HardyWeinberg and Constraints on Genetic Variation

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
cooccurring 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
p^{2}
pq 
a
Aa
aa 
q
pq
q^{2} 

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 = q^{2}

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.
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