A genealogical interpretation of linkage disequilibrium

Integrating patterns of polymorphism at SNPs and STRs

Single nucleotide polymorphisms (SNPs) and short tandem repeats (STRs) differ in mutation rate and mechanism. As a result of these differences, simultaneous consideration of polymorphism patterns at SNPs and STRs can provide insights that are difficult to obtain from analysis of either marker type in isolation. Here, we use coalescent simulations to model the opposing effects of contrasting mutational dynamics and of shared genealogical history on the correlation between polymorphism at linked SNPs and STRs. Results show that polymorphism patterns are correlated only weakly despite the shared underlying genealogy, underscoring the importance of divergent mutational processes. Examples illustrate how knowledge of these relationships could aid population genetic inference, indicating the need for thorough theoretical studies.

Linkage disequilibrium between incompatibility locus region genes in the plant Arabidopsis lyrata

We have studied diversity in Arabidopsis lyrata of sequences orthologous to the ARK3 gene of A. thaliana. Our main goal was to test for recombination in the S-locus region. In A. thaliana, the single-copy ARK3 gene is closely linked to the non-functional copies of the self-incompatibility loci, and the ortholog in A. lyrata (a self-incompatible species) is in the homologous genome region and is known as Aly8. It is thus of interest to test whether Aly8 sequence diversity is elevated due to close linkage to the highly polymorphic incompatibility locus, as is theoretically predicted. However, Aly8 is not a single-copy gene, and the presence of paralogs could also lead to the appearance of elevated diversity. We established a typing approach based on different lengths of Aly8 PCR products and show that most A. lyrata haplotypes have a single copy, but some have two gene copies, both closely linked to the incompatibility locus, one being a pseudogene. We determined the phase of multiple haplotypes in families of plants from Icelandic and other populations. Different Aly8 sequence types are associated with different SRK alleles, while haplotypes with the same SRK sequences tend to have the same Aly8 sequence. There is evidence of some exchange of sequences between different Aly8 sequences, making it difficult to determine which ones are allelic or to estimate the diversity. However, the homogeneity of the Aly8 sequences of each S-haplotype suggests that recombination between the loci has been very infrequent over the evolutionary history of these populations. Overall, the results suggest that recombination rarely occurs in the interval between the S-loci and Aly8 and that linkage to the S-loci can probably account for the observed high Aly8 diversity.

A simple and robust statistical test for detecting the presence of recombination

Recombination is a powerful evolutionary force that merges historically distinct genotypes. But the extent of recombination within many organisms is unknown, and even determining its presence within a set of homologous sequences is a difficult question. Here we develop a new statistic, phi(w), that can be used to test for recombination. We show through simulation that our test can discriminate effectively between the presence and absence of recombination, even in diverse situations such as exponential growth (star-like topologies) and patterns of substitution rate correlation. A number of other tests, Max chi2, NSS, a coalescent-based likelihood permutation test (from LDHat), and correlation of linkage disequilibrium (both r2 and /D'/) with distance, all tend to underestimate the presence of recombination under strong population growth. Moreover, both Max chi2 and NSS falsely infer the presence of recombination under a simple model of mutation rate correlation. Results on empirical data show that our test can be used to detect recombination between closely as well as distantly related samples, regardless of the suspected rate of recombination. The results suggest that phi(w) is one of the best approaches to distinguish recurrent mutation from recombination in a wide variety of circumstances.

Recombination estimation under complex evolutionary models with the coalescent composite-likelihood method

