weak selection

Gardner A, West SA & Barton NH 2007 The relation between multilocus population genetics and social evolution theory. Am Nat 169:207-226.

  • recent years have seen the development of a multilocus methodology for modeling evolution at arbitrary numbers of gene positions
  • the approach is conceptually analogous to social evolutionary methodology
  • simplifying assumptions, such as statistical independence within and between loci (Hardy-Weinberg equilibrium and linkage equilibrium) and independence in fitness effects (additivity, multiplicativity), make analysis tractable but can give strongly misleading predictions
  • this article is intended as a synthesis of multilocus and social evolution theory
  • the results derived within each of these bodies of theory may be readily interpreted in terms of the other
  • the formal basis of all of evolutionary theory is population genetics
  • the link between quantitative and population genetics is given by Price's theorem
  • an aim of this article is to include kin selection within this generalized view of hitchhiking
  • this separation of timescales is justified when processes that lead to the buildup of linkage disequilibrium (e.g., selection) are weak relative to those that lead to the breakup of linkage disequilibrium (e.g., recombination)
  • the QLE state is also attained when a very rare gene invades a population
  • in order to assess invasibility, one considers the asymptotic rate of increase of the gene at this QLE state
  • there is an equivalence between group selection and kin selection
  • they are the same process
  • neighbor-modulated fitness describes the fitness effect of a focal individual's behavior and the behaviors of its social partners on the focal individual's fitness
  • properly this is averaged over all carriers of a variant gene
  • it provides a quantity that is maximized (a maximand) under the action of selection
  • it is the gene rather than the individual that is assigned a neighbor-modulated fitness
  • this leads to the view of the gene as maximizing agent (Dawkins 1976)
  • Hamilton (1964, 1970, 1996) was interested in recovering a maximizing principle for individuals, in the tradition of Darwin (1859) and Fisher (1930), and developed inclusive fitness accordingly
  • this has led to Hamilton's rule being regarded as an approximate, heuristic result based on a simplified model
  • the derivation of Hamilton's rule using Price's theorem (Hamilton 1970) applies very generally
  • the cost of this generality is that it hides a lot of detail
  • so naive application of Hamilton's rule may lead to mistakes
  • Queller's (1985) interpretation of that analysis is that the Hamilton's rule Rb − c > 0 is incorrect for nonadditive fitness components
  • a new "synergy" coefficient (S = R + (1 − R)p), analogous to the coefficient of relatedness, is required to make Hamilton's rule "work"
  • the inequality Rb − c > 0 is a naive statement of Hamilton's rule and in particular is not the rule derived by Hamilton (1970)
  • Hamilton's rule remains a correct statement (Grafen 1985b), albeit one in which the cost and benefit terms are somewhat complicated
  • a central message of this article is that the foundations of social evolution theory are solid and encompass models of arbitrary complexity
  • it is generally regarded that Hamilton’s rule is a heuristic result that works only under the assumption of weak selection
  • as we have shown, Hamilton's rule is of such generality that it remains valid for multilocus models, models of interspecific mutualism, and arbitrary strength of selection
  • Hamilton's rule and Price's theorem should generally be used in the interpretation of theory and not as the starting points in the analysis of specific problems