• Model of genotype frequency change from one generation to the next is a key to modeling evolution.
• Evolution = allele frequency change over time
• Start with the simplest case
• Diploid (2N)
• Sexual reproduction
• Generations do not overlap
• Random mating
• Large population
• No migration
• No mutation
• No selection
• Probability theory --> the probability of two independent events co-occurring is the product of the probabilities of the individual events .
• Coin toss

p(H) = 1/2
p(T) = 1/2
• Toss coin twice

p(HH) = p(H) x p(H) = 1/2 x 1/2 = 1/4
p(TT) = p(T) x p(T) = 1/2 x 1/2 = 1/4
p(HT) = p(H) x p(T) + p(T) x p(H) = 1/4 + 1/4 = 1/2
sum of all possible probabilities = 1
• Biased coin

p(H) = 0.6
p(T) = 0.4

p(HH) = 0.6 x 0.6 = 0.36
p(TT) = 0.4 x 0.4 = 0.16
p(HT) = 0.6 x 0.4 + 0.4 * 0.6 = 0.48
sum of all possible probabilities = 1.0

Fertilization works the same way:

Sperm
Eggs
allele A  a	frequency p q	A  AA  aA		p p2 pq	a  Aa aa	q pq q2

• If a population is mating randomly, not migrating, not mutating, and not experiencing selection, then the genotype frequencies should be in these proportions:
• frequency of AA genotype = p ²
• frequency of Aa genotype = 2 pq
• frequency of aa genotype = q²
• Any deviation from these expected frequencies indicates one of the assumptions has been violated (mutation, migration, selection, random mating).
• Test for deviations from expected using Chi Square analysis.

This page last modified Monday, 09-Sep-2002 21:03:34 EDT