Understanding the impacts of extreme weather on biological control through traveling wave analysis of a prey-predator model

This study investigates the effects of extreme weather events on the efficacy of biological control of invasive species using a prey-predator reaction-diffusion model with the Allee effect. The model incorporates weather and environmental factors that affect species mortality, growth, and interaction rates. We first derive exact traveling wave solutions of the reduced model using the generalized exponential rational function method. The stability of the wave solutions is then numerically confirmed by demonstrating that the model solutions, perturbed by various levels of noise in the initial condition, converge to the traveling wave solutions. This suggests that extreme weather events that only impact the initial population sizes have only transient effects and do not change the fate of the species. Nevertheless, asymptotic analysis of the full model reveals conditions for the existence of bistable traveling wave solutions. This implies that extreme weather events may lead to predator extinction and the subsequent establishment of prey in a spatial domain. Hence, extreme weather events may lead to failure of biological control efforts and the persistence of invasive species. In addition, we establish conditions under which extreme weather events drive both prey and predator populations to extinction, which would be an ideal outcome for biological control of invasive species. This study highlights the importance of refining widely accepted ecological models to enhance the forecasting of ecological outcomes under extreme weather events.