Genetic Drift between two generations in the Wright - Fisher Model
Starting in generation t with 20
alleles for N =
20 haploid individuals, with f(A) = 8/20 =
0.40. Generation t+1
comprises the same number of alleles & individuals (20),
but a modified f(A)
= 5/20 = 0.25, due solely to random sampling
error, which the evolutionary biologist Sewall Wright called genetic drift.
The process of random sampling can be visualized as a draw-&-replacement exercise. Place 8 red and 12 blue marbles in a bag. Draw one at random: note its color, and return the marble to the bag. Repeat the process a total of 20 times. Create a new bag representing the next generation, containing 20 marbles in the proportions obtained by the random draw. Repeat.
The Wright - Fisher Model considers haploid individuals, but can be adjusted for diploid populations. Here, the 20 haploid individuals can be treated as ten diploid individuals with two alleles each. This is equivalent to the 'tide pool ' model used to derive the Hardy-Weinberg Theorem for random union of gametes. As a diploid model, it remains slightly unrealistic in that it ignores two-allele mating combinations, and allows self-fertilization (if the same marble were drawn twice in a row).
The process of random sampling can be visualized as a draw-&-replacement exercise. Place 8 red and 12 blue marbles in a bag. Draw one at random: note its color, and return the marble to the bag. Repeat the process a total of 20 times. Create a new bag representing the next generation, containing 20 marbles in the proportions obtained by the random draw. Repeat.
The Wright - Fisher Model considers haploid individuals, but can be adjusted for diploid populations. Here, the 20 haploid individuals can be treated as ten diploid individuals with two alleles each. This is equivalent to the 'tide pool ' model used to derive the Hardy-Weinberg Theorem for random union of gametes. As a diploid model, it remains slightly unrealistic in that it ignores two-allele mating combinations, and allows self-fertilization (if the same marble were drawn twice in a row).