J. Phys. I France
Volume 6, Numéro 4, April 1996
Page(s) 445 - 453
DOI: 10.1051/jp1:1996223
J. Phys. I France 6 (1996) 445-453

A Stochastic Model for Evolution of Altruistic Genes

Roberta Donato

Department of Physics, University "La Sapienza", Piazzale Aldo Moro 2, 00185 Roma, Italy

(Received 5 October 1995, accepted 5 January 1995)

We study numerically a stochastic model for evolution and maintenance of a population which reproduces asexually under selective pressure and is divided into smaller groups of variable size. An altruistic trait is defined as lowering the fitness of the carrier, but the survival probability of all the members of a group with a large enough number of altruists is enhanced. Numerical results show that there is a transition in the average proportion of altruists versus the relative advantage conferred by the presence of altruists to all the members of the group. At the transition the distribution of altruistic frequence in the groups is not trivial, and average deme size reaches a minimum. We found also an error-threshold in mutation rate analogous to the quasi-species model of M. Eigen.

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