population expansion - senecio7の日記

Waxman D 2012 Population growth enhances the mean fixation time of neutral mutations and the persistence of neutral variation. Genetics 191:561-577.

for populations that increase in size, the mean time of fixation can be enhanced, sometimes substantially so, over 4N_e,0 generations
N_e,0 is the effective population size at the time the mutation arises
such an enhancement is associated with
(i) an increased probability of neutral polymorphism in a population and
(ii) an enhanced persistence of high-frequency neutral variation

Otto and Whitlock (1997) listed the following as possible reasons for changing population numbers in the wild
(i) varying physical conditions
(ii) resource availability
(iii) habit availability
(iv) predator density
(v) human disturbance
human beings constitute an example of a population whose size is changing at a varying rate of growth

from the first appearance of the allele to its fixation, which we assume takes T generations, all 2N resident alleles of the population are lost
the disappearance of resident alleles thus occurs at an average rate of 2N / T alleles per generation
using the estimate T = 4N_e generations leads to an average rate of loss of resident alleles of N / (2N_e) alleles per generation

we assume the simplest relation between the actual and effective population sizes
N_e(t) = constant × N(t)

a particularly interesting regime is where the rate of loss of resident alleles due to random genetic drift can be overcome by the effect of population size increase, which increases the number of resident alleles
this will occur when γ is sufficiently large compared with N / N_e
we should then expect that fixation could take much longer to occur
if the population growth persisted at such a rate indefinitely, the mean time to fixation could, plausibly, become infinite

the question we address concerns features of the fixation process when the actual and effective population sizes have known historical variation over time
we view N(t) and N_e(t) as being completely determined and not having any stochasticity
it would be inappropriate to carry out any averaging over these functions
addressing questions of a different nature may require population-size averaging

even in populations of constant size, neutral alleles constitute a special case since they take longer (on average) to fix than beneficial or equally deleterious alleles under genic selection (Maruyama 1977, pp. 80 and 81)

an increasing population enhances the persistence of the neutral variation associated with the most observable mutant alleles, that is to say those that achieve intermediate and high frequencies and proceed to fix

from the simulations, an increasing population size is found to shift the decay of Prob(T_fix > t) to larger values of t
this explains why an increased mean time of fixation is accompanied by an enhanced persistence of variation

selective neutrality may be a transient property
under environmental changes, originally neutral loci may become selected
the associated variation then becomes converted to nonneutral variation that becomes a target for selection, as has been discussed in the literature for, e.g., alleles associated with 6PG allozymes (Dykehuizen [Dykhuizen] and Hartl 1980)
the potential to evolve and the direction of evolution are closely associated with the presence of neutral alleles in a population and hence on the time they take to achieve fixation