Strategies and trajectories of coral reef fish larvae optimizing self-recruitment

Like many marine organisms, most coral reef fishes have a dispersive larval phase. The fate of this phase is of great concern for their ecology as it may determine population demography and connectivity. As direct study of the larval phase is difficult, we tackle the question of dispersion from an opposite point of view and study self-recruitment. In this paper, we propose a mathematical model of the pelagic phase, parameterized by a limited number of factors (currents, predator and prey distributions, energy budgets) and which focuses on the behavioral response of the larvae to these factors. We evaluate optimal behavioral strategies of the larvae (i.e. strategies that maximize the probability of return to the natal reef) and examine the trajectories of dispersal that they induce. Mathematically, larval behavior is described by a controlled Markov process. A strategy induces a sequence, indexed by time steps, of "decisions" (e.g. looking for food, swimming in a given direction). Biological, physical and topographic constraints are captured through the transition probabilities and the sets of possible decisions. Optimal strategies are found by means of the so-called stochastic dynamic programming equation. A computer program is developed and optimal decisions and trajectories are numerically derived. We conclude that this technique can be considered as a good tool to represent plausible larval behaviors and that it has great potential in terms of theoretical investigations and also for field applications.