The composite-likelihood estimator (CLE) of the population recombination rate considers only sites with exactly two alleles under a finite-sites mutation model (McVean, G. A. T., P. Awadalla, and P. Fearnhead. 2002. A coalescent-based method for detecting and estimating recombination from gene sequences. Genetics 160:1231-1241). While in such a model the identity of alleles is not considered, the CLE has been shown to be robust to minor misspecification of the underlying mutational model. However, there are many situations where the putative mutation and demographic history can be quite complex. One good example is rapidly evolving pathogens, like HIV-1. First we evaluated the performance of the CLE and the likelihood permutation test (LPT) under more complex, realistic models, including a general time reversible (GTR) substitution model, rate heterogeneity among sites (Gamma), positive selection, population growth, population structure, and noncontemporaneous sampling. Second, we relaxed some of the assumptions of the CLE allowing for a four-allele, GTR + Gamma model in an attempt to use the data more efficiently. Through simulations and the analysis of real data, we concluded that the CLE is robust to severe misspecifications of the substitution model, but underestimates the recombination rate in the presence of exponential growth, population mixture, selection, or noncontemporaneous sampling. In such cases, the use of more complex models slightly increases performance in some occasions, especially in the case of the LPT. Thus, our results provide for a more robust application of the estimation of recombination rates.

Approximating the coalescent with recombination

The coalescent with recombination describes the distribution of genealogical histories and resulting patterns of genetic variation in samples of DNA sequences from natural populations. However, using the model as the basis for inference is currently severely restricted by the computational challenge of estimating the likelihood. We discuss why the coalescent with recombination is so challenging to work with and explore whether simpler models, under which inference is more tractable, may prove useful for genealogy-based inference. We introduce a simplification of the coalescent process in which coalescence between lineages with no overlapping ancestral material is banned. The resulting process has a simple Markovian structure when generating genealogies sequentially along a sequence, yet has very similar properties to the full model, both in terms of describing patterns of genetic variation and as the basis for statistical inference.

Gene-history correlation and population structure

Correlation of gene histories in the human genome determines the patterns of genetic variation (haplotype structure) and is crucial to understanding genetic factors in common diseases. We derive closed analytical expressions for the correlation of gene histories in established demographic models for genetic evolution and show how to extend the analysis to more realistic (but more complicated) models of demographic structure. We identify two contributions to the correlation of gene histories in divergent populations: linkage disequilibrium, and differences in the demographic history of individuals in the sample. These two factors contribute to correlations at different length scales: the former at small, and the latter at large scales. We show that recent mixing events in divergent populations limit the range of correlations and compare our findings to empirical results on the correlation of gene histories in the human genome.

High local genetic diversity and low outcrossing rate in Caenorhabditis elegans natural populations

BACKGROUND

Caenorhabditis elegans is a major model system in biology, yet very little is known about its biology outside the laboratory. In particular, its unusual mode of reproduction with self-fertile hermaphrodites and facultative males raises the question of its frequency of outcrossing in natural populations.

RESULTS

We describe the first analysis of C. elegans individuals sampled directly from natural populations. C. elegans is found predominantly in the dauer stage and with a very low frequency of males versus hermaphrodites. Whereas C. elegans was previously shown to display a low worldwide genetic diversity, we find by comparison a surprisingly high local genetic diversity of C. elegans populations; this local diversity is contributed in great part by immigration of new alleles rather than by mutation. Our results on heterozygote frequency, male frequency, and linkage disequilibrium furthermore show that selfing is the predominant mode of reproduction in C. elegans natural populations but that infrequent outcrossing events occur, at a rate of approximately 1%.

CONCLUSIONS

Our results give a first insight in the biology of C. elegans in the natural populations. They demonstrate that local populations of C. elegans are genetically diverse and that a low frequency of outcrossing allows for the recombination of these locally diverse genotypes.

A comparison of three estimators of the population-scaled recombination rate: accuracy and robustness

We have performed simulations to assess the performance of three population genetics approximate-likelihood methods in estimating the population-scaled recombination rate from sequence data. We measured performance in two ways: accuracy when the sequence data were simulated according to the (simplistic) standard model underlying the methods and robustness to violations of many different aspects of the standard model. Although we found some differences between the methods, performance tended to be similar for all three methods. Despite the fact that the methods are not robust to violations of the underlying model, our simulations indicate that patterns of relative recombination rates should be inferred reasonably well even if the standard model does not hold. In addition, we assess various techniques for improving the performance of approximate-likelihood methods. In particular we find that the composite-likelihood method of Hudson (2001) can be improved by including log-likelihood contributions only for pairs of sites that are separated by some prespecified distance.

