Modelling the wind effect in predator–prey interactions

Abstract

Understanding how abiotic factors affect predator–prey interaction is essential due to rapid anthropogenic climate change. Field experiments showed that wind speed (one of the most common abiotic factors) significantly affects the predator’s attack rate, which could be positive or negative. Motivated by the experimental study of Quinn and Cresswell (2004), in the present paper, we investigate the impact of wind speed on a well-known Gause-type model and consider that moderate wind speed benefits predators by increasing their attack rate, whereas enormous wind speed is detrimental for predators by decreasing their attack rate. We explore the system’s dynamical behaviour in biparameter space and provide theoretical proof of global stability of the unique coexistence equilibrium. We observe the existence of a unique and stable limit cycle, two successive transcritical bifurcations, the bubbling phenomenon, etc. Our findings reveal that under the low carrying capacity of prey, the coexistence of the species is possible only for an intermediate range of wind strength. We also observe that wind strength acts as a control parameter in forming and eliminating oscillations within the system. So, wind can have both stabilizing and destabilizing effects. Further, we explore the variation of population densities by changing the wind strength and carrying capacity. We observe that the prey density depends only on the wind strength. In contrast, the predator density depends on both wind strength and carrying capacity, where half of the prey’s carrying capacity plays a vital role in the variation of density. So, the effect of wind on predator–prey interactions is diverse and depends on several factors, including the species’ environmental carrying capacity.