Another Way to Calculate Fitness from Life History Variables: Solution of the Age-Structured Logistic Equation

Abstract

r-selection refers to evolutionary competition in the rate of a population's exponential increase. This is contrasted with K-selection, in which populations in steady-state compete in efficiency of resource conversion. Evolution in nature is thought to combine these two in various proportions. But in modeling the evolution of life histories, theorists have used r-selection exclusively; up until now, there has not been a practical algorithm for computing the target function of K-selection. The Malthusian parameter, as computed from the Euler-Lotka equation, is a quantitative rendering of the r in r-selection, computed from the fundamental life history variables mortality and fertility. Herein, a quantitative formulation of K is derived in similar terms. The basis for our model is the logistic equation which, we argue, applies more generally than is commonly appreciated. Support is offered for the utility of this paradigm, and one example computation is exhibited, in which K-selection appears to support pleiotropic explanations for senescence only one fourth as well as r-selection.