Academic journal article Genetics

Empirical Bayes Inference of Pairwise F^sub ST^ and Its Distribution in the Genome

Academic journal article Genetics

Empirical Bayes Inference of Pairwise F^sub ST^ and Its Distribution in the Genome

Article excerpt

ABSTRACT

Populations often have very complex hierarchical structure. Therefore, it is crucial in genetic monitoring and conservation biology to have a reliable estimate of the pattern of population subdivision. F^sub ST^'s for pairs of sampled localities or subpopulations are crucial statistics for the exploratory analysis of population structures, such as cluster analysis and multidimensional scaling. However, the estimation of F^sub ST^ is not precise enough to reliably estimate the population structure and the extent of heterogeneity. This article proposes an empirical Bayes procedure to estimate locus-specific pairwise F^sub ST^'s. The posterior mean of the pairwise F^sub ST^ can be interpreted as a shrinkage estimator, which reduces the variance of conventional estimators largely at the expense of a small bias. The global F^sub ST^ of a population generally varies among loci in the genome. Our maximum-likelihood estimates of global F^sub ST^'s can be used as sufficient statistics to estimate the distribution of F^sub ST^ in the genome. We demonstrate the efficacy and robustness of our model by simulation and by an analysis of the microsatellite allele frequencies of the Pacific herring. The heterogeneity of the global F^sub ST^ in the genome is discussed on the basis of the estimated distribution of the global F^sub ST^ for the herring and examples of human single nucleotide polymorphisms (SNPs).

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INFERRING genetic population structure has been a major theme in population biology, ecology, and human genetics. The fixation index F^sub ST^, introduced by Wright (1951), is a key parameter for such studies and is most commonly used to measure genetic divergence among subpopulations (Palsbøll et al. 2007). It is defined as the correlation between random gametes drawn from the same subpopulation relative to the total population. Anothermeasure used frequently is Cockerham's (1969, 1973) coancestry coefficient, which is the probability that two random genes from different individuals are identical by descent, and the average overall pairs of individuals within the same subpopulation equal Wright's F^sub ST^ (Excoffier 2003). We use the notation uWC for the average coancestry coefficient and uWC = F^sub ST^ as shown by Weir and Cockerham (1984). Nei's (1973) GST is analogous to F^sub ST^ and identical to F^sub ST^ for diploid random-mating populations (Excoffier 2003).

Nei and Chesser (1983) proposed an estimator for F^sub ST^ and GST. The estimation of these parameters accounts only for the sampling error within subpopulations and therefore assumes that all subpopulations have been sampled (Cockerham and Weir 1986; Excoffier 2003). Weir and Cockerham (1984) developed the moment estimator uWC for the coancestry coefficient uWC, which takes the sampling error for the subpopulations into account. Severalmoment estimators with different weighting schemes have also been derived (Robertson and Hill 1984; Weir and Cockerham 1984). An alternative estimation has been discussed using the method of ordinary least squares (Reynolds et al. 1983). Weir and Hill (2002) extended uWC to a population-specific parameter to allow different levels of coancestry for different populations. They also derived an estimator for uWC with confidence intervals using a normal theory approach.

Despite the development of methods for assigning individuals to populations (Paetkau et al. 1995; Pritchard et al. 2000; Huelsenbeck and Andolfatto 2007), the differentiation estimators remain the most commonly used tools for describing population structure (Balloux and Lugon-Moulin 2002).Weir and Cockerham (1984) showed that their estimator uWC provides the smallest bias among the moment estimators. Goudet et al. (1996) confirmed this using simulations and showed that uWC generates the least-biased estimate of F^sub ST^ but has the largest variance when F^sub ST^ is small. Raufaste and Bonhomme (2000) showed that uWC is nearly unbiased, with minimal variance for large F^sub ST^, and that the estimator of Robertson and Hill (1984) uRH is negatively biased, with minimal variance for small F^sub ST^. …

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