Spatial modelling of multinomial data with latent structure: an application to geographical mapping of human gene and haplotype frequencies.

We develop hierarchical models for spatial multinomial data with missing categories, to analyse a database of HLA-A and -B gene and haplotype frequencies from Papua New Guinea, with a highly variable number of samples per spatial unit. The spatial structure of the multinomial data is incorporated by adopting conditional autoregressive (CAR) priors for the random effects, reflecting extra-multinomial variation. Different spatial structures are investigated, and covariate effects are evaluated using a novel model selection criterion. Tables and maps reveal strong spatial association and the importance of altitude, a covariate anticipated to be significant in explaining genetic variation. Our approach can be used in identifying associations with environmental factors, linguistic or epidemiological patterns and hence potential causes of genetic diversity (population movements, natural selection, stochastic effects).