spreading beneficial mutation, which results in local removal of standing genetic variation, allows such an analysis using DNA sequence polymorphism. However, the current mathematical theory that predicts the pattern of genetic hitchhiking relies on the assumption that a beneficial mutation increases to a high frequency in a single random-mating population, which is certainly violated in reality. Individuals in natural populations are distributed over a geographic space. The spread of a beneficial allele can be delayed by limited migration of individuals over the space and its hitchhiking effect can also be affected. To study this effect of geographic structure on genetic hitchhiking, we analyze a simple model of directional selection in a subdivided population. In contrast to previous studies on hitchhiking in subdivided populations, we mainly investigate the range of sufficiently high migration rates that would homogenize genetic variation at neutral loci. We provide a heuristic mathematical analysis that describes how the genealogical structure at a neutral locus linked to the locus under selection is expected to change in a population divided into two demes. Our results indicate that the overall strength of genetic hitchhiking--the degree to which expected heterozygosity decreases--is diminished by population subdivision, mainly because opportunity for the breakdown of hitchhiking by recombination increases as the spread of the beneficial mutation across demes is delayed when migration rate is much smaller than the strength of selection. Furthermore, the amount of genetic variation after a selective sweep is expected to be unequal over demes: a greater reduction in expected heterozygosity occurs in the subpopulation from which the beneficial mutation originates than in its neighboring subpopulations. This raises a possibility of detecting a "hidden" geographic structure of population by carefully analyzing the pattern of a selective sweep.