Application of slow - fast population dynamic models

The Beverton-Holt and Ricker functions are two distinct ecological descriptions of the link between a parental population size and subsequent offspring that may survive to become part of the fish stock. This report presents a model consisting of a system of ordinary differential equations (ODEs), which couples a pre-recruit stage with several adult stages. Elements of slow-fast dynamics capture the different time-scales of the population dynamics and lead to a singular perturbation problem. The novelty of the model presented here is its capability to replicate a broad spectrum of the stock-recruitment relationship (SRR), including the Beverton-Holt and Ricker dynamics. The results are explained using geometric singular perturbation theory and illustrated by numerical simulations.