Fitness Functions Determine Optimal Parental Allocation: Redefining Trivers Willard Theory

Abstract

According to Trivers-Willard theory1, females in a good condition should carry more male offspring to maximize their fitness while should carry more females in a poor condition. Diverse theoretical and empirical studies has been performed to verify the validity of this claim2,3. Some portion of the empirical observations, however, exhibited contrary outcome to Trivers-Willard theory4. To resolve this problem, we computationally and mathematically show in here that reversed Trivers-Willard theory actually could be the outcome of the parental fitness optimization. In our models with identical fitness functions, we found that selective equitable care is optimal, and the number of the cared offspring should monotonically increase with maternal condition (or expendable parental investment). In some of our models with two distinguished male and female fitness functions, optimizations results were congruent with the conventional Trivers-Willard theory. In other models of ours, contrary to Trivers-Willard theory, it was optimal to invest in males when maternal condition was low. The results along with our hypothesis can explain the empirical observations that were previously thought to be the counterexample of Trivers-Willard theory. We propose that Trivers-Willard theory should be interpreted in multidimensional way, and more elaborate empirical data need to be collected to verify such propositions.