title: Evolution of density-dependent cooperation.
abstract: Cooperation is surprisingly common in life despite of its vulnerability to selfish cheating, i.e. defecting. Defectors do not contribute to common resources but take the advantage of cooperators' investments. Therefore, the emergence and maintenance of cooperation have been considered irrational phenomena. In this study, we focus on plastic, quantitative cooperation behaviour, especially on its evolution. We assume that individuals are capable to sense the population density in their neighbourhood and adjust their real-valued investments on public goods based on that information. The ecological setting is described with stochastic demographic events, e.g. birth and death, occurring at individual level. Individuals form small populations, which further constitute a structured metapopulation. For evolutionary investigations, we apply the adaptive dynamics framework. The cost of cooperative investment is incorporated into the model in two ways, by decreasing the birth rate or by increasing the death rate. In the first case, density-dependent cooperation evolves to be a decreasing function of population size as expected. In the latter case, however, the density-dependent cooperative investment can have a qualitatively different form as it may evolve to be highest in intermediate-sized populations. Indeed, we emphasize that some details in modelling may have a significant impact on the results obtained.
authors.affiliation: Department of Mathematics and Statistics, University of Turku, FIN-20014 , Turku, Finland, anne.seppanen@utu.fi.
authors.forename: Anne
authors.initials: A
authors.lastname: Seppänen
authors.forename: Kalle
authors.initials: K
authors.lastname: Parvinen
mesh_terms: D000818:Animals; D005075:Biological Evolution; D001723:Birth Rate; D003299:Cooperative Behavior; D005716:Game Theory; D006801:Humans; D055641:Mathematical Concepts; D009026:Mortality; D009154:Mutation; D011156:Population Density; D011157:Population Dynamics; D013269:Stochastic Processes