Selection response in finite populations

Abstract

Formulae were derived to predict genetic response under various selection schemes assuming an infinitesimal model. Account was taken of genetic drift, gametic (linkage) disequilibrium (Bulmer effect), inbreeding depression, common environmental variance, and both initial segregating variance within families (σ(AW0)/2) and mutational (σ(M)/2) variance. The cumulative response to selection until generation t(CR(t)) can be approximated as CR(t) ≃ R0[t - β(1 - σ(AW(z))/2/σ(AW(o)/2)) t2/4N(r)] - D t/2N(r), where N, is the effective population size, σ(AW(z))/2 = N(r)σ(M)/2 is the genetic variance within families at the steady state (or one-half the genic variance, which is unaffected by selection), and D is the inbreeding depression per unit of inbreeding. R0 is the selection response at generation 0 assuming preselection so that the linkage disequilibrium effect has stabilized. β is the derivative of the logarithm of the asymptotic response with respect to the logarithm of the within-family genetic variance, i.e., their relative rate of change. R0 is the major determinant of the short term selection response, but σ(M)/2, N(r) and β are also important for the long term. A selection method of high accuracy using family information gives a small N(r) and will lead to a larger response in the short term and a smaller response in the long term, utilizing mutation less efficiently.