Estimation of the rate and effects of deleterious genomic mutations in finite populations with linkage disequilibrium

Under several assumptions such as infinite population size with unlinked loci at linkage equilibrium (LD) under mutation selection (M-S) balance, the rate (U), and the average effects (dominance and selection coefficients (h) over bar and (s) over bar) of deleterious genomic mutations (DGM) can be estimated by the Deng-Lynch method in some natural populations. However, all natural populations are finite in size and many of them are not large enough to be considered as approximately infinite. In the absence of an analytical estimation approach to characterize DGM in finite populations, we test the robustness and applicability of the Deng-Lynch method in finite populations with computer simulations. The results indicate that the estimation obtained by the Deng-Lynch method in finite populations with LD is generally robust when population size is greater than 400. With constant mutation effects, in outcrossing populations, the estimates (U) over cap and (h) over cap are unbiased or only slightly upwardly biased, and (s) over cap is unbiased for most cases. In highly selfing populations, (U) over cap and (h) over cap are upwardly biased, (U) over cap is no more than 1.5U and (h) over cap is less than 1.1 h, and (s) over cap is either unbiased or slightly downwardly biased. With variable mutation effects, (U) over cap ranges from 0.56 to 0.72U, and (S) over cap ranges from 1.4 to 1.8 (s) over bar. Generally speaking, with the same finite population size, the estimation in outcrossing populations is better than in highly selfing populations. Given that even the order of the magnitude of the parameters of DMG (U in particular) is controversial, our investigation here may provide a basis for using the Deng-Lynch method to characterize DGM in finite populations of size greater than 400 in the presence of LD.