Hardy-Weinberg Principle
Scientists often find it helpful to determine what happens when NO change takes place in
a population to clarify how evolution operates. The Hardy-Weinberg principle helps to
demonstrate what happens when no change (evolution) takes place. It states that: allele
frequencies in a population will remain constant unless one or more factors cause those
frequencies to change. This constant state is genetic equilibrium.
Hardy-Weinberg Assumptions: 5 conditions are required in order for a state of genetic
equilibrium to persist generation after generation.
1. Random mating
2. Population must be large
3. No movement into or out of the population
4. No mutations
5. No natural selection
**If these conditions occur in a population it will not evolve. This is not the case in
naturally occurring populations.
Hardy-Weinberg Law: a mathematical model used in the study of population genetics. It
can be used to:
1. Determine the allele frequencies in a population which indicates whether or not the
population is in evolutionary equilibrium (not evolving).
2. Estimate the frequency of heterozygotes in a population.
3. Identify forces that cause evolution by specifying the conditions under which allele
frequencies will not change.
4. It shows what will happen to the genotype and phenotype frequencies of a population
under certain assumptions.
Hardy-Weinberg Equation



p2 + 2pq + q2 = 1, where
p = frequency of the dominant allele
q = frequency of the recessive allele
For a trait controlled by a pair of alleles (A and a):
 p = all the alleles in individuals who are (AA) and half of the alleles in people who are
(Aa).
 q =all of the alleles in individuals who are (aa) and the other half of the alleles in people
who are (Aa).
In mathematical terms:


p = AA + 1⁄2Aa
q = aa + 1⁄2Aa
Because there are only two alleles, the frequency of one plus the frequency of the other
must =100%.
• p+q=1
Since this is logically true, then:
 p=1-q
 q=1-p
The chances of all possible combinations of alleles occurring randomly is

(p + q)2 = 1
Or more simply,




p2 + 2pq + q2= 1, where
p2 is the frequency of people with genotype (AA) in a population.
2pq is the frequency of people with genotype (Aa) in a population.
q2 is the frequency of people with genotype (aa) in a population.
PROBLEMS:
1. Assume random mating, no mutation and no migration, determine the allele frequencies in
the populaton.
N = total number (100)
Generation #AA #Aa #aa p(AA/N)+1/2(Aa/N)
q (1-p)
Initial
42
46
12
?
?
40
45
15
?
?
(P1)
F1
2. The Hardy-Weinberg law can be used to determine genotype frequencies if given allele
frequencies.
a) Given the allele frequencies, p= 0.65 and p= 0.35
b) Genotype frequencies can be determined where the homozygous dominant
individuals are p2, the heterozygotes are 2pq and the homozygous recessives are q2.