Joint estimation of gene conversion rates and mean conversion tract lengths from population SNP data

Novel Insights into the Landscape of Crossover and Noncrossover Events in Rhesus Macaques (Macaca mulatta)

Meiotic recombination landscapes differ greatly between distantly and closely related taxa, populations, individuals, sexes, and even within genomes; however, the factors driving this variation are yet to be well elucidated. Here, we directly estimate contemporary crossover rates and, for the first time, noncrossover rates in rhesus macaques (Macaca mulatta) from four three-generation pedigrees comprising 32 individuals. We further compare these results with historical, demography-aware, linkage disequilibrium-based recombination rate estimates. From paternal meioses in the pedigrees, 165 crossover events with a median resolution of 22.3 kb were observed, corresponding to a male autosomal map length of 2,357 cM-approximately 15% longer than an existing linkage map based on human microsatellite loci. In addition, 85 noncrossover events with a mean tract length of 155 bp were identified-similar to the tract lengths observed in the only other two primates in which noncrossovers have been studied to date, humans and baboons. Consistent with observations in other placental mammals with PRDM9-directed recombination, crossover (and to a lesser extent noncrossover) events in rhesus macaques clustered in intergenic regions and toward the chromosomal ends in males-a pattern in broad agreement with the historical, sex-averaged recombination rate estimates-and evidence of GC-biased gene conversion was observed at noncrossover sites.

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.

High-Resolution Estimates of Crossover and Noncrossover Recombination from a Captive Baboon Colony

Homologous recombination has been extensively studied in humans and a handful of model organisms. Much less is known about recombination in other species, including nonhuman primates. Here, we present a study of crossovers (COs) and noncrossover (NCO) recombination in olive baboons (Papio anubis) from two pedigrees containing a total of 20 paternal and 17 maternal meioses, and compare these results to linkage disequilibrium (LD) based recombination estimates from 36 unrelated olive baboons. We demonstrate how COs, combined with LD-based recombination estimates, can be used to identify genome assembly errors. We also quantify sex-specific differences in recombination rates, including elevated male CO and reduced female CO rates near telomeres. Finally, we add to the increasing body of evidence suggesting that while most NCO recombination tracts in mammals are short (e.g., <500 bp), there is a non-negligible fraction of longer (e.g., >1 kb) NCO tracts. For NCO tracts shorter than 10 kb, we fit a mixture of two (truncated) geometric distributions model to the NCO tract length distribution and estimate that >99% of all NCO tracts are very short (mean 24 bp), but the remaining tracts can be quite long (mean 4.3 kb). A single geometric distribution model for NCO tract lengths is incompatible with the data, suggesting that LD-based methods for estimating NCO recombination rates that make this assumption may need to be modified.

Hypothesis testing of meiotic recombination rates from population genetic data

Background

Meiotic recombination, one of the central biological processes studied in population genetics, comes in two known forms: crossovers and gene conversions. A number of previous studies have shown that when one of these two events is nonexistent in the genealogical model, the point estimation of the corresponding recombination rate by population genetic methods tends to be inflated. Therefore, it has become necessary to obtain statistical evidence from population genetic data about whether one of the two recombination events is absent.

Results

In this paper, we formulate this problem in a hypothesis testing framework and devise a testing procedure based on the likelihood ratio test (LRT). However, because the null value (i.e., zero) lies on the boundary of the parameter space, the regularity conditions for the large‐sample approximation to the distribution of the LRT statistic do not apply. In turn, the standard chi‐squared approximation is inaccurate. To address this critical issue, we propose a parametric bootstrap procedure to obtain an approximate p‐value for the observed test statistic. Coalescent simulations are conducted to show that our approach yields accurate null p‐values that closely follow the theoretical prediction while the estimated alternative p‐values tend to concentrate closer to zero. Finally, the method is demonstrated on a real biological data set from the telomere of the X chromosome of African Drosophila melanogaster.

Conclusions

Our methodology provides a necessary complement to the existing procedures of estimating meiotic recombination rates from population genetic data.

Electronic supplementary material

The online version of this article (doi:10.1186/s12863-014-0122-7) contains supplementary material, which is available to authorized users.

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.

