A Bayesian Approach to Inferring Rates of Selfing and Locus-Specific Mutation

Abstract

We present a Bayesian method for characterizing the mating system of populations reproducing through a mixture of selffertilization and random outcrossing. Our method uses patterns of genetic variation across the genome as a basis for inference about reproduction under pure hermaphroditism, gynodioecy, and a model developed to describe the self-fertilizing killifish Kryptolebias marmoratus. We extend the standard coalescence model to accommodate these mating systems, accounting explicitly for multilocus identity disequilibrium, inbreeding depression, and variation in fertility among mating types. We incorporate the Ewens sampling formula (ESF) under the infinite-alleles model of mutation to obtain a novel expression for the likelihood of mating system parameters. Our Markov chain Monte Carlo (MCMC) algorithm assigns locus-specific mutation rates, drawn from a common mutation rate distribution that is itself estimated from the data using a Dirichlet process prior model. Our sampler is designed to accommodate additional information, including observations pertaining to the sex ratio, the intensity of inbreeding depression, and other aspects of reproduction. It can provide joint posterior distributions for the population-wide proportion of uniparental individuals, locus-specific mutation rates, and the number of generations since the most recent outcrossing event for each sampled individual. Further, estimation of all basic parameters of a given model permits estimation of functions of those parameters, including the proportion of the gene pool contributed by each sex and relative effective numbers.KEYWORDS selfing rate; Ewens sampling formula; Bayesian; MCMC; mating system I NBREEDING generates genome-wide, multilocus disequilibria of various orders, transforming the context in which evolution proceeds. Here, we address a simple form of inbreeding: a mixture of self-fertilization (selfing) and random outcrossing (Clegg 1980;Ritland 2002).Various methods exist for the estimation of selfing rates from genetic data. Wright's (1921) fundamental approach bases the estimation of selfing rates on the coefficient of inbreeding (F IS ), a summary of the departure from HardyWeinberg proportions of genotypes for a given set of allele frequencies. The maximum-likelihood method of Enjalbert and David (2000) detects inbreeding from departures of multiple unlinked loci from Hardy-Weinberg proportions, estimating allele frequencies for each locus and accounting for correlations in heterozygosity among loci [identity disequilibrium (Cockerham and Weir 1968)]. David et al. (2007) extend the approach of Enjalbert and David (2000) to accommodate errors in scoring heterozygotes as homozygotes. A primary objective of InStruct (Gao et al. 2007) is the estimation of admixture. It extends the widely used program structure (Pritchard et al. 2000), which bases the estimation of admixture on disequilibria of various forms, by accounting for disequilibria due to selfing. Progeny array methods (see Ritland 2002), which base the estima...

Evolution of the sex ratio and effective number under gynodioecy and androdioecy

“…Crow and Denniston (1988) denoted the inverse of the rate of parent-sharing (N P ) as "inbreeding effective size." Redelings et al (2015) defined relative effective number (R) as the ratio of inbreeding effective size and the total effective number of reproductives (N = N G + N H ):…”

“…Empirical observations: Redelings et al (2015) developed a Bayesian method for the estimation of the rate of self-fertilization in pure hermaphrodite, gyndiodioecious, and androdioecious populations. It provides a means of inferring all model parameters, including the determinants of relative effective number R (2).…”

“…It provides a means of inferring all model parameters, including the determinants of relative effective number R (2). Figure 1 presents posterior distributions of R (2) for the three data sets studied by Redelings et al (2015), including those derived from two populations of the androdioecious killifish Kryptolebias marmoratus (Mackiewicz et al 2006;Tatarenkov et al 2012). An intriguing empirical observation is the near-maximization of relative effective number R in all three populations.…”

“…Estimation of relative viability: By incorporating our theoretical analysis into a previously-developed Bayesian inference framework (Redelings et al 2015), we develop a new method for inferring the viability of gonochores (males or females) relative to hermaphrodites.…”

Inductive determination of allele frequency spectrum probabilities in structured populations

“…While the probability that the next-sampled gene is novel (4) is well-known, the usual demonstration involves observing that it is a corollary of the ESF (e.g., Karlin and McGregor 1972). Redelings et al (2015) presented a first-principles derivation of (4) that does not require knowledge of the ESF in advance.…”