I’ve decided to jot down some simple* formalisms which I can refer new readers to on this website. So today….
You know that if you have a novel mutation within a population, its probability of fixation if it is neutral is:
1/(2N), where N = effective population, in a neutral scenario where the mutation confers neither advantage or disadvantage. So in a population of 100, a new mutant has a 1 out of 200 chance of fixation, going from 0.5% in the initial generation, to 100% in the generation of fixation. In a population of 1000, a new mutation has a .05% chance of fixation, and so forth.
In a non-neutral case, fixation probability is 2s, where s equals the positive selective advantage conferred by the allele against the population mean fitness. So if the selection coefficient is 0.01, the probability of fixation is 2%.
In regards to the time until fixation, for a neutral allele iit s 4N, where N is the effective population, and the product is generations.
For a selectively beneficial allele, it is (2/s)(ln(2N)). The “left side” of this relation is more important since the parameter N is converted into its natural log.
* In the first draft of this post I used the word “trivial,” but I don’t think these formalisms are necessarily clear and obvious intuitive statements, even if they are the most basic of algebras. So I’ve reedited it to “simple,” as I think keeping in mind relations like 1/(2N) and 4N are important insights which are necessary for a gestalt comprehension of evolutionary dynamics.
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