The extent and importance of intragenic recombination

We have studied the recombination rate behaviour of a set of 140 genes which were investigated for their potential importance in inflammatory disease. Each gene was extensively sequenced in 24 individuals of African descent and 23 individuals of European descent, and the recombination process was studied separately in the two population samples. The results obtained from the two populations were highly correlated, suggesting that demographic bias does not affect our population genetic estimation procedure. We found evidence that levels of recombination correlate with levels of nucleotide diversity. High marker density allowed us to study recombination rate variation on a very fine spatial scale. We found that about 40 per cent of genes showed evidence of uniform recombination, while approximately 12 per cent of genes carried distinct signatures of recombination hotspots. On studying the locations of these hotspots, we found that they are not always confined to introns but can also stretch across exons. An investigation of the protein products of these genes suggested that recombination hotspots can sometimes separate exons belonging to different protein domains; however, this occurs much less frequently than might be expected based on evolutionary studies into the origins of recombination. This suggests that evolutionary analysis of the recombination process is greatly aided by considering nucleotide sequences and protein products jointly.

Local genetic population structure in an endangered plant species, Silene tatarica (Caryophyllaceae)

Genetic substructuring in plant populations may evolve as a consequence of sampling events that occur when the population is founded or regenerated, or if gene dispersal by pollen and seeds is restricted within a population. Silene tatarica is an endangered, perennial plant species growing along periodically disturbed riverbanks in northern Finland. We investigated the mechanism behind the microspatial genetic structure of S. tatarica in four subpopulations using amplified fragment length polymorphism markers. Spatial autocorrelation revealed clear spatial genetic structure in each subpopulation, even though the pattern diminished in older subpopulations. Parentage analysis in an isolated island subpopulation indicated a very low level of selfing and avoidance of breeding between close relatives. The mean estimated pollen dispersal distance (24.10 m; SD = 10.5) was significantly longer and the mean seed dispersal distance (9.07 m; SD = 9.23) was considerably shorter than the mean distance between the individuals (19.20 m; SD = 13.80). The estimated indirect and direct estimates of neighbourhood sizes in this subpopulation were very similar, 32.1 and 37.6, respectively. Our results suggested that the local spatial genetic structure in S. tatarica was attributed merely to the isolation-by-distance process rather than founder effect, and despite free pollen movement across population, restricted seed dispersal maintains local genetic structure in this species.

The molecular population genetics of HIV-1 group O

HIV-1 group O originated through cross-species transmission of SIV from chimpanzees to humans and has established a relatively low prevalence in Central Africa. Here, we infer the population genetics and epidemic history of HIV-1 group O from viral gene sequence data and evaluate the effect of variable evolutionary rates and recombination on our estimates. First, model selection tools were used to specify suitable evolutionary and coalescent models for HIV group O. Second, divergence times and population genetic parameters were estimated in a Bayesian framework using Markov chain Monte Carlo sampling, under both strict and relaxed molecular clock methods. Our results date the origin of the group O radiation to around 1920 (1890-1940), a time frame similar to that estimated for HIV-1 group M. However, group O infections, which remain almost wholly restricted to Cameroon, show a slower rate of exponential growth during the twentieth century, explaining their lower current prevalence. To explore the effect of recombination, the Bayesian framework is extended to incorporate multiple unlinked loci. Although recombination can bias estimates of the time to the most recent common ancestor, this effect does not appear to be important for HIV-1 group O. In addition, we show that evolutionary rate estimates for different HIV genes accurately reflect differential selective constraints along the HIV genome.

