Population Genetics Hardy Weinberg Equilibrium

Population Genetics Hardy-Weinberg Principle/equilibrium –G. H. Hardy ( ) English mathematician –Wilhelm Weinberg ( ) 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? –What is the frequency of the dominant allele? 172/4030 = 0.04, so 4% 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

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

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

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, 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