A Geometric Model for Optimal Life History

Abstract

Many authors (Williams, 1966; Gadgil and Bossert, 1970; Taylor et al., 1974; Schaffer, 1979) have considered models of optimal life history strategies. Most generally an organism at any particular age or size has a quantity of available resources which he can spend on maintenance, growth and/or reproduction, and his problem is to allocate these resources optimally. His objective is to maximize some measure of fitness or lifetime reproductive value. This optimization problem can be quite complex because decisions made at one stage may affect resources available at subsequent stages. Thus the mathematical analysis can be difficult and simple general patterns are hard to perceive. Our purpose is to consider a simple model which is quite general, and for which optimal allocation of resources can be determined by graphical analysis of suitable functions.