Markov Chain Monte Carlo sampling on multilocus genotypes

Abstract

Markov Chain Monte Carlo (MCMC) methods are used to solve complex problems in animal genetics. The MCMC samplers may mix slowly, making computation impractical. In this paper the behaviour of the whole locus sampler (L-sampler) in analysis of multilocus data was examined. To evaluate the mixing we monitored estimates for number of genes shared identical by descent between relatives. It was demonstrated in simulation study that linkage between loci may drastically reduce the efficiency of the L-sampler, leading to incorrect inference. Two samplers were considered to improve mixing of Markov chain: the multimeiosis sampler (MM-sampler) and the multilocus sampler (ML-sampler). It was concluded that MM- and ML-samplers improve mixing but do not guarantee practical irreducibility. A situation causing bad mixing was identified and some tips to tackle the problem were given.