Optimal Life Histories for Structured Populations in Fluctuating Environments

I consider a population structured by age, size, condition, or any other relevant state variable. The environment fluctuates from year to year. Each year population members must make a reproductive decision before the environmental conditions of that year are known. I follow the standard approach in which one considers a subpopulation composed of individuals of the same genotype in an asexual species (or of individuals sharing the same allele for controlling behaviour in a sexual species). The fitness of the genotype is then defined as an appropriate growth rate for this subpopulation. The structure vector for the subpopulation describes the distribution of individual states of subpopulation members. Here the collective action of subpopulation members is viewed as giving an immediate reward to the genotype (or allele) and influencing the distribution of the structure vector next year. Fitness is characterised as the long-term average reward so obtained. Reproductive value is defined on structure vectors, that is, on distributions of states, not on individual states. An optimal strategy maximises the sum of the current reward and the expected reproductive value of the structure vector in one yearʹs time. In this definition of optimality, individuals are allowed to base their actions on the current structure vector and hence on the current states of kin. When individuals are only allowed to base their actions on their own state, an optimal strategy maximises an appropriate average of current reward plus expected future reproductive value. The optimality criteria described lead to natural methods by which optimal strategies can be calculated.