Statistical interpretation of DNA evidence

The aim of this research is to assess the effect of recent admixture on the evaluation of DNA evidence. We develop an admixture model based on the distribution of individual admixture proportion in the population and allow us to relax the assumption of ramdom mating. Genetic disequilibrium depends on the variance and other higher moments of the distribution of individual admixture proportion. Although between locus disequilibrium is reduced by a half after each random mating, change in the mating pattern can lead to increase in the disequilibrium. Markov Chain Monte Carlo method is used to estimate important parameters such as population admixture proportions and allele frequencies in the parental populations. This is important especially for analysis of the New Zealand Maori population since allele frequencies for the ancestral population cannot be estimated directly. Simulation showed that the estimation algorithm is robust to the specification of the prior distributions. The gentoype frequency can be evaluated conditional on the individual's family history and the posterior density of observing the genotype at the crime scene can be estimated using importance sampling. This posterior predictive probability is equivalent to the match probability commonly used in forensic casework. We compare the match probability estimated under the admixture model and that under the substructure model using simulation and data from the New Zealand DNA database. Equivalent coancestry coefficient the value of θ which can be used in the substructure match probability to obtain a similar estimate compare to the admixture model, can be estimated. We show that the distribution of equivalent coancestry coefficient can be used to determine a value of θ which can be used to provide conservative estimate of the match probability under both population strucutres.