zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Hawk-dove game and competition dynamics. (English) Zbl 1185.91065
Summary: We consider two populations subdivided into two categories of individuals (hawks and doves). Individuals fight to have access to a resource necessary for their growth. Conflicts occur between hawks of the same population and hawks of different populations. The aim of this work is to investigate the long term effects of these conflicts on coexistence and stability of the community of the two populations. This model involves four variables corresponding to the two tactics of individuals of the two populations. The model is composed of two parts, a fast part describing the encounters and fights, and the slow part describing the long term effects of encounters on the growth of the populations. We use aggregation methods allowing us to reduce this model into a system of two ODEs for the total densities of the two populations. This is found to be a classical Lotka-Volterra competition model. We study the effects of the different fast equilibrium proportions of hawks and doves in both populations on the global coexistence and the mutual exclusion of the two populations. We show that in some cases, mixed hawk and dove populations coexist. Aggressive populations of hawks exclude doves except in the case of interpopulation costs being smaller than intrapopulation ones.

MSC:
91A80Applications of game theory
37N25Dynamical systems in biology
92D25Population dynamics (general)
WorldCat.org
Full Text: DOI
References:
[1] Hofbauer, J.; Sigmund, K.: The theory of evolution and dynamical systems: mathematical aspects of selection. (1988) · Zbl 0678.92010
[2] Maynard-Smith, J.: Evolution and the theory of games. (1982) · Zbl 0526.90102
[3] Iwasa, Y.; Endreasen, V.; Levin, S. A.: Aggregation in model ecosystems I. Perfect aggregation. Ecol. modelling 37, 287-302 (1987)
[4] Auger, P.; Poggiale, J. C.: Emerging properties in population dynamics with different time scales. J. biological systems 3, 591-602 (1995)
[5] Akin, E.: The geometry of population genetics. Lecture notes in biomathematics 31 (1979) · Zbl 0437.92016
[6] Crow, J. F.; Kimura, M.: An introduction to population genetics theory. (1970) · Zbl 0246.92003
[7] Kimura, M.: On the change of population fitness by natural selection. Heredity 12, 145-167 (1958)
[8] Iwasa, Y.; Levin, S. A.; Endreasen, V.: Aggregation in model ecosystems II. Approximate aggregation. IMA J. Math. appl. Med. biol. 6, 1-23 (1989) · Zbl 0659.92023
[9] Auger, P.; Roussarie, R.: Complex ecological models with simple dynamics: from individuals to populations. Ada biotheoretica 42, 111-136 (1994)
[10] Auger, P.: Dynamics and theormodynamics in hierarchically organized systems. (1989)
[11] De La Parra, R. Bravo; Auger, P.; Sánchez, E.: Aggregation methods in time discrete models. J. biological systems 3, 603-612 (1995)