A classification of dynamic optimization problems in fluctuating environments

I consider how to classify and analyse models of the adaptive behaviour of an organism over a season. The classification is motivated by models of the timing of growth and reproduction in annual organisms, but applies to any model in which the population is unstructured at some convenient annual census time. During the season an organism makes a sequence of discrete behavioural choices. Each choice can be based on time in the season, any aspects of the organism’s state, such as its size or energy reserves, and current environmental conditions. The organism may be subject to sources of demographic stochasticity that act independently on different population members. There may also be a source of environmental stochasticity, such as weather conditions that cause the environment as a whole to fluctuate. The classification of models given here is based on the types of stochasticity that act. I identify those models where the optimal strategy can be found simply by employing a dynamic optimization technique such as dynamic programming. For problems that are not solvable in this way, I outline other approaches that can be used to find a solution.