  We study the dynamics of predator-prey systems where prey are confined to a
single region of space and where predators move randomly according to a
power-law (L\'evy) dispersal kernel. Site fidelity, an important feature of
animal behaviour, is incorporated in the model through a stochastic resetting
dynamics of the predators to the prey patch. We solve in the long time limit
the rate equations of Lotka-Volterra type that describe the evolution of the
two species densities. Fixing the demographic parameters and the L\'evy
exponent, the total population of predators can be maximized for a certain
value of the resetting rate. This optimal value achieves a compromise between
over-exploitation and under-utilization of the habitat. Similarly, at fixed
resetting rate, there exists a L\'evy exponent which is optimal regarding
predator abundance. These findings are supported by 2D stochastic simulations
and show that the combined effects of diffusion and resetting can broadly
extend the region of species coexistence in ecosystems facing resources
scarcity.