Meiotic gene-conversion rate and tract length variation in the human genome

Meiotic recombination occurs in the form of two different mechanisms called crossing-over and gene-conversion and both processes have an important role in shaping genetic variation in populations. Although variation in crossing-over rates has been studied extensively using sperm-typing experiments, pedigree studies and population genetic approaches, our knowledge of variation in gene-conversion parameters (ie, rates and mean tract lengths) remains far from complete. To explore variability in population gene-conversion rates and its relationship to crossing-over rate variation patterns, we have developed and validated using coalescent simulations a comprehensive Bayesian full-likelihood method that can jointly infer crossing-over and gene-conversion rates as well as tract lengths from population genomic data under general variable rate models with recombination hotspots. Here, we apply this new method to SNP data from multiple human populations and attempt to characterize for the first time the fine-scale variation in gene-conversion parameters along the human genome. We find that the estimated ratio of gene-conversion to crossing-over rates varies considerably across genomic regions as well as between populations. However, there is a great degree of uncertainty associated with such estimates. We also find substantial evidence for variation in the mean conversion tract length. The estimated tract lengths did not show any negative relationship with the local heterozygosity levels in our analysis.European Journal of Human Genetics advance online publication, 27 February 2013; doi:10.1038/ejhg.2013.30.

Population Genomics of sub-saharan Drosophila melanogaster: African diversity and non-African admixture

Drosophila melanogaster has played a pivotal role in the development of modern population genetics. However, many basic questions regarding the demographic and adaptive history of this species remain unresolved. We report the genome sequencing of 139 wild-derived strains of D. melanogaster, representing 22 population samples from the sub-Saharan ancestral range of this species, along with one European population. Most genomes were sequenced above 25X depth from haploid embryos. Results indicated a pervasive influence of non-African admixture in many African populations, motivating the development and application of a novel admixture detection method. Admixture proportions varied among populations, with greater admixture in urban locations. Admixture levels also varied across the genome, with localized peaks and valleys suggestive of a non-neutral introgression process. Genomes from the same location differed starkly in ancestry, suggesting that isolation mechanisms may exist within African populations. After removing putatively admixed genomic segments, the greatest genetic diversity was observed in southern Africa (e.g. Zambia), while diversity in other populations was largely consistent with a geographic expansion from this potentially ancestral region. The European population showed different levels of diversity reduction on each chromosome arm, and some African populations displayed chromosome arm-specific diversity reductions. Inversions in the European sample were associated with strong elevations in diversity across chromosome arms. Genomic scans were conducted to identify loci that may represent targets of positive selection within an African population, between African populations, and between European and African populations. A disproportionate number of candidate selective sweep regions were located near genes with varied roles in gene regulation. Outliers for Europe-Africa F(ST) were found to be enriched in genomic regions of locally elevated cosmopolitan admixture, possibly reflecting a role for some of these loci in driving the introgression of non-African alleles into African populations.

A sequentially Markov conditional sampling distribution for structured populations with migration and recombination

Conditional sampling distributions (CSDs), sometimes referred to as copying models, underlie numerous practical tools in population genomic analyses. Though an important application that has received much attention is the inference of population structure, the explicit exchange of migrants at specified rates has not hitherto been incorporated into the CSD in a principled framework. Recently, in the case of a single panmictic population, a sequentially Markov CSD has been developed as an accurate, efficient approximation to a principled CSD derived from the diffusion process dual to the coalescent with recombination. In this paper, the sequentially Markov CSD framework is extended to incorporate subdivided population structure, thus providing an efficiently computable CSD that admits a genealogical interpretation related to the structured coalescent with migration and recombination. As a concrete application, it is demonstrated empirically that the CSD developed here can be employed to yield accurate estimation of a wide range of migration rates.

Blockwise HMM computation for large-scale population genomic inference

MOTIVATION

A promising class of methods for large-scale population genomic inference use the conditional sampling distribution (CSD), which approximates the probability of sampling an individual with a particular DNA sequence, given that a collection of sequences from the population has already been observed. The CSD has a wide range of applications, including imputing missing sequence data, estimating recombination rates, inferring human colonization history and identifying tracts of distinct ancestry in admixed populations. Most well-used CSDs are based on hidden Markov models (HMMs). Although computationally efficient in principle, methods resulting from the common implementation of the relevant HMM techniques remain intractable for large genomic datasets.

