PREDICTING RISK-TAKING BEHAVIOR FROM LIFE-HISTORY THEORY USING STATIC OPTIMIZATION TECHNIQUE

Gilliam improved the possibility of predicting habitat choice and risk-taking behaviour in juvenile animals by the rule of "minimization of mortality rate over growth rate (mu/g)", derived by using dynamic optimization technique. I have derived a similar expression (M/k) by using static optimization. M is instantaneous mortality rate, and k is the growth constant from the von Bertalanffy growth function. Both Gilliam's and my expressions were derived for situations where animals maximize fitness in stable populations (per capita growth rate r = 0). The more general expression from my analysis becomes (M+r)/k. Independent of the level of maximum fitness, the slope of the M-k curve at optimum growth and mortality conditions was found to be constant. This slope was determined by fecundity, size at reproduction, and maximum attainable size. In order to avoid using fitness explicitly in the final solution, I derived an alternative expression for predicting risk-taking behaviour. The resulting expression became s(W+g/W (= sG), where s is survival rate, W is individual weight, and g is growth rate. This expression was derived from the Euler-Lotka equation. The marginal risk describing the optimum trade off between growth and mortality became partial-mu/partial-g = (1-mu)/(W+g). Short-term sG-maximization should be appropriate in many different situations, but not for those which involves high initial costs such as long distance migration, and metamorphosis. In most situations (mu+r)/g-minimizers (mu/g when r = 0) and sG-maximizers should qualitatively behave similarly due to changes in growth and/or mortality conditions. Both rules may be used to predict ontogenetic niche shifts, but only sG can explicity predict at what body size the shift from one habitat to another should occur, W* = (s2g2-s1g1)/(s1-s2).