Validity of the Quadratic Fitness Function

Abstract

MANLY¹ has questioned whether the quadratic fitness function can be applied in general to the measurement of selection for quantitative characters. As he points out, if individuals survive with a probability w per day, then after t days the probability of survival is w^t. If then the fitness function is quadratic, we have But after t′ days, the fitness function would then be which is not quadratic. Manly argues that selection cannot therefore be generally described by a quadratic fitness function. Selection can only be quadratic if t′=t. Manly prefers the “nor-optimal” fitness function^2,3 which takes the form of the normal frequency density and which does not change its form when raised to any power.