Question
Consider a very long (eventually infinite) DNA sequence of neutral sites. Consider a panmictic population of constant size $N$ with a per site mutation rate of $\mu$ where all individuals have the exact same fitness.
What is the fraction of sites that we'd expect to be polymorphic in the population (SNPs)?
Motivation behind this question
I am asking this question to verify the results of simulations I run. For example, I run a simulation with $x$ ($x$ will be varying below) neutral sites, with a per-site mutation rate $\mu = 10^{-9}$ and a population size of $N=100$. I run the simulations for 10,000 generations. There is no recombination. When the number of sites:
- $x=10^3$ I get 0 SNP
- $x=10^4$ I get 1 SNP
- $x=10^5$ I get 3 SNPs
- $x=10^6$ I get 25 SNPs
- $x=10^7$ I get 238 SNPs
Is there a bug in my model or is it what we'd expect given the parameters?
In the human genome, 1 out of 300 sites are polymorphic (SNPs) (ref.). This is a frequency of SNPs that is 100 times greater than what I observe in my simulations. Note however, that the assumption of neutrality and out demographic assumptions would not perfectly hold and this result could pretty far off neutral expectation. My goal is not to reproduce something that look like the human genome but only to reproduce the neutral expectations for the moment.