Maximum-Likelihood and Markov Chain Monte Carlo Approaches to Estimate Inbreeding and Effective Size From Allele Frequency Changes

Maximum-likelihood and Bayesian (MCMC algorithm) estimates of the increase of the Wright-Malécot inbreeding coefficient, Ft, between two temporally spaced samples, were developed from the Dirichlet approximation of allelic frequency distribution (model MD) and from the admixture of the Dirichlet approximation and the probabilities of fixation and loss of alleles (model MDL). Their accuracy was tested using computer simulations in which Ft = 10% or less. The maximum-likelihood method based on the model MDL was found to be the best estimate of Ft provided that initial frequencies are known exactly. When founder frequencies are estimated from a limited set of founder animals, only the estimates based on the model MD can be used for the moment. In this case no method was found to be the best in all situations investigated. The likelihood and Bayesian approaches give better results than the classical F-statistics when markers exhibiting a low polymorphism (such as the SNP markers) are used. Concerning the estimations of the effective population size all the new estimates presented here were found to be better than the F-statistics classically used.