 # The Wright-Fisher Model Analysis

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4. Genetic drift is an intriguing concept in genetics that focuses on explaining the random variation in changes of allele frequencies from one generation to the next in populations. The variation comes from sampling error because in many genetic models populations are assumed to be infinitely large, which is seldom the case. A simple mathematical approach to modelling genetic drift is the Wright-Fisher model. In this essay the general principles of the Wright-Fisher model will be explained, and from this initial framework the binomial and Markov chain models will be briefly discussed. Modelling software will then be applied to evaluate the effects of population size and initial allele frequencies on patterns of genetic drift in actual populations. …show more content…
In the population, it is assumed that there are two allele frequencies: p and q, and so there are only two options. The binomial distribution is well studied in statistics so to model genetic drift the formula was adapted so that the probability of selecting an allele of interest can be calculated using equation 10.
P_(i=A)=(■(2N@i)) p^i q^(2N-i), where (■(2N@i))=(2N)!/i!(2N-i)! Equation 10
Where P is the probability of selecting i number of A alleles from 2N gametes, N is the population size, p and q are the allele frequencies of alleles A and a, respectively, and 2N draw i is the number of possible permutations for the selection of i number of A alleles from the
First, the effect of genetic drift becomes much more pronounced in smaller populations. In a large simulated population (Fig. 1c, N = 200), only three of the five replicate populations reached fixation or loss (equilibrium), and the degree of change in allele frequency from one generation to the next is far less dramatic than in populations half its size (Fig. 2b, N = 100), or a tenth its size (Fig. 1a, N = 20). In the two smaller populations, the population size also impacts the average time to equilibrium. For the smallest population, the mean time to fixation is 53.67 generations, and to loss is 109 generations (Fig. 2a). Compared to the next largest population with a mean time to fixation of 300.5 generations, and 244.67 generations to loss (Fig. 2b). These results make sense in that with smaller populations error rate increases and this results in larger shifts in magnitude of the allele frequencies, which in turn impact the times to fixation or loss. It can also be seen that in these populations with a starting allele frequency of p = 0.5, the directions of the allele frequency changes are random, with about half the replicate populations reaching either fixation or loss. This also makes sense, since sampling a population is random, and the initial frequency represents the probability of

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