Effect of introducing a competitor on cyclic dominance of sockeye salmon

We study the effects of introducing a competing species into a 3-species model for the population dynamics of sockeye salmon, thereby converting a food chain into a diamond module. We find that this often leads to the disappearance of the 4-year oscillation of sockeye salmon known as cyclic dominance when parameters are chosen such that all four species can coexist. Only when the population size of the competitor is small the phenomenon of cyclic dominance can persist. There is also a large region of parameter space where either the sockeye salmon or the competitor goes extinct. We discuss how these findings can be reconciled with the prevalence of cyclic dominance in many sockeye brood lakes.