title: Functional response and population dynamics for fighting predator, based on activity distribution.
abstract: The classical Holling type II functional response, describing the per capita predation as a function of prey density, was modified by Beddington and de Angelis 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-de Angelis 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 the predator and to analyse the corresponding dynamics, when predator-predator-prey encounters also occur. From this general approach, the Holling type functional responses can also be 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.
authors.affiliation: Research Group of Theoretical Biology and Ecology of Hungarian Academy of Sciences and Department of Plant Systematics, Ecology and Theoretical Biology, L. Eötvös University, Pázmány P. sétány 1/C, H-1117 Budapest, Hungary. Electronic address: garayj@caesar.elte.hu.
authors.forename: József
authors.initials: J
authors.lastname: Garay
authors.affiliation: Institute of Mathematics and Informatics, Szent István University, Páter K. u. 1., H-2103 Gödöllő, Hungary.
authors.forename: Zoltán
authors.initials: Z
authors.lastname: Varga
authors.affiliation: Center for Agribusiness Biotechnology Research, Almeria University, Ctra. Sacramento s/n, ES-04120 Almeria, Spain.
authors.forename: Manuel
authors.initials: M
authors.lastname: Gámez
authors.affiliation: Center for Agribusiness Biotechnology Research, Almeria University, Ctra. Sacramento s/n, ES-04120 Almeria, Spain.
authors.forename: Tomás
authors.initials: T
authors.lastname: Cabello
mesh_terms: D000465:Algorithms; D000818:Animals; D017753:Ecosystem; D008954:Models, Biological; D011157:Population Dynamics; D011235:Predatory Behavior / Q000502:physiology*
keywords: Activity distribution; Beddington–de Angelis functional response; Fighting between predators; Population dynamics; Prey-predator system