Does evolution lead to maximizing behavior?

A long-standing question in biology and economics is whether individual organisms evolve to behave as if they were striving to maximize some goal function. We here formalize the \as if" question in a patch-structured population in which individuals obtain material payoffs from (perhaps very complex) multimove social interactions. These material payoffs determine personal fitness and, ultimately, invasion fitness. We ask what goal function, if any, individuals will appear to be maximizing, in uninvadable population states, when what is really being maximized is invasion fitness at the genetic level. We reach two broad conclusions. First, no simple and general individual-based goal function emerges from the analysis. This stems from the fact that invasion fitness is a complex multi-generational measure of evolutionary success. Second, when selection is weak, all multi-generational effects of selection can be summarized in a neutral type- distribution quantifying identity-by-descent within patches. Individuals then behave as if they were striving to maximize a weighted sum of material payoffs (own and others). At an uninvadable state it is as if individuals choose their actions and play a Nash equilibrium of a game with a goal function that combines selfishness (own material payoff), Kantian morality (group material payoff if everyone does the same), and local rivalry (material payoff differences).