The magnitude of the effect of a change in Ne on nucleotide substitutions is determined by the distribution of selective effects of mutations. To illustrate this, consider two lineages with different effective population sizes, the larger NeL and the smaller NeS. If we assume that advantageous mutations are rare and most of the mutations that go to fixation are slightly deleterious, then the difference in substitution rate between these lineages will be largely determined by the proportion of mutations that have selective coefficients between 1/NeL and 1/NeS (). This proportion, in turn, is determined by the distribution of selective effects.
Figure 1 The distributions of fitness effects modelled by Ohta (1977) (exponential or gamma with β=1, dashed curve) and Kimura (1979) (gamma with β=0.5, solid curve). In a small population, with effective population size NeS, mutations with selection (more ...) Ohta (1977)
assumed that the distribution of selection coefficients for new mutations was exponential. Under this distribution, and given a realistic mean strength of selection, a substantial proportion of mutations have fitness effects of the order of 1/Ne
for many natural populations, and the effect of a change in population size on the rate of molecular evolution is expected to be quite large. This model was modified by Kimura (1979)
who proposed that negative selection coefficients followed a more leptokurtic distribution. For a given strength of selection, fewer mutations will typically fall in the range from 1/NeL
under this distribution, and so the difference in substitution rate between lineages with different Ne
will also be less, although a negative correlation between Ne
and fixation rate is still predicted.
Neither of these distributions were chosen on the basis of biological data (Gillespie 1991
), but a number of empirical estimates of the distribution of fitness effects of deleterious mutations have recently been made. Results vary between datasets and between taxa, with the estimated distributions including normal (Nielsen & Yang 2003
), lognormal (Loewe & Charlesworth 2006
) and strongly leptokurtic gamma distributions (Keightley & Eyre-Walker 2007
) (). These estimates are based on the data from relatively few species, but indicate that the distribution of mutant effects is likely to vary between taxa. Adding further complexity, recent experimental work has suggested that a species' distribution of fitness effects is dynamic, and may change as organismal fitness and/or effective population size change (Silander et al. 2007
Figure 2 Example distributions of fitness effects estimated from different datasets, including lognormal for Drosophila miranda and Drosophila pseudoobscura (Loewe & Charlesworth 2006; dotted curve), strongly leptokurtic gamma for Drosophila melanogaster (more ...)
The prediction of increased rate of evolution in species with small Ne
relies on the assumption that advantageous mutations are rare: positive selection is less efficacious in small populations, so fixation of advantageous mutations will be reduced rather than increased in species with low Ne
. Slightly advantageous mutations are in fact likely to be relatively common (Charlesworth & Eyre-Walker 2007
), but theoretical work that incorporates positive selection on such mutations shows that a negative correlation between overall rate of substitution and effective population size is still predicted (Ohta 1992
). More problematically, some studies have suggested that, far from being rare, strongly advantageous mutations may comprise a substantial proportion of those mutations that contribute to substitution in humans and Drosophila
), and this may further weaken the inverse relationship between Ne
and substitution rate.