The estimation of a bivariate fitness function from two samples taken from a population

Summary The fitness of animals subjected to natural selection can be defined as the probability of surviving selection for a given interval of time, or some convenient multiple of this. If the fitness is related to some measurable variablesX, Y, Z,… then the relationship is expressed mathematically in the fitness functionw(x, y, z,…) and this function can be estimated by comparing the joint distribution ofX, Y, Z,… in samples taken before and after selection. In an earlier paper (Manly, 1975) the problems involved in estimating a fitness function of one variable were discussed. In the present paper various methods for estimating a bivariate fitness function are proposed and compared on some semiartificial sample data. It is concluded that either a generalized version ofO’Donald’s (1968) method of moments or a weighted multiple regression method will be most satisfactory. Alternative methods involving assumptions of normality will need to be used with great care.