Variation in genetic relatedness is determined by the aggregate recombination process

Abstract

The genomic proportion that two relatives share identically by descent--their genetic relatedness-- can vary depending on the history of recombination and segregation in their pedigree. This variation is important in many applications of genetics, including pedigree-based estimation of the genetic variance and heritability of traits, and estimation of pedigree relationships from sequence data. Here, we calculate the variance of genetic relatedness for general pedigree relationships, making no assumptions about the recombination process. For the specific relationships of grandparent-grandoffspring and siblings, the variance of genetic relatedness is a simple decreasing function of [Formula], the average proportion of locus pairs that recombine in meiosis. For general pedigree relationships, the variance of genetic relatedness is likewise the average of some function of pairwise recombination rates. Therefore, features of the aggregate recombination process that affect [Formula] and analogs also affect variance in genetic relatedness. Such features include the number of chromosomes and heterogeneity in their size, and the number of crossovers and their location along chromosomes. Our calculations help to explain several recent observations about variance in genetic relatedness, including that it is reduced by crossover interference (which is known to increase [Formula]). Our methods further allow us to calculate the neutral variance of ancestry among F2s in a hybrid cross, enabling precise statistical inference in F2-based tests for various kinds of selection.