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)

T_n is the total branch length of the genealogy for a sample of size n, and ξ_n is the proportion of T_n accounted for by external branches. Both statistics are expressed relative to their neutral expectations, such that E(T_n)=E(ξ_n)=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 s_k (k∈{1, 2,..., K}). The number of sites of type k is denoted by L_k. 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 γ_k=Ns_k. 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.