Figure 1. Coalescence Rates for Pairs of Random Chromosomes (Red) and for Pairs of Chromosomes from Affected Individuals (Green).

Notice that chromosomes from affected individuals have a small excess probability of coalescing very rapidly (i.e., in the most recent ten generations or so). Otherwise, their coalescence rates are essentially like those of random chromosomes. The region at the left-hand side of the graph between the red and green lines represents the excess probability of very recent coalescence among case chromosomes (denoted R in the text). This is what gives rise to the effect of cryptic relatedness. For larger t, the line for cases drops slightly below the line for random individuals, since both distributions integrate to 1. These plots assume an additive genetic model, with λ_s = 60, the “half”-relationships mating model, and a population size of 2,000. The line for cases was generated under the approximation that the excess relatedness is completely limited to the first n = 10 generations. In this case, the maximum coalescent probability for case chromosomes is 0.00275, when t = 1; R ≈ 0.00334. As expected, the mean coalescence time is ≈ 4,000 generations for both distributions. Alterations in n yield similar results (unpublished data).