Transcript Hardy-Weinberg Equilibrium

Population
Genetics
Hardy
Weinberg
Equilibrium
Population Genetics
• Hardy-Weinberg
Principle/equilibrium
– G. H. Hardy (18771947)
• English
mathematician
– Wilhelm Weinberg
(1862-1937)
• German physician &
geneticist
Population
Genetics
• Essential concept:
Gene pool
– “Collection” of all
alleles of all
individuals in a
population
– Within a gene pool,
alleles have
frequencies
– Allele frequency =
proportion of an
allele among all
alleles of a given
gene.
Allele Frequency
• There are 2015 individuals in a
population.
– How many alleles exist for a specific trait
that follows mendelian inheritance?
4030
Allele Frequency
• There are 2015 individuals (4030
alleles) in a population.
– If 172 of those alleles are recessive, what
is the frequency of the recessive allele?
172/4030 = 0.04, so 4%
– What is the frequency of the dominant
allele?
3858/4030 = 0.96, so 96%
Allele Frequency
• There are 312 individuals in a
population.
– If 172 of those alleles are recessive, what
is the frequency of the recessive allele?
• 28% (172/624)
– What is the frequency of the dominant
allele?
• 72% (624-172)/624
Allele Frequency
• By convention, we use p to
represent the dominant allele.
• By convention, we use q to
represent the recessive allele.
p+q=1
Allele Frequency
• There are 312 individuals in a
population.
– If 172 of those alleles are recessive, what
is the frequency of the recessive allele?
• 28% (172/624)
– What is the frequency of the dominant
allele?
• 72% (624-172)/624
Population Genetics
• If we know allele
frequencies, we can
calculate genotypic
and phenotypic
frequencies.
Population Genetics
• Let’s say a population contains 70%
dominant and 30% recessive
alleles…
Hardy Weinberg Equilibrium
2
p
+ 2pq +
2
q
=1
Population Genetics
• Hardy-Weinberg Principle/equilibrium
– Allele frequencies remain unchanged
generation to generation
Population Genetics
• Hardy-Weinberg Principle/equilibrium
– Mathematical model
– Assumptions/conditions
•
•
•
•
•
Large population
Random interbreeding
No mutation
No gene flow (migration among populations)
No selection
Hardy
Weinberg
Conditions
• MUST be a
large population
– Founder
effect
– Bottleneck
effect
Bottleneck
Hardy
Weinberg
Conditions
• MUST be a large
population
– Founder
effect
– Bottleneck
effect
– Genetic drift
Genetic Drift
Hardy Weinberg Conditions
Must have Random breeding
Violations of conditions:
• Sexual selection & female choice
– Pea-fowl
• Male dominance, combat
– Big-horn sheep
Hardy Weinberg Conditions
• No immigration / emigration
Hardy Weinberg Conditions
No migration
between
populations
Hardy Weinberg Conditions
No selective pressure
Heterozygote advantage
There are two color
morphs of tigers. The
gene that results in the
white color morph is
recessive.
Let’s say white
tigers make up
10% of a
population.
How do we
calculate genotype
frequencies?
Calculations:
If 10% of the population is white, q2 = .10
If q2 = .10, q = .32
If q = .32, p = .68
If p = .68, p2 = .46
2pq = .44
Genotype
Frequencies
p2 = .46
2pq = .44
q2 = .10