A framework to model a web of linkage disequilibria for natural allotetraploid populations

Linkage disequilibrium (LD) is an important genetic parameter used to infer the genetic diversity of natural populations and their evolutionary history. Traditionally, LD is defined as the non-random association of non-alleles at different loci in gametes for diploids, but has a limited use for polyploids. We formulate a framework to define tetraploid-specific LD including (a) Hardy–Weinberg disequilibria at each locus, (b) composite digenic disequilibrium, (c) trigenic disequilibrium and (d) composite quadrigenic disequilibrium at different loci. These four types of disequilibria affect population variation singly or jointly through a web. We implement the EM algorithm to estimate each disequilibrium parameter and test its significance in allotetraploid populations. We perform computer simulation to examine the statistical properties of our computational model. Through analysing a population genetic data of allotetraploid switchgrass, we chart the genomic distribution of LD on different chromosomes from which the evolutionary history of switchgrass is inferred, demonstrating the practical usefulness of the model. We have developed a statistical model for LD analysis in allotetraploids. The model can be generalized as a tool to study the population diversity and evolution of polyploid populations.