Adaptive Dynamics of Altruistic Cooperation in a Metapopulation: Evolutionary Emergence of Cooperators and Defectors or Evolutionary Suicide?
- 237 Downloads
We investigate the evolution of public goods cooperation in a metapopulation model with small local populations, where altruistic cooperation can evolve due to assortment and kin selection, and the evolutionary emergence of cooperators and defectors via evolutionary branching is possible. Although evolutionary branching of cooperation has recently been demonstrated in the continuous snowdrift game and in another model of public goods cooperation, the required conditions on the cost and benefit functions are rather restrictive, e.g., altruistic cooperation cannot evolve in a defector population. We also observe selection for too low cooperation, such that the whole metapopulation goes extinct and evolutionary suicide occurs. We observed intuitive effects of various parameters on the numerical value of the monomorphic singular strategy. Their effect on the final coexisting cooperator–defector pair is more complex: changes expected to increase cooperation decrease the strategy value of the cooperator. However, at the same time the population size of the cooperator increases enough such that the average strategy does increase. We also extend the theory of structured metapopulation models by presenting a method to calculate the fitness gradient in a general class of metapopulation models, and try to make a connection with the kin selection approach.
KeywordsAdaptive dynamics Altruism Cooperation Kin selection Evolutionary suicide
Unable to display preview. Download preview PDF.
- Allee, W. C., Emerson, A., Park, T., & Schmidt, K. (1949). Principles of animal ecology. Philadelphia: Saunders. Google Scholar
- Faddeev, D. K., & Faddeeva, V. N. (1963). Computational methods of linear algebra. San Francisco: Freeman. Google Scholar
- Ferrière, R. (2000). Adaptive responses to environmental threats: evolutionary suicide, insurance, and rescue. In Options, Spring 2000 (pp. 12–16). Laxenburg: IIASA. Google Scholar
- Grafen, A. (1985). A geometric view of relatedness. Oxf. Surv. Evol. Biol., 2, 28–89. Google Scholar
- Le Galliard, J.-F., Ferriére, R., & Dieckmann, U. (2003). The adaptive dynamics of altruism in spatially heterogeneous populations. Evolution, 57, 1–17. Google Scholar
- Levins, R. (1969). Some demographic and genetic consequenses of environmental heterogeneity for biological control. Bull. Entomol. Soc. Am., 15, 237–240. Google Scholar
- Levins, R. (1970). Extinction. In M. Gerstenhaber (Ed.), Some mathematical problems in biology (pp. 77–107). Providence: American Mathematical Society. Google Scholar
- Mathias, A., Kisdi, É., & Olivieri, I. (2001). Divergent evolution of dispersal in a heterogeneous landscape. Evolution, 55, 246–259. Google Scholar
- Maynard Smith, J. (1976). Evolution and the theory of games. Am. Sci., 64, 41–45. Google Scholar
- Metz, J. A. J., Geritz, S. A. H., Meszéna, G., Jacobs, F. J. A., & van Heerwaarden, J. S. (1996). Adaptive dynamics, a geometrical study of the consequenses of nearly faithful reproduction. In S. J. van Strien & S. M. Verduyn Lunel (Eds.), Stochastic and spatial structures of dynamical systems (pp. 183–231). Amsterdam: North-Holland. Google Scholar
- Parvinen, K. (2007). Evolutionary suicide in a discrete-time metapopulation model. Evol. Ecol. Res., 9, 619–633. Google Scholar
- West, S. A., Griffin, A. S., & Gardner, A. (2008). Social semantics: how useful has group selection been? J. Evol. Biol., 21, 374–385. Google Scholar