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