On mechanisms of trophic cascade caused by anti-predation response in food chain systems

Abstract

Motivated by a recent field study [Nat. Commun. 7(2016), 10698] on the impact of fear of large carnivores on the populations in a cascading ecosystem of food chain type with the large carnivores as the top predator, in this paper we propose two model systems in the form of ordinary differential equations to mechanistically explore the cascade of such a fear effect. The models are of the Lotka-Volterra type, one is three imensional and the other four dimensional. The 3-D model only considers the cost of the anti-predation response reflected in the decrease of the production, while the 4-D model considers also the benefit of the response in reducing the predation rate, in addition to the cost by reducing the production. We perform a thorough analysis on the dynamics of the two models. The results reveal that the 3-D model and 4-model demonstrate opposite patterns for trophic cascade in terms of the dependence of population sizes for each species at the co-existence equilibrium on the anti-predation response level parameter, and such a difference is attributed to whether or not there is a benefit for the anti-predation response by the meso-carnivore species.
 

Computer‐assisted analysis of chaos in a three‐species food chain model

“…Some different predator-prey systems involving fear effect have been proposed and analyzed, see, for example, Refs. [5,6,9,23,32,33,49]. We describe the impact of fear factors on the food chain model and get the conclusion that fear factors will change the ecosystem from chaotic dynamics to a stable state.…”

Studying the fear effect in a predator-prey system with apparent competition

“…More recent work extends the study of fear effect to food-web systems where more than two trophic levels are incorporated [3,16,17,18,25,26]. In [3], the authors studied a three-species food chain model that includes a bottom prey, a middle predator, and a top predator and showed that the fear effect may drive the transition from chaotic behavior to a stable state for the system.…”

“…In [3], the authors studied a three-species food chain model that includes a bottom prey, a middle predator, and a top predator and showed that the fear effect may drive the transition from chaotic behavior to a stable state for the system. In [25], Wang and Zou analyzed the cascading effect of the fear from the top predator to the bottom prey where there is either one middle predator or two middle predators at different trophic levels. Other studies include the fear effect in a predator-prey system where there is an alternative food available, a predator-prey community of two predators and one prey, and the digestion delay in the biomass conversation from the prey to the predator [16,17,18,26].…”