title: The stability of cooperation involving variable investment.
abstract: In this paper, we attempt to reconcile the results of several studies which have investigated the evolution of cooperation between non-relatives in systems where investment in partners can vary. In contrast to previous proposals, we show for the first time that variable-investment cooperation can be readily maintained in inter-species mutualistic relationships even in the absence of spatial structure, but that the stability of this interaction is dependent on the particular investment-response rule that is employed. By allowing the evolution of investment-response parameters in both inter- and intra-specific versions of the continuous variable-investment Prisoners' Dilemma we show that, in the absence of further factors, the raise-the stakes (RTS) strategy is likely to evolve into a simpler, variable investment form of Give-as-Good-as-you-Get that initially offers a high fixed amount and subsequently matches its partner's investment. Nevertheless, we demonstrate that genuine RTS-like strategies will still be selected if two intuitively reasonable conditions hold: if individuals are limited in terms of the total they can invest in cooperative actions over their lifetimes, and if there are always some individuals in a population that cannot cooperate.
authors.affiliation: Department of Biological Sciences, University of Durham, South Road, DH1 3LE, UK. T.N.Sherratt@durham.ac.uk
authors.forename: Thomas N
authors.initials: TN
authors.lastname: Sherratt
authors.forename: Gilbert
authors.initials: G
authors.lastname: Roberts
mesh_terms: D000818:Animals; D005075:Biological Evolution; D003299:Cooperative Behavior; D005716:Game Theory; D008954:Models, Biological