In this article, we develop an admixture F model (AFM) for the estimation of population-level coancestry coefficients from neutral molecular markers. In contrast to the previously published F model, the AFM enables disentangling small population size and lack of migration as causes of genetic differentiation behind a given level of F ST . We develop a Bayesian estimation scheme for fitting the AFM to multiallelic data acquired from a number of local populations. We demonstrate the performance of the AFM, using simulated data sets and real data on ninespine sticklebacks (Pungitius pungitius) and common shrews (Sorex araneus). The results show that the parameterization of the AFM conveys more information about the evolutionary history than a simple summary parameter such as F ST . The methods are implemented in the R package RAFM.
IN the fields of animal and plant breeding, coancestry coefficients are often used as measures of relatedness between individuals (Bink et al. 2008). For example, in a noninbred population the coancestry between full-sibs or between a parent and an offspring is 1 4 , and the coancestry between half-sibs is 1 8 (Lynch and Walsh 1998). Coancestry is the same as probability of identity by descent (IBD) at the limit of a low mutation rate and given a noninbred ancestral population. Two genes are said to be identical by descent if and only if they have not mutated since the most recent common ancestor.Individual-level coancestry coefficients (or probabilities of IBD) are useful in gene mapping, because they tell how much the genomes of two individuals are expected to resemble each other; i.e., they summarize the expected level of genetic similarity. In analogy, population-level coancestry coefficients can be used as measures of relatedness between local populations, and they can be combined with phenotypic data to detect signals of selection in quantitative traits, as opposed to those caused by random drift (Merilä and Crnokrak 2001;Mckay and Latta 2002;Ovaskainen et al. 2011).Coancestry coefficients can be calculated directly, if pedigree information is available, but their estimation for natural populations is often challenging. One approach for doing so is to use the link between coancestry coefficients and coalescence times (Rousset 2004). Coalescence time distributions can be solved, at least numerically, for a population that is in a stationary state, assuming that the demographic parameters are known (Bahlo and Griffiths 2001). However, in the context of evolutionary ecology of natural populations, this is rarely the case, as there is often limited direct information on demographic history, and it can be unrealistic to assume any kind of stationarity. Instead, a common approach is to infer the demographic history using neutral molecular markers genotyped from the present generation. One statistical framework for estimating coancestry coefficients in this way is given by the F model (Falush et al. 2003;Gaggiotti and Foll 2010). However, this approach suffers from the structural...