Spatial modelling of gene frequencies in the presence of undetectable alleles

Bayesian hierarchical models are developed to estimate the frequencies of the alleles at the HLA-C locus in the presence of non-identifiable alleles and possible spatial correlations in a large but sparse, spatially defined database from Papua New Guinea. Bayesian model selection methods are applied to investigate the effects of altitude and language on the genetic diversity of HLA-C alleles. The general model includes fixed altitudinal effects, random language effects and random spatially structured location effects. Conditional autoregressive priors are used to incorporate the geographical structure of the map, and Markov chain Monte Carlo simulation methods are applied for estimation and inference. The results show that HLA-C allele frequencies are explained more by linguistic than altitudinal differences, indicating that genetic diversity at this locus in Papua New Guinea probably tracks population movements and is less influenced by natural selection than is variation at HLA-A and HLA-B.