Why 4Ne Rather Than 2Ne?

Question

[Lds]

Effect population size (Ne) is an important parameter in population genetics. The recombination rate (c) and mutation rate (u) can be extended to population scale rho and theta, respectively, by multiplied by 4N{e}, that is,

rho = 4N{e}c

theta = 4N{e}u

As human is diploid, it supposed to multiply 2N{e}, but why not? Meanwhile, suppose we have a population consisted of 50 males and 50 females undergoing HWE along history. Under HWE, individuals can random mate with each other (obviously, the random mating can only happened between males and females). Does the N{e} equal 50 or 100?

Thanks in advance.

Answer 1

[Casey Bergman]

Your first question is a good one, and one I've struggled with a few times in the past. Below is my understanding of the issue. Please note that I am not a theoretical population geneticist, so you should try to confirm this with someone more knowledgable about this issue than me.

First, you are correct that the population scaled rates of mutation and recombination are 4N{e}c and 4N{e}u for diploids, but you should also note that these values are 2N{e}c and 2N{e}u for haploids

To understand why these values have a factor of 4 for diploids, you need to understand that the expected time for coalescence of 2 alleles from a diploid population undergoing a neutral evolution is 2N{e}. This is the average time period that could accumulate mutations or recombination events, which occur at a rate of 2u, since a mutation can occur at rate u on either of branch of the geneology leading to the two alleles. Thus, the amount of expected variation between two alleles is 2N{e} * 2u = 4N{e}u = theta, the expected heterozygosity between a pair of alleles. The haploid values for the expected time to coalescence are reduced by a factor of two, and therefore the population scaled level of variation is reduced by a factor of two as well. Similar arguments can be constructed for recombination events.

For you second question, if N{males}=N{females} then N{e} = 2N{males} = 2N{females} (see general formula here for all sex ratios). So in your example N{e}=100.

[anuragm]

"expected time for coalescence of 2 alleles from a diploid population undergoing a neutral evolution is 2N{e}" - Could you please explain how ? I am sorry I could not fully grasp that part.