Relatedness coefficients and their applications for triplets and quartets of genes

Abstract

ABSTRACTRelatedness coefficients which measure the genetic similarity of groups of genes (either three or four) are described. Cumulants and not moments are needed for four-gene probabilities, and also, the normalized fourth cumulant is the probability of identical-by-descent of all four genes. With four genes, a covariance of homozygosity between pairs of genes arises when populations follow a mixture distribution. Applications of three gene coefficients mainly involve conditional regression, and applications of four gene coefficients can involve identity disequilibrium. A novel estimator for identity disequilibrium emerges from calculations involving the cumulant. -Estimation of three- and four-gene relatedness using genetic marker data is briefly discussed. Three- and four-gene estimators explore new territory but suffer from statistical and numerical problems, including higher statistical variance, complexity of estimation formula, and non-estimability at some intermediate allele frequencies.