Genetic Drift - A Population Size Which Would Be Small Enough

[Uncommon Ancestor]

Hi,

I was wondering wich population size would be small enough in order to make genetic drift to become at least as important as selection in determining evolution. I think I'd read in an old book by Dobzhansky that Nμ≥1 (N being the effective population size and μ being the mutation rate) was a good mesure, but I'm not sure wether that's still considered valid or if any new mesures are widespread or standard among scientists.

Anyone has a clue on this?

Thank you all

PD: Should I rather post this thread on the Evolution, Morphology and Exobiology subforum or is it OK here?

[CharonY]

It really depends on selective force. Assuming no selection, the number generations required to fix an allele is: 

E(T) = -4N_e [p ln p + (1-p) ln (1-p)]

With N_e being the effective population size and probability of allele frequency. The latter is important as in a large population p approaches the expected statistical distribution (i.e. 50:50 in case of two alleles) but with declining population sampling error occurs and you may have a skewed distribution, which is effectively what the drift is. As you can see, the time is maximized for p=0.5 and drops off it we see it skewed.

However, if we add selection to the mix, it gets more complicated depending on how it acts on the population. It could accelerate the effect if the the particular allele is positively selected (and by how much depends on the selective force each generation). However, selection could go into the opposite direction (i.e. favoring the allele with lower frequency). In that case the balance of the two competing events would determine fixation rate.

[Uncommon Ancestor]

Oh, thanks! That's both really meaningful and useful for my purpouses. Thank you so much!

Also, I've read this from the Wiki: 

Quote

Weakly deleterious mutations can fix in smaller populations through chance, and the probability of fixation will depend on rates of drift 1/N_e and selection (s), where N_e is the effective population size. The ratio N_es determines whether selection or drift dominates, and as long as this ratio is not too negative, there will be an appreciable chance that a mildly deleterious allele will fix. For example, in a diploid population of size N, a deleterious allele with selection coefficient -s has a probability fixation equal to (a-e^-2N_es/N)/(1-e^-4N_es). This estimate can be obtained directly from Kimura's 1962 work.^[4] Deleterious alleles with selection coefficients -s satisfying 2N_es<<1 are effectively neutral, and consequently have a probability of fixation approximately equal to 1/2N.

That works for situations where there is a competence between the diretion of selection and the (kind of) direction of drift. However, is there a similar equation for situations of convergence between both selection's and drift's directions?

Thank you all

Edited August 15, 2017 by Uncommon Ancestor