Review
of
Popu l a tion
Gen e tics
Equation s
1.
Hardy-Weinberg Equation:
p2 + 2pq + q2 = 1
Derivation: Take a gene with two alleles; call them A1 and A2. (Dominance doesn’t
matter for our purposes; this works equally well with codominance or incomplete
dominance.) In a population, some members will have the A1 A1 genotype, some will
have the A1 A2 genotype, and some will have A2 A2.
Now, imagine that you can somehow take all the gametes produced by the members of
the population—for simplicity, we’ll assume that these are eggs and sperm. Some
gametes, of course, carry A1, and some A2.
p = freq (A1)
q = freq (A2)
NOTICE that: the frequency of an allele is equal to the probability that a randomly
chosen gamete will be carrying that allele. Also notice that p+q=1.
What’s the chance that an egg and sperm drawn randomly will both be carrying A1?
Obviously, it’s p × p, or p2. And the chance that both gametes will both bear A2 is q × q,
or q2. There are two other possibilities: sperm with A1 and egg with A2, or sperm with A2
and egg with A1. The chance of either one happening is p × q, and the total probability of
producing a zygote with the A1 A2 genotype is twice that: 2pq. All of these probabilities
sum to 1. So p2 + 2pq + q2= 1. [Since p+q=1, (p+q)2 = p2 + 2pq + q2 = 12 =1.]
WHO CARES? It’s like this: this equation links allele frequency to genotype frequency,
assuming certain conditions are met. This means that:
1) If you know allele frequencies, you can predict the genotype frequencies, and compare
them with the actual frequencies. If they don’t match, then one of your assumptions is
violated—maybe there is natural selection going on, or immigration, or non-random
mating. . .
2) If you know genotype frequencies, you can predict allele frequencies, and compare
them with the actual frequencies. Again, if they don’t match, then one of your
assumptions is violated.
3) If you know phenotype frequencies, then you can estimate genotype and allele
frequencies—but you can’t test the underlying assumptions.
