A general model is presented for the evolution of social behavior by reciprocation. The results of our model apply to social traits which are transmitted from one generation to the next by a process which guarantees that the frequency of the trait in one generation is directly related to its fitness in the preceding generation. The basic parameters of the model are α, the number of interactions per generation, and β, the number of these interactions which are with individuals who are perceived as strangers. It is shown that so long as α/β can be made large, social reciprocation may increase when arbitrarily rare even in the absence of population structure. This conclusion appears to be at odds with several recent investigations of Axelrod & Hamilton (1981) and Boorman & Levitt (1980). We use our model to reconcile these various approaches. By casting Axelrod & Hamilton's (1981) single-partner model in terms of the general parameters, α and β, we show that social reciprocation can increase when arbitrarily rare in a homogeneous population dominated by non-cooperators. Using a gene frequency approach, Boorman & Levitt (1973, 1980) demonstrated the existence of a selection threshold in frequency of the social trait, which must be surmounted for social reciprocation to increase. We show our analysis of reciprocation to be consistent with Boorman and Levitt's result, since for our general model the cost to the social individuals of learning the non-social's identity goes to zero as the ratio α/β gets large. We also use our general model to study two multi-partner models not considered elsewhere, which differ in regards to the memory capabilities assigned to the organism. Finally we use our model to compare directly the evolution of social behavior by reciprocation with the main alternate hypothesis, kin selection. We show that an act which accrues some cost -c to the fitness of the donor while benefiting a recipient by b, will increase in frequency so long as c/b < Φ (equation (30)), where Φ is defined as the "coefficient of reciprocation" or probability that a cooperative act is reciprocated. By comparing the coefficient of reciprocation with the coefficient of relatedness of kin selection, direct comparisons of the two hypotheses may be made.
ASJC Scopus subject areas
- Statistics and Probability
- Modeling and Simulation
- Biochemistry, Genetics and Molecular Biology(all)
- Immunology and Microbiology(all)
- Agricultural and Biological Sciences(all)
- Applied Mathematics