On the stock-recruitment relationships in fish population models

The framework of this article is modelling applied to fisheries. It aims at relating some classical stock-recruitment curves to a dynamic structured model, consisting of the adults stages of the stock and a pre-recruits stage (i.e. eggs, larvae, juveniles). The main result is that no functional stock-recruitment relationship can be found, unless further restrictive assumptions are added to the model (slow-fast dynamics and uniformity). Among the curves thus obtained is the Beverton--Holt curve, but not Ricker's.