On the stock–recruitment relationships in fish population models

The framework of this article is modeling 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.