markovian

Kopp M & Hermisson J 2009 The genetic basis of phenotypic adaptation II: the distribution of adaptive substitutions in the moving optimum model. Genetics 183:1453-1476.

  • a new mutation reaches fixation if and only if it survives stochastic loss while rare
  • the fate of a new mutation (fixation or loss) is decided immediately at its origin
  • a successful mutation instantly reaches fixation
  • the population is nearly always monomorphic
  • adaptation occurs in well-defined, quasi-instantaneous steps
  • a sequence of such steps is called an adaptive walk
  • the adaptive-walk approximation is a standard tool for studying the adaptive process (cf. Kauffman 1993; Orr 2005a)
  • due to the assumption of instantaneous fixation, it ignores interactions between cosegregating alleles, which may arise from linkage or epistasis
  • previous studies of adaptation to a single sudden change in the environment suggest that the distribution of adaptive substitutions should often be roughly exponential (Orr 1998, 2005a)
  • an exponential distribution of adaptive substitutions has been obtained for both Fisher's geometric model (Orr 1998) and Gillespie's mutational landscape model (Orr 2002)
  • these two models are different in many aspects
  • mutational effects are measured as phenotypic distances in Fisher's model and as fitness effects in the mutational landscape model
  • there are two main reasons why the two models show similar results
  • first, in both models, the distribution of new mutations is biased toward small mutations
  • second, in both models, each adaptive step leads to a rescaling of the original situation
  • the initial steps lead to sizable increases in fitness
  • the later steps are mere "fine tuning"
  • it is this second point that is fundamentally different in the moving optimum model
  • Orr (2005b) predicted that the distribution of adaptive substitutions in a moving optimum version of Fisher's geometric model should resemble that of the first step (originally calculated by Kimura), which is unimodal rather than exponential
  • this is, indeed, what was found in the present study