Asymptotic tests for Hardy-Weinberg equilibrium in hexaploids

Hexaploids, a group of organisms containing three complete sets of chromosomes in a single nucleus, are of utmost importance to evolutionary studies and breeding programs. Many studies have focused on hexaploid linkage analysis and QTL mapping in controlled crosses, but little methodology has been developed to reveal how hexaploids diversify and evolve in natural populations. We formulate a general framework for studying the pattern of genetic variation in autohexaploid populations through testing deviation from Hardy-Weinberg equilibrium (HWE) at individual molecular markers. We confirm that hexaploids cannot reach exact HWE but can approach asymptotic HWE at 8-9 generations of random mating. We derive a statistical algorithm for testing HWE and the occurrence of double reduction for autopolyploids, a phenomenon that affects population variation during long evolutionary processes. We perform computer simulation to validate the statistical behavior of our test procedure and demonstrate its usefulness by analyzing a real data set for autohexaploid chrysanthemum. When extended to allohexaploids, our test procedure will provide a generic tool for illustrating the genome structure of hexaploids in the quest to infer their evolutionary status and design association studies of complex traits.