Meet My Good Friends Hardy and Weinberg!!

Biologists use models to study populations. Biologists use models to study populations. Hardy and Weinberg developed a mathematical model to show when a population is not evolving (or is in equilibrium). Hardy and Weinberg developed a mathematical model to show when a population is not evolving (or is in equilibrium).

–a population is a localized group of interbreeding individuals –gene pool is a collection of alleles in a particular population –allele frequency is how common that allele is in the population (how many of green or brown alelles are in ole population)

Evolution of populations  By comparing allele frequencies in populations at one point in time to the allele frequencies in the same population at a different point in time- we can see if evolution is occurring.

Alelle frequencies stay the same if five conditions are met. Alelle frequencies stay the same if five conditions are met. –very large population: no genetic drift –no emigration or immigration: no gene flow –no mutations: no new alleles added to gene pool –random mating: no sexual selection –no natural selection: all traits aid equally in survival

Hardy-Weinberg theory  Counting Alleles  assume 2 alleles = B, b  frequency of dominant allele (B) = p  frequency of recessive allele (b) = q  frequencies must add up to 1 (100%), so: p + q = 1 bbBbBB

Hardy-Weinberg theory  Counting Genotypes  frequency of homozygous dominant: p x p = p 2  frequency of homozygous recessive: q x q = q 2  frequency of heterozygotes: (p x q) + (q x p) = 2pq  frequencies of all individuals must add to 1 (100%), so: p 2 + 2pq + q 2 = 1 p 2 + 2pq + q 2 = 1 bbBbBB

H-W formulas Alleles:p + q = 1 Alleles:p + q = 1 Genotypes:p 2 + 2pq + q 2 = 1 Genotypes:p 2 + 2pq + q 2 = 1 bbBbBB Bb Bbbb

What are the genotype frequencies? Using Hardy-Weinberg equation population: 100 cats 84 black, 16 white How many of each genotype? population: 100 cats 84 black, 16 white How many of each genotype? bbBbBB First calculate frequency of b from the known number of bb genotypes.

What equation is used for genotype frequency calculation? Using Hardy-Weinberg equation q 2 (bb)= 16/100 = q (b): √.16 = 0.4 Now work out p 0.6 p (B)= = 0.6 q 2 (bb)= 16/100 = q (b): √.16 = 0.4 Now work out p 0.6 p (B)= = 0.6 population: 100 cats 84 black, 16 white How many of each allele? population: 100 cats 84 black, 16 white How many of each allele? bbBbBB

Using Hardy-Weinberg equation q 2 (bb): 16/100 = q (b): √.16 = p (B): = 0.6 Now work out genotype frequencies q 2 (bb): 16/100 = q (b): √.16 = p (B): = 0.6 Now work out genotype frequencies population: 100 cats 84 black, 16 white How many of each genotype? p 2 + 2pq + q 2 = 1 population: 100 cats 84 black, 16 white How many of each genotype? p 2 + 2pq + q 2 = 1 bb Bb BB p 2 =0.36 2pq=0.48 q 2 =0.16