meaning of Theta and Ne

[Sunjin]

Hi, Ryan.

I've calculated two theta. One is derived from the function 'dadi.Inference.optimal_sfs_scaling', and the other is from the genetic diversity, Watterson's estimator. These thetas shows similar value. 

I'm wondering the meaning of dadi's theta when we deal with just one population with a bottleneck. 

We've obtain a parameter of bottleneck strength, saying 0.001, for current population, we may estimate current population's Ne from the ancestral Ne that is derived from the dadi's theta. So, current population's theta should be 0.001 times less than the dadi's theta that is corresponding to the theta derived from Watterson's estimator. 

Meanwhile, we can calculate current population's Ne, from θ = 2N_e(f)μ, where μ is the substitution rate per generation with estimations of theta and mu. We can easily find this sort of calculation from references. But, this Ne is corresponding to the ancestral Ne in the dadi. And, current Ne is 0.001 times of ancestral Ne from dadi.

How can we interpret these Nes?

Best,

Sunjin

[Gutenkunst, Ryan N - (rgutenk)]

Hello Sunjin,

There are several ways to estimate the population genetic parameter theta = 4 Ne mu, which make different assumptions. Watterson's estimator for assumes stationary demographic history. (This is where the harmonic sum in the calculation of Watterson's theta comes from.) If your population has undergone a bottleneck, then Watterson's estimator is biased (whether you're trying to estimate ancestral or current Ne.) The value from optimal_sfs_scaling corresponds to theta = 4 Na mu, where Na is the ancestral population size. So if the best-fit model is a 0.001 bottleneck, then the corresponding dadi estimate for the population size in the bottleneck is theta/(4 mu) * 0.001 = Na*0.001.

I think the confusion is that people rarely think about the (strong) assumption Watterson's estimator makes that the demographic history is stationary. dadi's estimate is more sophisticated, because it attempts to correct for demographic history effects.

Does this answer your question?

Best,

Ryan

-- 

Ryan Gutenkunst

Assistant Professor

Molecular and Cellular Biology

University of Arizona

phone: (520) 626-0569

http://gutengroup.mcb.arizona.edu

[Sunjin]

Thank you very much for your reply.
The more I use dadi, the more I like it.

Best,
Sunjin