Noisy predator-prey model explains oscillation patterns in sockeye salmon data.

A model of sockeye salmon population dynamics that incorporates predator-prey dynamics in the nursery lakes, salmon migration and stochastic effects is compared to Fraser River sockeye salmon spawner numbers with respect to cyclic dominance. For this comparison we use a method developed by White et al. (2014) to calculate measures for the consistency and strength of cyclic dominance in the time series using its wavelet transform. We find that the model can match the oscillation patterns found in nature, both for persistently oscillating populations and for intermittent oscillations. It matches persistently oscillating populations much better than a model that does not incorporate predator-prey interaction. Persistent oscillations are more likely to occur in the model if the growth conditions for the sockeye fry are good and the coupling to the predator is strong.

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.

The robustness of cyclic dominance under random fluctuations.

We investigate the influence of random perturbations on a recently introduced three-species model that reproduces the empirically observed pattern of cyclic dominance in Fraser River sockeye salmon. Since the sockeye populations are subject to various types of fluctuations affecting their growth and survival, we investigate the robustness of the model under several types of noise. In particular, we evaluate the variation of population sizes around their values in the deterministic model, the frequency of phase shifts in the 4-year oscillation, the extent of synchronization between different sockeye populations, and the response to strong one-time perturbations. Our main conclusion is that cyclic dominance is very stable even under strong noise in this model.