Model and Algorithm for Linkage Disequilibrium Analysis in a Non-Equilibrium Population

The multilocus analysis of polymorphisms has emerged as a vital ingredient of population genetics and evolutionary biology. A fundamental assumption used for existing multilocus analysis approaches is Hardy-Weinberg equilibrium at which maternally- and paternally-derived gametes unite randomly during fertilization. Given the fact that natural populations are rarely panmictic, these approaches will have a significant limitation for practical use. We present a robust model for multilocus linkage disequilibrium analysis which does not rely on the assumption of random mating. This new disequilibrium model capitalizes on Weir's definition of zygotic disequilibria and is based on an open-pollinated design in which multiple maternal individuals and their half-sib families are sampled from a natural population. This design captures two levels of associations: one is at the upper level that describes the pattern of cosegregation between different loci in the parental population and the other is at the lower level that specifies the extent of co-transmission of non-alleles at different loci from parents to their offspring. An MCMC method was implemented to estimate genetic parameters that define these associations. Simulation studies were used to validate the statistical behavior of the new model.