Transcript Aim: What is the Hardy-Weinberg Theorem?

Aim: What is the HardyWeinberg Theorem?
What is the Modern Theory of
Evolution?
A population is a localized group of
individuals that belong to the same species.
It is the population, not its individual, that
evolves.
Population Evolution = the change in the
allelic frequencies of a population over time.
Alleles are different versions of the same
trait.
Example: In guinea pigs, black fur is dominant
over white fur. The genotype of a white guinea
pig contains two recessive alleles.
Modern Theory of Evolution
states:
1) overproduction – more offspring are
produced than can survive and
reproduce.
2) variation – individuals of the same
species vary and must compete in order
to survive. (Darwin did not know the
mechanism for variation! We know it
involves crossing over during gamete
formation, mutation, random mating of
sex cells, and independent assortment.
3) variations are inheritable if they are
carried in the genome of the sex cells
Modern Theory of Evolution states:
4) Only the most fit organisms are able to
survive in the environment. Note: the most fit
does not necessarily have to be the strongest!
5) Natural selection occurs as fit organisms
survive and have the opportunity to reproduce.
Note: somatic variations, such as skin
cancers, do not effect evolution if they are
not transmitted to the next generation
through sex cells.
Natural selection can act on genetic variations
only when they are expressed in the
phenotype.
Black polar bears would not be able to
survive well on the polar ice and would be
‘naturally selected’ against.
What is population genetics?
Population genetics studies gene frequencies
in a population.
Gene pool – sum total of all the genes
possessed by all the individuals in a
population.
Evolution is evident in a population when the
gene frequencies in a population change over
many generations.
What is the Hardy-Weinberg
Theorem?
The Hardy-Weinberg theorem describes
the gene pool of a nonevolving population.
The theorem states that under certain
conditions of stability in the population, both
phenotypic and allelic frequencies remain
constant from generation to generation in a
sexually-producing population.
The shuffling of alleles after meiosis and
random fertilization should have no effect on
the overall gene pool of a population.
Conditions for Hardy-Weinberg
Theorem to be met:
1) the population must be large enough to
make it highly unlikely that chance alone
could significantly affect the population.
2) mutations must not occur or must be
counter-balanced by reverse mutations.
3) no immigration or emigration
4) mating must be completely random
5) no natural selection
Example of population
genetics
Trait = guinea pig hair color
B = black (dominant) (frequency of 90%)
b = white (recessive) (frequency of 10%)
Cross heterozygous black with heterozygous
black (Bb X Bb)
A (.9)
a (.1)
A (.9)
AA
(.81)
Aa
(.09)
a (.1)
Aa
(.09)
aa
(.01)
Using the Hardy-Weinberg
theorem
Generalizing the Hardy-Weinberg
theorem, population geneticists use p to
represent the frequency of one allele
and q to represent the frequency of the
other allele.
The combined frequencies must add to
100%; therefore p + q = 1.
If p + q = 1, then p = 1 - q and q = 1 - p.
•In the guinea pig example p is the frequency of
black fur alleles (B) and q of white alleles (b).
•The probability of generating an BB offspring is p2 (an
application of the rule of multiplication).
•In our example, p = 0.9 and p2 = 0.81
•The probability of generating an bb offspring is q2.
•In our example, q = 0.1 and q2 = 0.01
•The probability of generating Bb offspring is 2pq.
•In our example, 2 x 0.9 x 0.1 = 0.18
•The genotype frequencies should add to 1:
p2 + 2pq + q2 = 1
•For the guinea pigs, 0.81 + 0.18 + 0.01 = 1.
•This general formula is the Hardy-Weinberg
equation.
•Using this formula, we can calculate frequencies
of alleles in a gene pool if we know the
frequency of genotypes; the frequency of
genotypes if we know the frequencies of alleles.