Effects of Predator-Driven Prey Dispersal on Sustainable Harvesting Yield

Journal article, 2022

Dispersal of organisms between patches is a common phenomenon in ecology and plays an
important role in predator–prey population dynamics. We propose a nonsmooth Filippov
predator–prey model in a two-patch environment characterized by a generalist predator-driven
intermittent refuge protection of an apprehensive prey along with a balanced dispersal of the
prey between refuge and nonrefuge areas. By employing qualitative techniques of nonsmooth
dynamical systems, we see that the switching surface is a repeller whenever the interior equilibria
are virtual, causing long-term population fluctuations.We find that the level of prey vigilance
and the rate of prey dispersal play pivotal roles in the total harvesting yield. We observe that
a sustainable high harvesting yield is possible when the prey is less vigilant and obtain the
harvesting efforts for maximum sustainable total yield (MSTY). We further modify the model
by considering a continuous threshold predator-driven prey dispersal and show that the model
exhibits a Hopf bifurcation when the level of prey vigilance exceeds some critical threshold value.
By comparing the dynamics of the two models we see that for a sustainable high harvesting yield
of the system with continuous threshold dispersal, the prey needs to be highly vigilant compared
to that of the system with intermittent dispersal of the prey. Further, we find numerically that
the estimated MSTY from both models remains the same.