Inferring the evolutionary history of outcrossing populations through computing a multiallelic linkage–linkage disequilibrium map

Summary Linkage disequilibrium (LD), the non-random association of alleles at different loci, has been used as an important parameter to study the genetic diversity and evolutionary history of natural populations. A joint analysis of LD with the linkage of the same marker pair has proven to gain more insight into the genetic signature of population diversification than LD analysis alone. We develop a unifying framework for simultaneously estimating the linkage and LD across pairs of multiallelic markers. The framework has particular power to construct the LD map from any markers with an arbitrary number of alleles per locus. We provide an efficient strategy to manipulate disequilibrium parameters whose number increases exponentially with the number of alleles. The model was tested through extensive simulation studies and validated by analysing a real marker data set from a population genetic research project of euphrates poplar, a desert tree, distributed in the north-western China. For widespread undomesticated natural populations, compared with biallelic markers, multiallelic markers with a high level of polymorphism are more powerful to study their genetic structure and organization of an outcrossing population. The model developed will potentially have an immediate implication for population and evolutionary genetic studies.