Table 1. Patterns of diversity under a background selection model with complete linkage and variation in selection coefficients.
Case |
E(T2) |
E(T20) |
E(ξ20) |
||||
---|---|---|---|---|---|---|---|
Equation (6) | Forward | Coalescent | Forward | Coalescent | Forward | Coalescent | |
1 | 0.472 | 0.515 (0.418) | 0.550 (0.487) | 0.587 (0.162) | 0.623 (0.178) | 1.300 (0.385) | 1.295 (0.386) |
2 | 0.449 | 0.485 (0.411) | 0.521 (0.461) | 0.552 (0.156) | 0.593 (0.169) | 1.306 (0.379) | 1.297 (0.385) |
3 | 0.311 | 0.391 (0.314) | 0.414 (0.330) | 0.481 (0.122) | 0.510 (0.126) | 1.454 (0.374) | 1.459 (0.371) |
4 | 0.069 | 0.238 (0.173) | 0.224 (0.136) | 0.327 (0.074) | 0.327 (0.059) | 1.688 (0.355) | 1.783 (0.322) |
5 | 0.263 | 0.351 (0.275) | 0.370 (0.286) | 0.436 (0.109) | 0.463 (0.110) | 1.490 (0.367) | 1.502 (0.367) |
Tn is the total branch length of the genealogy for a sample of size n, and ξn is the proportion of Tn accounted for by external branches. Both statistics are expressed relative to their neutral expectations, such that E(Tn)=E(ξn)=1 under neutrality. The numbers shown in parentheses are s.d. There are K types of sites in the focal region, with mutations of type k having selective effect sk (k∈{1, 2,..., K}). The number of sites of type k is denoted by Lk. In all the simulations, the per-site mutation rate u is uniform across the region. The mutation and selection parameters are scaled by N, the population size, such that θ=Nu and γk=Nsk. In the absence of recombination, the properties of the statistics are unaffected by the physical organization of the selected sites and the presence/absence of neutral sites. For case 1, θ=0.005, K=2, L1=L2=1000, γ1=10 and γ2=20. For case 2, θ=0.005, K=3, L1=L2=L3=1000, γ1=10, γ2=25 and γ3=50. For case 3, θ=0.005, K=2, L1=1000, L2=2000, γ1=10 and γ2=15. Cases 4 and 5 are similar, both with K=2, L1=1334, L2=2668, γ1=10 and γ2=20; however, the scaled mutation for case 4 is θ=0.01, which is twofold higher than the value of 0.005 for case 5.