Population
Genetics
Hardy
Weinberg
Equilibrium

Population Genetics
• Hardy-Weinberg
Principle/equilibrium
– G. H. Hardy (1877-
1947)
• 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 p 2 + 2pq + q 2 = 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

Let’s say white tigers make up
10% of a population.
How do we calculate genotype frequencies?
There are two color morphs of tigers. The gene that results in the white color morph is recessive.

Calculations:
If 10% of the population is white, q 2 = .10
If q 2 = .10, q = .32
If q = .32, p = .68
If p = .68, p 2 = .46
2pq = .44
Genotype
Frequencies p 2 = .46
2pq = .44
q 2 = .10