A fitness function for optimal life history in relation to density effects, competition, predation and stability of the environment

A fitness function (function maximized under natural selection) is studied in a population model in which the growth of a population is suppressed by crowding, density‐independent continuous mortality (by euryphagous predators) and periodic disturbances. The dynamics of the population density between occurrence of disturbance can be expressed as, dN/dt=(F(N/K)−D)N , where N is the population density, K is the carrying capacity, D is the density‐independent continuous mortality, and F is the growth regulation factor described as a function of crowding ( N/K ). The period of disturbance is S . The survival rate under disturbance is u . It is concluded that the fitness function is (approximately) a product of competitive ability ( C ), carrying capacity, and degree of saturation, and is given by CKF −1 ( D −(ln u )/ S ). The degree of saturation is the inverse function of regulation factor ( F ) at the death rate due to predators and disturbance. I assume a population in which density is regulated only through survival. In this case, a low survival rate at the critical age‐group means a high value of CKF −1 ( D −(ln u )/ S ). Therefore, the reciprocal of the density‐dependent survival rate at critical age‐group is a measure of the fitness function. Using this measure, I predict the optimal age (body size) at first reproduction of a species of salamander. I also found that fitness calculated from observed values of l(x) and m(x) includes a tautology. When the concept of fitness function is compared with the ESS method, the latter is more flexible. However, there is a possibility that an ESS is at the minimum of fitness function.