Effect of heterogeneity in recombination rate on variation in realised relationship

Individuals of a specified pedigree relationship vary in the proportion of the genome they share identical by descent, i.e. in their realised or actual relationship. Predictions of the variance in realised relationship have previously been based solely on the proportion of the map length shared, which requires the implicit assumption that both recombination rate and genetic information are uniformly distributed along the genome. This ignores the possible existence of recombination hotspots, and fails to distinguish between coding and non-coding sequences. In this paper, we therefore quantify the effects of heterogeneity in recombination rate at broad and fine-scale levels on the variation in realised relationship. Variance is usually greater on a chromosome with a non-uniform recombination rate than on a chromosome with the same map length and uniform recombination rate, especially if recombination rates are higher towards chromosome ends. Reductions in variance can also be obtained, however, and the overall pattern of change is quite complex. In general, local (fine-scale) variation in recombination rate, e.g. hotspots, has a small influence on the variance in realised relationship. Differences in rates across longer regions and between chromosome ends can increase or decrease the variance in a realised relationship, depending on the genomic architecture.