Genetics - A. V. Sivolob 2008

Population Genetics
Factors of the Dynamics of Population Genetic Structure
Mutations

Mutations serve as the primary source of genetic variation in populations, driving changes in both allele and genotype frequencies. Let us consider a scenario where, due to forward mutations, allele A transforms into a (A → a) at a rate of u, while reverse mutations a → A occur at a rate of v. Under specific conditions regarding The ratio of u to v, an equilibrium ratio of genotypes AA, Aa, and aa will eventually be established in the population.

First, let us evaluate the pressure exerted by forward mutations. Suppose the frequency of allele A in the initial generation is p_o. In the next generation, this frequency will decrease As a result of mutations:

Class="center">p₁ = p_o- up_o= р_o(1 - u).

In the second generation, the frequency will be

р₂ = p₁- up₁= p₁(1-u) = p₀(1-u)²,

and for generation t, the frequency of allele A will be

p_t= p_о(1 - u)^t.

Over time, mutation pressure alone would theoretically eliminate allele A from the population. However, this process is extremely slow: for the allele frequency to drop from 1 to 0.99 at u = 10^-5 per gamete per generation, approximately 1,000 generations are required. This calculation does not yet account for The Effect of reverse mutations.

If the initial frequencies of alleles A and a are p₀ and q₀, respectively, and the rates of forward and reverse mutations are u and v, then in the first generation, the proportion of allele A will decrease due to forward mutations and increase due to reverse mutations:

p₁ = p₀ - up₀ + vq₀,

and the net change in allele frequency driven by mutations will be

∆p = p₁ - p₀ = vq₀ - up₀.

This shift in frequencies will continue until an equilibrium state is reached, halting any further changes: ∆р = 0. Under this condition, the frequencies of alleles A and a will reach equilibrium

From the last expression, Setting ∆р = 0, we obtain

After simple algebraic transformations, we get