# Microevolution and Changing Alleles

Part 2

## The Hardy-Weinberg Law

If there is no selective pressure imposed on a pair of alleles, one dominant the other recessive, their frequencies should remain constant. This is known as genetic equilibrium.

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The Hardy-Weinberg Law states:

both gene and genotype frequencies will remain unchanged -- in equilibrium -- unless outside forces change those frequencies.

How the Hardy-Weinberg Law works.

When only 2 alleles (A, a) are involved, the relative proportions -- that is the frequencies of A & a -- must equal 1.

If in a population where 80% of the alleles of the gene under study are allele A, the frequencies will be: A= 0.8 and a = 1- 0.8 = 0.2

Mathematically the Hardy Weinberg law is stated as:
p2 + 2pq + q2 = p + q or

A2 + 2Aa + a2 = 1

using the information above we can find the frequencies of the homozygous and heterozygous genotypes;

(0.8)2+2(0.8 x 0.2) + (0.2)2 =1

SO:

AA = (.8)2 = .64

2Aa = 2(.8 x .2) =.32

aa = (.2)2 = .04

The modified Punnett square would be:

If we can identify the individuals in a population that are homozygous for a particular allele of interest we can then calculate the frequency of that allele. If for instance 1/10,000 babies are born with a certain recessive genetic defect we can easily determine the allele frequencies of A & a

aa = a2 = 0.0001

a = = 0.01

therefore A=.99

2Aa = 2(.01 x .99) = .0198 or about 2% are heterozygous.

### Conditions Necessary for the Hardy-Weinberg Law

In order for allele frequencies to remain unchanged (i.e. no evolution) the following restrictions must hold:

1. Mating must be completely random
2. There can be no mutations
3. Gene flow must not occur (no migration)
4. The population in question must be very large (infinite in size)
5. The alleles must segregate according to Mendel's first law
6. There can be no selection on the population

Links to Hardy-Weinberg Law

Page updated March 7, 2003