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The Hardy- Weinberg Theorem
"Under certain conditions of stability both allelic frequencies and genotypic ratios remain
constant from generation to generation in sexually reproducing populations."
The Equations of The Hardy-Weinberg Equilibrium
The same results we got in the punnett square can be obtained with a simple algebraic formula.
Eg. #1 If P = frequency of allele A = 0.9 and q = frequency of allele a = 0.1 Then expansion of the
binomial expression (p + q)2= p2 + 2pq + q2 = 1, Is the "Hardy-Weinberg formula" If we
substitute the allelic frequencies into the formula: p2 + 2pq + q2 = 1
(0.9)(0.9) + 2(0.9)(0.1) + (0.1)(0.1) = 1
0.81 + 0.18 + 0.01 = 1
Therefore the term p2 = frequency of genotype AA = 0.81. The term 2pq = frequency of
genotype Aa = 0.18, and the term q2 = frequency of genotype aa = 0.01
Eg. #2 What if we know the genotypic frequency but wish to calculate the frequency of the
alleles in a population? Use the same formula.
Let say that a recessive allele "a" causes produces blond hair, and 4% of a population have
blond hair, therefore what are the allelic frequencies?
If only homozygous recessives have blond hair then aa = blond
There are 4% blond or 0.04 = aa. Therefore q2 = aa = 0.04. Therefore q = square root of 0.04=
0.2
Recall that p + q = 1 always (since they are frequencies). Therefore if q = 0.2, then 1 - 0.2 = p =
0.8 since (p = 1 - q). Therefore q = 0.2 and p = 0.8
Substituting into the Hardy-Weinberg equation: p2 + 2pq + q2 = 1
(0.8)2 + 2(0.8)(0.2) + (0.2)2 = 1
AA = 0.64, Aa = 0.32, aa = 0.04
What are the conditions of "The Hardy-Weinberg Theorem"?
In such a stable population there are no processes that act to change the allelic frequencies
from one generation to the next. This requires certain conditions:
1) The population must be large enough to make it highly unlikely that chance alone could
significantly alter allelic frequencies.
2) Mutations must not occur (or else there must be mutational equilibrium).
3) There must be no immigration or emigration.
4) Reproduction must be totally random.
Since we see that populations do evolve, what forces or processes are at work that violate
these conditions?
Condition #1
This would require that a population be of infinite size which is clearly impossible. Chance
events may cause changes in allelic frequencies ie. evolutionary changes, in small populations.
Such random chance events are called Genetic Drift. One example of such a random chance
event is known as the "Founder effect"
A small sample of a large population randomly chosen from the original population, becomes
separated and forms a new population. This could happen if a storm was to blow some birds
from the mainland out onto a small island. This new population could have a significantly
different allelic frequency than the original large population, depending on which birds just
happened to be blown out by the storm.
Condition #2
Mutation is always occurring and rarely are they in equilibrium. i.e. A mutates to ----> a (1), a
mutates to ----> A (2)
Process 1 rarely equals process 2 therefore, A% slowly moves to a % Called mutation pressure.
Condition #3
No new genes can be introduced to the population from outside the population by
immigration, and no genes are lost through emigration. That is there is NO GENE FLOW. This
could only happen if the population is extremely isolated.
Condition #4
Reproduction within the population is seldom totally random. It means all genotypes have
exactly the same reproductive success. This condition is probably never meet in any real
population. Finally "Selection pressure" or natural selection is always working to upset the
Hardy-Weinberg Theorem.
SO WHY go to so much trouble to explain the Hardy-Weinberg Theorem, only to show that it
describes a situation that never occurs in nature?
For one compelling reason: The Hardy-Weinberg Theorem sets up the "Null-hypothesis" - NO
EVOLUTION. Which because it is so easily disproved provides an indirect demonstration that
populations must constantly be evolving.