dN/dS is often used as a measure of the intensity of selective pressure on a mutation or gene, but I'm curious about how it can be written as a function of the selection coefficient. I'm specifically interested in the scenario of somatic mutations in human cells; suppose there's a gene, and all non-silent mutations in the gene are equivalent (such as if they're all loss of function mutations). The mutation rate is μ mutations per bp per cell division and once both alleles are (nonsilently) mutated, there's no fitness gain (or loss) from additional mutations. The selection coefficient for mutations in the gene for homozygous mutations is:
w_hom = 1 + s
and for heterozygous:
w_het = 1 + hs
How would one derive the expected dN/dS ratio (where the selection coefficient of a silent mutation is 0)? I realize there are a few questions for which answers must be assumed to begin to answer this question, such as:
- Is population static, or growing?
- Is dN/dS only including clonal/fixed mutations, or perhaps all mutations with a frequency in the population greater than or equal to some value?
I'd be interested in what the relationship with dN/dS is even under the simplest assumptions, e.g. h = 1, only considering clonal mutations, and static population. I've found one paper that posits such a formula, citing a finding from another paper, but I don't think either shows all the math.