Genetical Research

A Bayesian approach to the identification of panmictic populations and the assignment of individuals

KEVIN J.  DAWSON  a1 a2 c1 and KHALID  BELKHIR  a1
a1 Laboratoire Génome, Populations et Interactions, CNRS UMR 5000, Université de Montpellier II, Place Eugène Bataillon, 34095 Montpellier Cedex 5, France
a2 IACR, Long Ashton Research Station, Department of Agricultural Science, University of Bristol, Bristol BS41 9AF, UK


We present likelihood-based methods for assigning the individuals in a sample to source populations, on the basis of their genotypes at co-dominant marker loci. The source populations are assumed to be at Hardy–Weinberg and linkage equilibrium, but the allelic composition of these source populations and even the number of source populations represented in the sample are treated as uncertain. The parameter of interest is the partition of the set of sampled individuals, induced by the assignment of individuals to source populations. We present a maximum likelihood method, and then a more powerful Bayesian approach for estimating this sample partition. In general, it will not be feasible to evaluate the evidence supporting each possible partition of the sample. Furthermore, when the number of individuals in the sample is large, it may not even be feasible to evaluate the evidence supporting, individually, each of the most plausible partitions because there may be many individuals which are difficult to assign. To overcome these problems, we use low-dimensional marginals (the ‘co-assignment probabilities’) of the posterior distribution of the sample partition as measures of ‘similarity’, and then apply a hierarchical clustering algorithm to identify clusters of individuals whose assignment together is well supported by the posterior distribution. A binary tree provides a visual representation of how well the posterior distribution supports each cluster in the hierarchy. These methods are applicable to other problems where the parameter of interest is a partition of a set. Because the co-assignment probabilities are independent of the arbitrary labelling of source populations, we avoid the label-switching problem of previous Bayesian methods.

(Received September 11 2000)
(Revised December 22 2000)

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