Optimal Allocation of Resources to Growth and Reproduction

In this paper we present a model in continuous time that allows us to analyse how an individual should allocate resources to growth and reproduction in order to maximize its lifetime contribution to future generations. Assuming that the death rate only depends on age, the allocation of energy is the solution of an optimization problem defined by a life history model. Making particular assumptions for the individual′s potential for growth and reproduction covering many situations of biological interest, the precise solution can be written up explicitely. Hence the effect of the various parameters may be analysed in detail. In general, the individual should first use all its energy to growth, then at a certain age invest a proportion of energy into reproduction. This fraction increases as the individual grow older. In some situations growth finally stops, while for other parameter values the individual continue to grow until it dies. This model was used to examine, for the von Bertanlanffy′s growth curve, the effects on age and size at maturity of changing the age-specific mortality rates. In general, the growth changes From a determinate growth to an indeterminate growth pattern when the mortality rate increases. In particular, a strong effect was found when the juvenile mortality increased. Rapid growth was also found to favour early maturation.