RESULTS

To address this issue, a set of algorithmic improvements for performing the exact HMM computation is introduced here, by exploiting the particular structure of the CSD and typical characteristics of genomic data. It is empirically demonstrated that these improvements result in a speedup of several orders of magnitude for large datasets and that the speedup continues to increase with the number of sequences. The optimized algorithms can be adopted in methods for various applications, including the ones mentioned above and make previously impracticable analyses possible.

AVAILABILITY

Software available upon request.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

CONTACT

yss@eecs.berkeley.edu.

Fine scale analysis of crossover and non-crossover and detection of recombination sequence motifs in the honeybee (Apis mellifera)

BACKGROUND

Meiotic exchanges are non-uniformly distributed across the genome of most studied organisms. This uneven distribution suggests that recombination is initiated by specific signals and/or regulations. Some of these signals were recently identified in humans and mice. However, it is unclear whether or not sequence signals are also involved in chromosomal recombination of insects.

METHODOLOGY

We analyzed recombination frequencies in the honeybee, in which genome sequencing provided a large amount of SNPs spread over the entire set of chromosomes. As the genome sequences were obtained from a pool of haploid males, which were the progeny of a single queen, an oocyte method (study of recombination on haploid males that develop from unfertilized eggs and hence are the direct reflect of female gametes haplotypes) was developed to detect recombined pairs of SNP sites. Sequences were further compared between recombinant and non-recombinant fragments to detect recombination-specific motifs.

CONCLUSIONS

Recombination events between adjacent SNP sites were detected at an average distance of 92 bp and revealed the existence of high rates of recombination events. This study also shows the presence of conversion without crossover (i. e. non-crossover) events, the number of which largely outnumbers that of crossover events. Furthermore the comparison of sequences that have undergone recombination with sequences that have not, led to the discovery of sequence motifs (CGCA, GCCGC, CCGCA), which may correspond to recombination signals.

Estimating population divergence time and phylogeny from single-nucleotide polymorphisms data with outgroup ascertainment bias

The inference of population divergence times and branching patterns is of fundamental importance in many population genetic analyses. Many methods have been developed for estimating population divergence times, and recently, there has been particular attention towards genome-wide single-nucleotide polymorphisms (SNP) data. However, most SNP data have been affected by an ascertainment bias caused by the SNP selection and discovery protocols. Here, we present a modification of an existing maximum likelihood method that will allow approximately unbiased inferences when ascertainment is based on a set of outgroup populations. We also present a method for estimating trees from the asymmetric dissimilarity measures arising from pairwise divergence time estimation in population genetics. We evaluate the methods by simulations and by applying them to a large SNP data set of seven East Asian populations.

Bayesian population genomic inference of crossing over and gene conversion

Meiotic recombination is a fundamental cellular mechanism in sexually reproducing organisms and its different forms, crossing over and gene conversion both play an important role in shaping genetic variation in populations. Here, we describe a coalescent-based full-likelihood Markov chain Monte Carlo (MCMC) method for jointly estimating the crossing-over, gene-conversion, and mean tract length parameters from population genomic data under a Bayesian framework. Although computationally more expensive than methods that use approximate likelihoods, the relative efficiency of our method is expected to be optimal in theory. Furthermore, it is also possible to obtain a posterior sample of genealogies for the data using this method. We first check the performance of the new method on simulated data and verify its correctness. We also extend the method for inference under models with variable gene-conversion and crossing-over rates and demonstrate its ability to identify recombination hotspots. Then, we apply the method to two empirical data sets that were sequenced in the telomeric regions of the X chromosome of Drosophila melanogaster. Our results indicate that gene conversion occurs more frequently than crossing over in the su-w and su-s gene sequences while the local rates of crossing over as inferred by our program are not low. The mean tract lengths for gene-conversion events are estimated to be ∼70 bp and 430 bp, respectively, for these data sets. Finally, we discuss ideas and optimizations for reducing the execution time of our algorithm.

