Characterizing the existence of hydra effect in spatial predator-prey models and the influence of functional response types and species dispersal

Abstract

The hydra effect in ecology corresponds to the increase in the equilibrium or time-averaged density of a population when its mortality rate is augmented. The literature presents examples of the hydra effect in continuous as well as in discrete time population models described by nonlinear systems of ordinary differential and difference equations, respectively. The novelty of this work is that we show by means of numerical simulation the occurrence of the hydra effect in some stationary dynamics of one dimensional reaction-diffusion predator-prey models described by nonlinear systems of partial differential equations with distinct nonlinear functional responses. Reaction-diffusion models are a set of mathematical models that take into account population dynamics and dispersal (diffusivity) within a predefined spatial domain. We show that for a type 2 functional response an increasing diffusivity shortens the range of the hydra effect. Another interesting result concerns the fact that, together with the hydra effect, the prey density also increases with the increase of the per capita density-independent mortality rate of the predator. This result indicates that this top-down disturbance does not necessarily create a trophic cascade in a spatial predator-prey interaction at the steady-state regime.