Persistence due to the adverse effect of the resource on the consumer

Abstract

We consider a modified Rosenzweig–MacArthur model that incorporates the negative impact of resource on the consumer. This negative effect of the resource has been empirically examined within various ecological systems. It plays a crucial role in driving transitions towards consumer extinction through multistability. Specifically, we show that the negative effect results in the bistability between two steady-state solutions for smaller values of the positive impact of resource on the consumer, whereas higher positive impact facilitates the coexistence of oscillatory behaviour and steady-state solution. We show that the presence of the predator’s negative efficiency facilitates abrupt transitions to distinct dynamical states in both forward and backward traces. We also show that the preferred state of the finite steady state for the persistence of both consumer and resource populations can be achieved for intermediate ranges of consumer’s positive and negative efficiency rates, carrying capacity and mortality rate of the consumer. We find that a large consumer’s negative efficiency rate always drives the system to the extinction of the consumer. We have derived analytical stability conditions for transcritical, Hopf and saddle-node bifurcations by a linear stability analysis, which agrees with the simulation results depicted in the two-parameter phase diagrams.