Sociobiology and the structural stability of behavior patterns
type: Item
instance of: scholarly article
title: Sociobiology and the structural stability of behavior patterns
zbMATH Open document ID: 0682.92007
DOI: 10.1016/0025-5564(89)90016-3
author: Gebhard Geiger
published in: Mathematical Biosciences
publication date: 1989-01-01T00:00:00Z
review text: A structural stability approach to population-genetic systems and to dynamic evolutionary games is attempted in order to examine the theoretical significance of sociobiological selection models. A criterion of weak selection is derived that is not restricted to differential reproduction in polymorphic systems but describes possible directions of evolutionary change in time scales governed by genetic mutation rates. The criterion applies to the problems of how the initial mutational basis of an adaptive trait may be established and how this may happen, for analogous traits, independently in different species. Two basic sociobiological concepts are reconsidered with reference to the criterion. It is shown that W. D. Hamilton's condition of increases in inclusive fitness due to altruistic interactions among kin expresses the structural instability of populations against the evolution of altruistic behavior. Using the dynamic approach to evolutionary game theory, it is demonstrated that if a behavioral phenotype is an evolutionarily stable strategy, it is structurally stable against perturbations of the fitness payoffs, provided selection is weak. These results are applied to material problems of the evolution of animal social behavior.
Mathematics Subject Classification ID: 92D15
Mathematics Subject Classification ID: 92D50
zbMATH DE Number: 4118209
zbMATH Keywords: structural stability approach
zbMATH Keywords: population-genetic systems
zbMATH Keywords: dynamic evolutionary games
zbMATH Keywords: sociobiological selection models
zbMATH Keywords: weak selection
zbMATH Keywords: genetic mutation rates
zbMATH Keywords: adaptive trait
zbMATH Keywords: W. D. Hamilton's condition of increases in inclusive fitness
zbMATH Keywords: structural instability
zbMATH Keywords: evolution of altruistic behavior
zbMATH Keywords: evolutionarily stable strategy
zbMATH Keywords: animal social behavior
Wikidata QID: Q52453296
reviewed by: T. Postelnicu
MaRDI profile type: Publication
full work available at URL: 0025-5564(89)90016-3
OpenAlex ID: W2066175124
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description: scientific article; zbMATH DE number 4118209