The principle of genetic equilibrium is an idealistic model for population genetics that simply cannot hold for all genes in practice. For one, evolution has proven too powerful for equilibrium to possibly hold. At the same time, evolution works on the scale of eons, and at any given moment in time, most populations are essentially stable.
In this problem, we would like to obtain a simple mathematical model of genetic drift, and so we will need to make a number of simplifying assumptions. First, assume that individuals from different generations do not mate with each other, so that generations exist as discrete, non-overlapping quantities. Second, rather than selecting pairs of mating organisms, we simply randomly select the alleles for the individuals of the next generation based on the allelic frequency in the present generation. Third, the population size is stable, so that we do not need to take into account the population growing or shrinking between generations. Taken together, these three assumptions make up the Wright-Fisher model of genetic drift.
Consider flipping a weighted coin that gives "heads" with some fixed probability
We generalize the notion of binomial random variable from “Independent Segregation of Chromosomes” to quantify the sum of the weighted coin flips.
Such a random variable
To quantify the Wright-Fisher Model of genetic drift, consider a population of
Given: Positive integers
Return: The probability that in a population of
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