Population persistence and spatially limited social interaction
type: Item
instance of: scholarly article
title: Population persistence and spatially limited social interaction
zbMATH Open document ID: 0842.92028
author: Yuko Harada
author: Hideo Ezoe
author: Yoh Iwasa
author: Hirotsugu Matsuda
author: Kazunori Sato
published in: Theoretical Population Biology
publication date: 1996-07-31T00:00:00Z
review text: We study a lattice structured population model in which the mortality of each individual is affected by the number of nearest neighbors. We examine the case in which mortality decreases with the number of neighboring individuals (beneficial or cooperative interaction) and the case in which mortality increases with the number of neighboring individuals (harmful or competitive interaction). Since the reproduction is possible only to neighboring vacant sites, the effect of local density (or a crowding effect) is naturally included. A similar model was studied by \textit{H. Matsuda} et al. [see Lect. Notes Biomath. 71, 154-161 (1987; Zbl 0642.92011)], who calculated, for example, the invadability condition for altruists into a population dominated by nonaltruists. Here we consider a model including only a single type, unlike in Matsuda et al., but instead we incorporate the migration of individuals, expressed as the movement of an individual to a vacant neighbor leaving the original site empty. Migration in effect causes the exchange of a nearest neighbor pair of occupied and vacant sites. By increasing the migration rate, we can change continuously from a perfectly sessile population, studied by Matsuda et al., through a population with limited dispersal, to a completely mixed population. In addition to pair approximation used by Matsuda et al., we also examined improved pair approximation introduced by \textit{K. Satō} et al. [J. Math. Biol. 32, No. 3, 251-268 (1994; Zbl 0790.92022)], and we further examine the modification of the method to allow a more accurate prediction of the equilibrium abundance.
Mathematics Subject Classification ID: 92D40
Mathematics Subject Classification ID: 60K35
zbMATH DE Number: 797081
zbMATH Keywords: socially interacting individuals
zbMATH Keywords: lattice structured population model
zbMATH Keywords: mortality
zbMATH Keywords: nearest neighbors
zbMATH Keywords: cooperative interaction
zbMATH Keywords: competitive interaction
zbMATH Keywords: migration of individuals
zbMATH Keywords: improved pair approximation
zbMATH Keywords: equilibrium abundance
MaRDI profile type: Publication
full work available at URL: tpbi.1995.1022
OpenAlex ID: W2021372875
Wikidata QID: Q52334215
DOI: 10.1006/TPBI.1995.1022
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description: scientific article; zbMATH DE number 797081