Efficiency of truncation selection

Abstract

Truncation selection is known to be the most efficient form of directional selection. When this is modified so that the fitness increases linearly over a range of one or two standard deviations of the value of the selected character, the efficiency is reduced, but not greatly. When truncation selection is compared to a system in which fitness is strictly proportional to the character value, the relative efficiency of truncation selection is given by f(c)/sigma, in which f(c) is the ordinate of the frequency distribution at the truncation point and sigma is the standard deviation of the character. It is shown, for mutations affecting viability in Drosophila, that truncation selection or reasonable departures therefrom can reduce the mutation load greatly. This may be one way to reconcile the very high mutation rate of such genes with a small mutation load. The truncation model with directional selection is appropriate for this situation because of the approximate additivity of these mutations. On the other hand, it is doubtful that this simple model can be applied to all genes affecting fitness, for which there are intermediate optima and antagonistic selection among components with negative correlations. Whether nature ranks and truncates, or approximates this behavior, is an empirical question, yet to be answered.