Coalescence time: Is it different for haploids and diploids in population genetics?
Coalescence time: Is it different for haploids and diploids in population genetics?


Short answer

The coalescent time is twice as high in a diploid population than in a haploid population

Long answer

Imagine you sample at random one chromosome. Then, you sample a second one and you ask the question, what is the probability that they coalesce in the previous generation. This probability is $\frac{1}{PN}$, where $N$ is the population size and $P$ is the ploidy number (1 for haploids, 2 for diploids). The probability that they do not coalesce is therefore $1-\frac{1}{PN}$. The probability that the two chromosomes coalesce $t$ generations ago is the probability that they don't coalesce for $t-1$ generations and then coalesce. That is the probability that the two chromosomes coalesce $t$ generations ago is

$$P(t) = \left(1-\frac{1}{PN}\right)^{t-1}\frac{1}{PN}$$

You might recognize here a geometric distribution, where the probability of success is $\frac{1}{PN}$. In order to simplify the math, let's assume that the population size is very large. In such case the above formulation is well approximated by 

$$P(t) = \frac{1}{PN} e^{-t\frac{1}{PN}} $$

You might now recognize the exponential distribution with rate $\frac{1}{PN}$. We can now compare the mean expected time to coalescent of a diploid population and a haploid population.

The mean of the above exponential distribution is simply $PN$. Therefore, the expected time to coalescent is $2N$ in diploids and only $N$ in haploids. 

Details of your post

In your post you talk about structured populations. The calculations are a little more complicated in structured populations and I don't remember on the top of my head how they work.

You talk about divergence $D$. I don't know what you mean by divergence. From coalescent results you can compute the expected heterozygosity, the number of pairwise differences, and even the whole site frequency spectrum. You can as well make those calculations for the structured coalescent model.