Abstract
The genomic proportion that two relatives share identically by descent—their genetic relatedness—can vary depending on the patterns of recombination and segregation in their pedigree. Here, we calculate the precise connection between genome-wide genetic shuffling and variance in genetic relatedness. For the relationships of grandparent-grandoffspring and siblings, the variance in genetic relatedness is a simple decreasing function of 
, the average proportion of locus pairs that recombine in gametogenesis. These formulations explain several recent observations about variance in genetic relatedness. They further allow us to calculate the neutral variance of ancestry among F2s in a hybrid cross, enabling F2-based tests for various kinds of selection, such as Dobzhansky-Muller incompatibilities and hybrid vigor. Our calculations also allow us to characterize how recombination affects the rate at which selection eliminates deleterious introgressed DNA after hybridization—by modulating the variance of introgressed ancestry across individuals. Species with low aggregate recombination rates, like Drosophila, purge introgressed DNA more rapidly and more completely than species with high aggregate recombination rates, like humans. These conclusions also hold for different genomic regions. Within the genomes of several species, positive correlations have been observed between local recombination rate and introgressed ancestry. Our results imply that these correlations can be driven more by recombination’s effect on the purging of deleterious introgressed alleles than its effect in unlinking neutral introgressed alleles from deleterious alleles. In general, our results demonstrate that the aggregate recombination process—as quantified by 
and analogs—acts as a variable barrier to gene flow between species.
