Natural selection and fitness entropy in a density-regulated population

The entropy H(po,p [equilibrium polymorphic]) of a population with the initial allele frequency po given the equilibrium polymorphic frequency p* has been proposed as a measure of natural selection. In the present paper, we have extended this concept to include a particular aspect of density-dependent selection. We compared size trajectory of a population initially at genetic equilibrium, Ṅ(t), with the size trajectories of populations not initially at p[equilibrium polymorphic],N(t), but which do eventually converge to a common equilibrium allele frequency and equilibrium density, N'. The following experimentally-testable hypothesis was established: the total area defined by the difference between the trajectories of Ṅ(t) and N(t) as they converge to N' is directly proportional to the fitness entropy when population size is transformed using the density-dependent fitness value. Two properties of this relationship were noted. First, it is independent of the magnitude of natural selection and, secondly, it does not depend upon the initial population density as long as the equilibrium and nonequilibrium populations have the same initial numbers. This hypothesis was evaluated with experimental data on the flour beetle Tribolium castaneum.