The effect of seasonal strength and abruptness on predator-prey dynamics.

Coupled dynamical systems in ecology are known to respond to the seasonal forcing of their parameters with multiple dynamical behaviours, ranging from seasonal cycles to chaos. Seasonal forcing is predominantly modelled as a sine wave. However, the transition between seasons is often more sudden as illustrated by the effect of snow cover on predation success. A handful of studies have mentioned the robustness of their results to the shape of the forcing signal but did not report any detailed analyses. Therefore, whether and how the shape of seasonal forcing could affect the dynamics of coupled dynamical systems remains unclear, while abrupt seasonal transitions are widespread in ecological systems. To provide some answers, we conduct a numerical analysis of the dynamical response of predator-prey communities to the shape of the forcing signal by exploring the joint effect of two features of seasonal forcing: the magnitude of the signal, which is classically the only one studied, and the shape of the signal, abrupt or sinusoidal. We consider both linear and saturating functional responses, and focus on seasonal forcing of the predator's discovery rate, which fluctuates with changing environmental conditions and prey's ability to escape predation. Our numerical results highlight that a more abrupt seasonal forcing mostly alters the magnitude of population fluctuations and triggers period-doubling bifurcations, as well as the emergence of chaos, at lower forcing strength than for sine waves. Controlling the variance of the forcing signal mitigates this trend but does not fully suppress it, which suggests that the variance is not the only feature of the shape of seasonal forcing that acts on community dynamics. Although theoretical studies may predict correctly the sequence of bifurcations using sine waves as a representation of seasonality, there is a rationale for applied studies to implement as realistic seasonal forcing as possible to make precise predictions of community dynamics.