Bayesian multilevel modelling of compositional data for simultaneous inferences on Allele compositions and inbreeding coefficients

Abstract

Sample data from a number of sub-populations are often investigated in order to integrate the findings of different research studies on a particular area. In case of compositional samples, like the allele frequencies collected at a single locus in different surveys, the data are independent multinomial vectors. Each multinomial distribution depends on a specific probability vector, that is, the unknown relative composition of the sub-population. A Bayesian hierarchy approach is proposed here to model the variability of the sub-composition vectors around a common mean with possibly different scales. The common mean can be seen as the relative composition of the aggregated population. Scale parameters are well known in Biology as the Wright's inbreeding coefficients. The method presented here extends some previous work by assuming less prior knowledge on the subject and constraints on the model. A relatively simple Monte Carlo algorithm is described to perform joint inferences on general and local compositions and inbreeding coefficients. The method is applied on two case studies. The first one is based on DNA samples from ten Italian regions at the loci TH01 and FES, obtained from a database currently used for forensic identification, in which inbreeding assessments can be crucial. The second application is based on a set of colour-blind sample rates in North-East Indian populations collected by Choudhury (1994). The Author found some controversial results from the classical test for comparing proportions. A clearer picture, instead, is obtained by the current Bayesian approach.