Evolution of altruistic behavior by kin selection: an alternative approach.

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Abstract
The evolution of altruistic and selfish behavior by kin selection has been analyzed previously by asking which types of behavior are favored by natural selection. A type of behavior is defined as a given cost/benefit ratio, c/b, in terms of Darwinian fitness. An alternative approach is to consider c/b itself as a quantitative character subject to natural selection and evolving toward an equilibrium. This approach allows consideration of a continuum of behavioral options as opposed to just two alternatives as in the previous work. Environmental restrictions on the availability of opportunities for fitness transactions are imposed so that the total benefit an individual can provide for or take from his relatives increases with his c/b ratio. General conditions for stable equilibria are derived. These depend only on the coefficient of relationship between donor and recipient (r) and the function describing the availability of benefit. They are independent of the heritability and variance in the population. Under weak selection, the equilibrium c/b ratio will be r/2 for altruistic behavior and 1/(2r) for selfish behavior. By contrast, standard theory predicts that all altruistic acts with c/b ratios less than r will be favored, and no equilibrium can be predicted except under certain special conditions where only two behavioral options are available. In general, these results show that evolution of the donor's behavior (altruism) tends to maximize the quantity rb--c, and evolution of the recipient (selfish behavior) maximizes b--rc.