An accurate sequentially Markov conditional sampling distribution for the coalescent with recombination

The sequentially Markov coalescent is a simplified genealogical process that aims to capture the essential features of the full coalescent model with recombination, while being scalable in the number of loci. In this article, the sequentially Markov framework is applied to the conditional sampling distribution (CSD), which is at the core of many statistical tools for population genetic analyses. Briefly, the CSD describes the probability that an additionally sampled DNA sequence is of a certain type, given that a collection of sequences has already been observed. A hidden Markov model (HMM) formulation of the sequentially Markov CSD is developed here, yielding an algorithm with time complexity linear in both the number of loci and the number of haplotypes. This work provides a highly accurate, practical approximation to a recently introduced CSD derived from the diffusion process associated with the coalescent with recombination. It is empirically demonstrated that the improvement in accuracy of the new CSD over previously proposed HMM-based CSDs increases substantially with the number of loci. The framework presented here can be adopted in a wide range of applications in population genetics, including imputing missing sequence data, estimating recombination rates, and inferring human colonization history.

A principled approach to deriving approximate conditional sampling distributions in population genetics models with recombination

The multilocus conditional sampling distribution (CSD) describes the probability that an additionally sampled DNA sequence is of a certain type, given that a collection of sequences has already been observed. The CSD has a wide range of applications in both computational biology and population genomics analysis, including phasing genotype data into haplotype data, imputing missing data, estimating recombination rates, inferring local ancestry in admixed populations, and importance sampling of coalescent genealogies. Unfortunately, the true CSD under the coalescent with recombination is not known, so approximations, formulated as hidden Markov models, have been proposed in the past. These approximations have led to a number of useful statistical tools, but it is important to recognize that they were not derived from, though were certainly motivated by, principles underlying the coalescent process. The goal of this article is to develop a principled approach to derive improved CSDs directly from the underlying population genetics model. Our approach is based on the diffusion process approximation and the resulting mathematical expressions admit intuitive genealogical interpretations, which we utilize to introduce further approximations and make our method scalable in the number of loci. The general algorithm presented here applies to an arbitrary number of loci and an arbitrary finite-alleles recurrent mutation model. Empirical results are provided to demonstrate that our new CSDs are in general substantially more accurate than previously proposed approximations.

Recombination yet inefficient selection along the Drosophila melanogaster subgroup's fourth chromosome

A central goal of evolutionary genetics is an understanding of the forces responsible for the observed variation, both within and between species. Theoretical and empirical work have demonstrated that genetic recombination contributes to this variation by breaking down linkage between nucleotide sites, thus allowing them to behave independently and for selective forces to act efficiently on them. The Drosophila fourth chromosome, which is believed to experience no-or very low-rates of recombination has been an important model for investigating these effects. Despite previous efforts, central questions regarding the extent of recombination and the predominant modes of selection acting on it remain open. In order to more comprehensively test hypotheses regarding recombination and its potential influence on selection along the fourth chromosome, we have resequenced regions from most of its genes from Drosophila melanogaster, D. simulans, and D. yakuba. These data, along with available outgroup sequence, demonstrate that recombination is low but significantly greater than zero for the three species. Despite there being recombination, there is strong evidence that its frequency is low enough to have rendered selection relatively inefficient. The signatures of relaxed constraint can be detected at both the level of polymorphism and divergence.

An approximate likelihood for genetic data under a model with recombination and population splitting

We describe a new approximate likelihood for population genetic data under a model in which a single ancestral population has split into two daughter populations. The approximate likelihood is based on the 'Product of Approximate Conditionals' likelihood and 'copying model' of Li and Stephens [Li, N., Stephens, M., 2003. Modeling linkage disequilibrium and identifying recombination hotspots using single-nucleotide polymorphism data. Genetics 165 (4), 2213-2233]. The approach developed here may be used for efficient approximate likelihood-based analyses of unlinked data. However our copying model also considers the effects of recombination. Hence, a more important application is to loosely-linked haplotype data, for which efficient statistical models explicitly featuring non-equilibrium population structure have so far been unavailable. Thus, in addition to the information in allele frequency differences about the timing of the population split, the method can also extract information from the lengths of haplotypes shared between the populations. There are a number of challenges posed by extracting such information, which makes parameter estimation difficult. We discuss how the approach could be extended to identify haplotypes introduced by migrants.