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Center for Nonlinear Studies |
Hamilton's rule has played a central role in the modern understanding of the evolution of social behavior. Hamilton's insight was to see that assortment was the key to the evolution of individually disadvantageous behaviors that increased the fitness of social partners. In his landmark 1964 papers, Hamilton argued that the probability that two individuals carried the same gene by common descent was the right measure of assortment, so that an altruistic gene could spread if rb – c > 0 where -c is the incremental fitness effect on the actor, b is the incremental fitness effect on the recipient, and r is the probability that the two individuals share the same allele by common descent. Recently it has been argued that Hamilton’s rule is only often incorrect and thus is both unnecessary and misleading (e.g. Nowak et al 2010). A much larger number of authors have argued that inclusive fitness usually predicts evolutionary dynamics because selection is often weak and genetic effects are approximately additive (Lehmann and Keller 2006). Others (Gardner et al 2011) argued that, appropriately modified, Hamilton’s rule is universal law that always predicts evolutionary outcomes. I will show that there are important problems for which r is not the right measure of assortment ant thus Hamilton’s rule cannot predict evolutionary outcomes. I will also explain why this result is consistent with Gardner et al.'s (2011) claim that Hamilton’s rule is a universal law, what it means for optimization approaches like that advocated by Taylor and Frank (1996), and suggest a computationally practical alternative for those cases in which Hamilton’s rule does not apply.
Host: David Wolpert, CCS-3, 665-7914, Game Theory Seminar Series