The Distribution of Altruism Among Kin: A Mathematical Model

Abstract

A number of sociobiologically oriented researchers have implied that the distribution of an individual's altruistic behavior among his kin in direct proportion to the coefficient of relationship (the Proportional Altruism Model) is a logical expectation arising from Hamilton's (1964) specifications for the evolution of altruism. Altmann (1979) has pointed out the logical fallacy in this reasoning. Extending Altmann's ideas, a mathematical model representing a diminishing returns investment function is formulated. Simulations involving a single altruist in a kin group distributing altruistic investment among his kin are performed. All recipients are assumed to have identical fitness accruement curves. Under these restrictions, a general pattern of increased altruistic investment with increased genetic relatedness is observed, with the precise pattern of distribution being a function of the costs, benefits, and units of energy investment associated with a particular altruistic act. Another general pattern that emerges from the simulations is that early in the rounds of investment, the altruist favors close kin, but as total investment increases, altruism becomes more evenly distributed among kin. This suggests that such factors as environmental quality and social status should affect patterns of altruism. The likely effects of multiple altruists, reciprocal altruism, and reproductive value upon the distribution of altruistic investment indicate the need for including these factors in any empirical testing of models of altruism.