markovian
Manhart M, Haldane A & Morozov AV 2012 A universal scaling law determines time reversibility and steady state of substitutions under selection. Theor Popul Biol 82:66-76.
- the condition necessary to guarantee a monomorphic population is μ ≤ 1 / (LN log N)
- if most mutations introduce significant selective effects, the fixation or extinction of mutants will occur more rapidly, weakening the condition on μ
- the monomorphic condition becomes μ ≤ 1 / (LN log (Ns))
- the locus of interest is unlinked to the rest of the genome (linkage equilibrium) by frequent recombination with rate ρ, which satisfies ρ≫NμL
- unlike the Moran model, the Wright–Fisher model is ill-suited to exact treatment
- hence the traditional approach to it has been the diffusion approximation
- there are two problems with the classical diffusion approach
- the moment functions M(x,r) and V(x,r) are typically expanded to the lowest order in r − 1 for the weak-selection regime
- all subsequent calculations, including those leading to the fixation probability in Eq. (29), are not strictly valid for selection strengths beyond s = r − 1 ~ O(N−1)
- this expansion in selection strength, however, is not necessary, as it is possible to carry out the diffusion approximation using the exact moments derived from Eq. (28)
- this approach yields accurate results in the polymorphic limit, but fails to give an accurate formula for the fixation probability
- this is due to the inherent breakdown of diffusion when the underlying discrete nature of the model becomes important, which is especially pronounced when selection effects are strong
