Nonlinear Feedback Dynamics in Fisheries: Analysis of the Deriso–Schnute Model

Fishery models of the Deriso–Schnute form are based on the dynamics of an age-structured population, together with a nonlinear stock–recruitment relationship. Cyclical dynamics are commonly observed in fisheries and have been attributed to feedback between stock and recruitment. In this paper, we do four things. First, we present analytical results on sustained oscillations driven by nonlinear recruitment. These results show explicitly how density dependence near equilibrium determines the character of sustained population oscillations. Second, we briefly characterize the dynamics of the Deriso–Schnute model when the density-dependent response becomes very strong. We find that the Deriso–Schnute model displays sustained, complex (probably chaotic) variability of large magnitude, but only typically when reproduction is concentrated at very few ages. Third, we dissect the nature of density dependence in recruitment, contrasting a "local" view that uses information about response to small variations in stock with a "global" view that uses a function such as Schnute's over the entire range of stock levels. Finally, we argue that the global approach leads to practical and theoretical difficulties and that a local view may be more biologically realistic.