A three-species model explaining cyclic dominance of pacific salmon

TL;DR

This paper presents a mathematical model explaining the cyclic dominance of Pacific salmon, specifically sockeye, as a stable dynamical attractor caused by a resonance near a bifurcation, accounting for observed population oscillations.

Contribution

It introduces a novel dynamical systems model that explains salmon population cycles as a resonance phenomenon, linking biological observations to mathematical bifurcation theory.

Findings

Oscillations explained as a stable attractor near a Neimark Sacker bifurcation

Model reproduces empirical salmon abundance sequences

Explains why oscillations occur only in certain salmon stocks

Abstract

The four-year oscillations of the number of spawning sockeye salmon (Oncorhynchus nerka) that return to their native stream within the Fraser River basin in Canada are a striking example of population oscillations. The period of the oscillation corresponds to the dominant generation time of these fish. Various - not fully convincing - explanations for these oscillations have been proposed, including stochastic influences, depensatory fishing, or genetic effects. Here, we show that the oscillations can be explained as a stable dynamical attractor of the population dynamics, resulting from a strong resonance near a Neimark Sacker bifurcation. This explains not only the long-term persistence of these oscillations, but also reproduces correctly the empirical sequence of salmon abundance within one period of the oscillations. Furthermore, it explains the observation that these oscillations occur only in sockeye stocks originating from large oligotrophic lakes, and that they are usually not observed in salmon species that have a longer generation time.