Modeling Extent and Distribution of Zygotic Disequilibrium: Implications for a Multigenerational Canine Pedigree

Unlike gametic linkage disequilibrium defined for a random-mating population, zygotic disequilibrium describes the nonrandom association between different loci in a nonequilibrium population that deviates from Hardy-Weinberg equilibrium. Zygotic disequilibrium specifies five different types of disequilibria simultaneously that are (1) Hardy-Weinberg disequilibria at each locus, (2) gametic disequilibrium (including two alleles in the same gamete, each from a different locus), (3) nongametic disequilibrium (including two alleles in different gametes, each from a different locus), (4) trigenic disequilibrium (including a zygote at one locus and an allele at the other), and (5) quadrigenic disequilibrium (including two zygotes each from a different locus). However, because of the uncertainty on the phase of the double heterozygote, gametic and nongametic disequilibria need to be combined into a composite digenic disequilibrium and further define a composite quadrigenic disequilibrium together with the quadrigenic disequilibrium. To investigate the extent and distribution of zygotic disequilibrium across the canine genome, a total of 148 dogs were genotyped at 247 microsatellite markers located on 39 pairs of chromosomes for an outbred multigenerational pedigree, initiated with a limited number of unrelated founders. A major portion of zygotic disequilibrium was contributed by the composite digenic and quadrigenic disequilibrium whose values and numbers of significant marker pairs are both greater than those of trigenic disequilibrium. All types of disequilibrium are extensive in the canine genome, although their values tend to decrease with extended map distances, but with a greater slope for trigenic disequilibrium than for the other types of disequilibrium. Considerable variation in the pattern of disequilibrium reduction was observed among different chromosomes. The results from this study provide scientific guidance about the determination of the number of markers used for whole-genome association studies.