Linkage disequilibrium as a signature of selective sweeps

The hitchhiking effect of a beneficial mutation, or a selective sweep, generates a unique distribution of allele frequencies and spatial distribution of polymorphic sites. A composite-likelihood test was previously designed to detect these signatures of a selective sweep, solely on the basis of the spatial distribution and marginal allele frequencies of polymorphisms. As an excess of linkage disequilibrium (LD) is also known to be a strong signature of a selective sweep, we investigate how much statistical power is increased by the inclusion of information regarding LD. The expected pattern of LD is predicted by a genealogical approach. Both theory and simulation suggest that strong LD is generated in narrow regions at both sides of the location of beneficial mutation. However, a lack of LD is expected across the two sides. We explore various ways to detect this signature of selective sweeps by statistical tests. A new composite-likelihood method is proposed to incorporate information regarding LD. This method enables us to detect selective sweeps and estimate the parameters of the selection model better than the previous composite-likelihood method that does not take LD into account. However, the improvement made by including LD is rather small, suggesting that most of the relevant information regarding selective sweeps is captured by the spatial distribution and marginal allele frequencies of polymorphisms.

Insights into recombination from patterns of linkage disequilibrium in humans

An ability to predict levels of linkage disequilibrium (LD) between linked markers would facilitate the design of association studies and help to distinguish between evolutionary models. Unfortunately, levels of LD depend crucially on the rate of recombination, a parameter that is difficult to measure. In humans, rates of genetic exchange between markers megabases apart can be estimated from a comparison of genetic and physical maps; these large-scale estimates can then be interpolated to predict LD at smaller ("local") scales. However, if there is extensive small-scale heterogeneity, as has been recently proposed, local rates of recombination could differ substantially from those averaged over much larger distances. We test this hypothesis by estimating local recombination rates indirectly from patterns of LD in 84 genomic regions surveyed by the SeattleSNPs project in a sample of individuals of European descent and of African-Americans. We find that LD-based estimates are significantly positively correlated with map-based estimates. This implies that large-scale, average rates are informative about local rates of recombination. Conversely, although LD-based estimates are based on a number of simplifying assumptions, it appears that they capture considerable information about the underlying recombination rate or at least about the ordering of regions by recombination rate. Using LD-based estimators, we also find evidence for homologous gene conversion in patterns of polymorphism. However, as we demonstrate by simulation, inferences about gene conversion are unreliable, even with extensive data from homogeneous regions of the genome, and are confounded by genotyping error.

The use of linkage disequilibrium to map quantitative trait loci

This paper reviews the causes of linkage disequilibrium and its use in mapping quantitative trait loci. The many causes of linkage disequilibrium can be understood as due to similarity in the coalescence tree of different loci. Consideration of the way this comes about allows us to divide linkage disequilibrium into 2 types: linkage disequilibrium between any 2 loci, even if they are unlinked, caused by variation in the relatedness of pairs of animals; and linkage disequilibrium due to the inheritance of chromosome segments that are identical by descent from a common ancestor. The extent of linkage disequilibrium due to the latter cause can be logically measured by the chromosome segment homozygosity which is the probability that chromosome segments taken at random from the population are identical by descent. This latter cause of linkage disequilibrium allows us to map quantitative trait loci to chromosome regions. The former cause of linkage disequilibrium can cause artefactual quantitative trait loci at any position in the genome. These artefacts can be avoided by fitting the relatedness of animals in the statistical model used to map quantitative trait loci. In the future it may be convenient to estimate this degree of relatedness between individuals from markers covering the whole genome. The statistical model for mapping quantitative trait loci also requires us to estimate the probability that 2 animals share quantitative trait loci alleles at a particular position because they have inherited a chromosome segment containing the quantitative trait loci identical by descent. Current methods to do this all involve approximations. Methods based on concepts of coalescence and chromosome segment homozygosity are useful, but improvements are needed for practical analysis of large datasets. Once these probabilities are estimated they can be used in flexible linear models that conveniently combine linkage and linkage disequilibrium information.

