HARDY-WEINBERG EQUILIBRIUM
What Darwin didn’t Get
 Darwin couldn’t figure out why there was so
much GENETIC VARIATION in natural
populations.
Darwin thought that selection should ALWAYS
favor the optimal form and eliminate
vaiation…… hmmm…. But…….
The reality is, there is A LOT of variation in populations
So how could this be?
Hardy and Weinberg (1908)
 Independently solved WHY
this genetic variation exists
 Hardy was a
mathematician
 Weinberg was a physician
They showed that the frequency of genotypes in a
population will stay the same from one generation
to the next.
That is if : SEVEN conditions are met
We call this HARDY-WEINBERG EQUILIBRIUM
THE BIG SEVEN
1. Mutation is not occurring
2. Natural selection is not occurring
3. The population is very large
4. All members of a population breed
5. All mating is totally random
6. Everyone produces the same number of offspring
7. There is no immigration or emigration happening in the
population
Ok, so how realistic is this???
Not very, but we can use an equation as a model for population genetics
First you need to know that:
•ALLELES represent GENES
•Individuals receive one allele from each parent
•This makes up an individuals genes
•The genes determine the phenotype
Therefore an individual will receive a combination of alleles in the form
of :
Dominant Dominant
Recessive Recessive
Dominant Recessive
AA
aa
Aa
The alleles are represented as letters
Capital letter = Dominant
Lowercase Letter = Recessive
 AA is called: HOMOZYGOUS DOMINANT
 Aa is called: HETEROZYGOUS DOMINANT
 aa is called: HOMOZYGOUS RECESSIVE
BREATH DEEP….here we go……
The HARDY- WEINBERG Equation (s)
p+q=1
2
2
p + 2pq + q = 1
These equations figure out:
•ALLELE FREQUENCY
•GENOTYPE FREQUENCY
AA + Aa + aa = 1
2
2
p + 2pq + q = 1
Formula for GENOTYPE Frequency
A+a=1
p+q=1
Formula for ALLELE frequency
Now that we know what
each formula represents,
figuring out each problem is
easy!!!!!!
You will ALWAYS be given
That the characteristic is either
DOMINANT or RECESSIVE
Example: the problem will tell you that
RED = R
WHITE = r
THEN you will be GIVEN
A VALUE of one of these:
A
a
AA
aa
And you already know that:
A=p
AA = p2
a=q
Aa = 2pq aa = q2
NOW all you have to do is..
Plug the values in!!!
But it’s kind of like a maze
Sooooooooo
1
STEP : write out both formulas
AA + Aa + aa = 1
p2 + 2pq + q2 = 1
AND
A+a=1
p+q=1
Step 2: Figure out what you’ve been given
and plug it in
Example:
if you are given the value of aa as 50% or .5o
Plug .50 into the q2 spot
AA + Aa + aa = 1
p2 + 2pq + q2 = 1
p2 + 2pq + .50 = 1
Now you can figure out q
.50
=
.71
A+a=1
p+ q = 1
P + .71 = 1
.29 + .71 = 1
AA + Aa + aa = 1
p2 + 2pq + q2 = 1
.084 + 2 (.29)(.71) + .50 = 1
.084 + .41 + .50 = 1
Lets look at a problem
The gene for an intelligent dolphin is
dominant to a gene for an aggressive
dolphin. In a population there are 25%
that have the gene for homozygous
recessive aggressiveness. Figure out the
gene frequency for the heterozygous
intelligent.
OK, so we know that:
We’re looking or GENE FREQUENCY
Intelligent = A
Aggressive = a
Homozygous recessive = aa = 25% = .25
Heterozygous = Aa