Forward and reverse response to artificial selection

The effect of t ' generations of reverse selection after t generations of forward selection can be described by expressing the change in the metric mean resulting from reverse selection (R) interms ofthe change in the metric mean due to the previous forward selection (Δx). An additive model of artificial selection in a population of effective size N with no natural selection has been considered.If reverse selection is continued for as many generations as the previous forward selection (t'=t), then the ratio R/Δx equals 1 - F where F is the inbreeding coefficient for a neutral locus at generation t and is estimated as [1-(1-1/2N)(t)]. The result of a single generation of reverse selection (t'=1) following t generations of forward selection can be described in terms of the ratio NR1/ηDx where R1 is the response to the first generation of reverse selection. The value of NR1/Δx is expected to be (1-F) /2F.For any period of reverse selection following any period of forward selection, the value of R/Δx never exceeds t '/t, and tends to decrease exponentially from this value as t increases.