Genome-Wide Linkage Disequilibrium and Haplotype Maps

There is currently a broad effort to produce genome-wide high-density linkage disequilibrium (LD) maps with single nucleotide polymorphisms. The hope is that the resulting maps can be exploited to find genes that affect the onset and severity of at least some common human diseases. These maps may also be useful for identifying genes that affect drug response or the likelihood of drug toxicities. The goal of this review is to provide a broad overview of some of the key concerns motivating the design of a major international project called the International Haplotype Map Project. The process of map production requires the identification of very large numbers of polymorphic sites, implementation of facile, highly accurate and inexpensive genotyping production pipelines, and provision for public access to the genotype data. Great progress has been made recently in genotyping methods and these advances are allowing very large-scale data collection. A major goal of these efforts is to enable the selection of subsets of markers that capture useful genetic information in short genomic intervals, while optimally reducing the number of markers that must be genotyped. Standard measures of LD provide a starting point but may not fully capture the complexity of the information inherent in the data. Extremely dense genotype data in several broadly representative populations (European, Chinese, Japanese, and Yoruba) should yield important insights into the genetic structure of most genes. Further study is required to determine how broadly applicable the data will be to other population groups. Significant challenges lie ahead in determining the best methods for the selection of markers in disease/phenotype studies, large-scale genotyping, and analysis of the resulting genetic data.

Estimating recombination rates from population-genetic data

Obtaining an accurate measure of how recombination rates vary across the genome has implications for understanding the molecular basis of recombination, its evolutionary significance and the distribution of linkage disequilibrium in natural populations. Although measuring the recombination rate is experimentally challenging, good estimates can be obtained by applying population-genetic methods to DNA sequences taken from natural populations. Statistical methods are now providing insights into the nature and scale of variation in the recombination rate, particularly in humans. Such knowledge will become increasingly important owing to the growing use of population-genetic methods in biomedical research.

Genetic structure and gene flow in a metapopulation of an endangered plant species, Silene tatarica

We investigated the distribution of genetic variation within and between seven subpopulations in a riparian population of Silene tatarica in northern Finland by using amplified fragment length polymorphism (AFLP) markers. A Bayesian approach-based clustering program indicated that the marker data contained not only one panmictic population, but consisted of seven clusters, and that each original sample site seems to consist of a distinct subpopulation. A coalescent-based simulation approach shows recurrent gene flow between subpopulations. Relative high FST values indicated a clear subpopulation differentiation. However, amova analysis and UPGMA-dendrogram did not suggest any hierarchical regional structuring among the subpopulations. There was no correlation between geographical and genetic distances among the subpopulations, nor any correlation between the subpopulation census size and amount of genetic variation. Estimates of gene flow suggested a low level of gene flow between the subpopulations, and the assignment tests proposed a few long-distance bidirectional dispersal events between the subpopulations. No apparent difference was found in within-subpopulation genetic diversity among upper, middle and lower regions along the river. Relative high amounts of linkage disequilibrium at subpopulation level indicated recent population bottlenecks or admixture, and at metapopulation levels a high subpopulation turnover rate. The overall pattern of genetic variation within and between subpopulations also suggested a 'classical' metapopulation structure of the species suggested by the ecological surveys.

Theory of the effects of population structure and sampling on patterns of linkage disequilibrium applied to genomic data from humans

We develop predictions for the correlation of heterozygosity and for linkage disequilibrium between two loci using a simple model of population structure that includes migration among local populations, or demes. We compare the results for a sample of size two from the same deme (a single-deme sample) to those for a sample of size two from two different demes (a scattered sample). The correlation in heterozygosity for a scattered sample is surprisingly insensitive to both the migration rate and the number of demes. In contrast, the correlation in heterozygosity for a single-deme sample is sensitive to both, and the effect of an increase in the number of demes is qualitatively similar to that of a decrease in the migration rate: both increase the correlation in heterozygosity. These same conclusions hold for a commonly used measure of linkage disequilibrium (r(2)). We compare the predictions of the theory to genomic data from humans and show that subdivision might account for a substantial portion of the genetic associations observed within the human genome, even though migration rates among local populations of humans are relatively large. Because correlations due to subdivision rather than to physical linkage can be large even in a single-deme sample, then if long-term migration has been important in shaping patterns of human polymorphism, the common practice of disease mapping using linkage disequilibrium in "isolated" local populations may be subject to error.