A parametrized stock-recruitment relationship derived from a slow-fast population dynamic model

作者：Schaarschmidt Ute; Steihaug Trond; Subbey Sam

来源：Mathematics and Computers in Simulation, 2018, 145: 171-185.

DOI：10.1016/j.matcom.2017.10.008

• Slow-fast
• Population dynamic
• Stock-recruitment relationship
• Geometric singular perturbation theory
• Stage-structured model

The Beverton-Holt, Ricker and Deriso functions are three distinct descriptions of the link between a parental population size and subsequent offspring that may survive to become part of the fish population.
This paper presents a model consisting of a system of ordinary differential equations, which couples a stage of young fish with several adult stages. The slow-fast dynamics captures the different time scales of the dynamics of the population and leads to a singular perturbation problem.
The novelty of the model presented here is its capability to replicate a rich class of the stock-recruitment relationship, including the Beverton-Holt, Ricker and Deriso dynamics. The results are explained using geometric singular perturbation theory and illustrated by numerical simulations.

• 出版日期2018-3