Hardy-Weinberg Equilibrium Review
By Sean McGrath

Hardy-Weinberg Theorem
 Laid out in 1908 by the two scientists who
independently discovered it
 States that frequencies of alleles within a
population that is not evolving will remain constant
from generation from generation
 Certain improbable conditions must be fulfilled in
order for this Theorem to apply
Conditions of the Theorem

Extremely Large Population Size: As population size decreases,
there are greater chance fluctuations in allele frequencies
(genetic drift)

No Gene Flow: Transfer of alleles between populations cannot
occur

No Mutations: Introducing or removing genes form
chromosomes will modify gene pool

Random Mating: Preferential mating based on certain
genotypes will not allow random mixing of gametes

No Natural Selection!: Differential survival and reproductive
success alters allele frequencies
Hardy-Weinberg Equilibrium

The Theorem can be used to calculate expected Genotype
frequencies, based on Allele frequencies within the
population, and vice versa

When ‘p’ represents the dominant allele’s frequency, and ‘q’
represents the recessive allele’s frequency, then p+q=1

When two haploid gametophytes merge, each with one copy
of gene, the resulting genotype frequencies can be calculated
based on (p+q)2 =12, or p2+2pq+q2=1

Thus p2=Homozygous Dominant Individuals,
2pq=Heterozygous Individuals, and q2=Homozygous Recessive
Individuals.
Example 1
 A population of velociraptors has two alleles for
color, the dominant allele is for purple scales, while
the recessive allele is for green scales.
 If the purple allele has a frequency of .3, what is the
frequency of the green scale allele?
 p+q=1
p=.3
.3+q=1 q=1-.3 q=.7
 Thus, the frequency of the green allele is .7
Example 2
 In a population of sweaters, one allele codes for stripes,
while the other allele codes for a plaid pattern.
 The plaid allele is dominant, with a frequency of .8
 What is the frequency of the recessive genotype?
(striped sweaters)
 If p=.8, then q=.2
 The frequency of the Recessive Genotype=q2
 .22=.04, thus the frequency of the recessive genotype is
.04
Example 3
 In a population of horses, there are brown horses and
black horses. If the brown allele is recessive with an
allelic frequency of .7, what is the frequency of the black
phenotype?
 If q=.7, then we can calculate that p=.3
 ‘p2’ gives us the Homozygous Dominant genotype and
Dominant phenotype, but ‘2pq’ also displays the
Dominant genotype despite being Heterozygous.
 p2=.33=.09
2pq=2×.3×.7=.42
 p2+2pq=.09+.42=.51  Black Colored Phenotype
Switching it Up
 So far, the examples have been used to calculate
genotype frequencies based on allele frequencies.
 In real life scenarios, often only the phenotypes
may be observed, and we can work backwards to
calculate allelic frequencies
 These methods are often used to estimate
percentages of the population carrying alleles for
inherited diseases
Example 4
 In a population of cats, brown eyes are dominant and
blue are recessive. 36% of the cats in the population
display blue eyes
 What are the allelic frequencies within the population?
 36% (.36) represents the Homozygous Recessive
frequency or q2. To find q, we take the square root of .36
 √.36 =.6 if q (recessive frequency)=.6, then p must =.4
(remember, p+q=1
Example 5

In a population of lab mice, brown fur is dominant, while
white is recessive. 57.75% of the mice are brown.

What are the allelic frequencies within the population?

If .5775 = the frequency of the dominant phenotype (p2+2pq)
then we can substitute this into the genotypic frequency
equation, resulting in .5775+q2=1

Subtracting, we find q2=.4225

√q2=√.4225, q=.65

The allelic frequency of white fur is .65, thus the frequency of
the allele for brown fur is .35
You’re Now a Hardy-Weinberg Expert
 Remember…the Hardy-Weinberg Theorem
describes a hypothetical population that is not
evolving, while in real populations allele and
genotype frequencies change over time
 Departure from the strict Hardy-Weinberg
conditions often causes evolution
 However, many populations evolve so slowly that
for the most part they display near-equilibrium. In
these cases, the Theorem may be applied.