Functional response and population dynamics for fighting predator, based on activity distribution

Garay, József and Varga, Zoltán and Gámez, Manuel and Cabello, Tomás Cabello (2015) Functional response and population dynamics for fighting predator, based on activity distribution. JOURNAL OF THEORETICAL BIOLOGY, 368 (7). pp. 74-82. ISSN 0022-5193

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Abstract

The classical Holling type II functional response, describing the per capita predation as function of prey density, was modified by Beddington and DeAngelis to include interference of predators that increases with predator density and decreases the number of killed prey. In the present paper we further generalize the Beddington–DeAngelis functional response, considering that all predator activities (searching and handling prey, fight and recovery) have time duration, the probabilities of predator activities depend on the encounter probabilities, and hence on the prey and predator abundance, too. Under these conditions, the aim of the study is to introduce a functional response for fighting predator and analyse the corresponding dynamics, when predator-predator-prey encounters also occur. From this general approach, the Holling type functional responses can be also obtained as particular cases. In terms of the activity distribution, we give biologically interpretable sufficient conditions for stable coexistence. We consider two-individual (predator-prey) and three-individual (predator-predator-prey) encounters. In the three-individual encounter model there is a relatively higher fighting rate and a lower killing rate. Using numerical simulation, we surprisingly found that when the intrinsic prey growth rate and the conversion rate are small enough, the equilibrium predator abundance is higher in the three-individual encounter case. The above means that, when the equilibrium abundance of the predator is small, coexistence appears first in the three-individual encounter model.

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