A mathematical model of growth of population of fish in the larval stage: density-dependence effects.

A mathematical model for the growth of a population of fish in the larval stage is proposed. The emphasis is put on the first part of the larval stage, when the larvae are still passive. It is assumed that during this stage, the larvae move with the phytoplankton on which they feed and share their food equally, leading to ratio-dependence. The other stages of the life cycle are modeled using simple demographic mechanisms. A distinguishing feature of the model is that the exit from the early larval stage as well as from the active one is determined in terms of a threshold to be reached by the larvae. Simplifying the model further on, the whole dynamics is reduced to a two dimensional system of state-dependent delay equations. The model is put in perspective with some of the main hypotheses proposed in the literature as an explanation to the massive destruction which occurs between the egg stage and the adult stage.