The Alternative Fitness Sets Which Preserve Allele Trajectories: A General Treatment

A general solution is presented of the problem of specifying all alternative, generally frequency-dependent, (absolute) fitness sets which give rise to the same allele frequency changes and population dynamics as a given fitness set. The one- and two-locus cases are analyzed in detail and the method is then extended to the n-locus case. It is shown that if biological constraints can be used to specify the mean fitness of the population and the relative fitnesses of the heterozygotes, then the allele frequency trajectories determine a unique fitness set.