1. Allele Frequencies Genotype Frequencies The Hardy-Weinberg Equation
Population Genetics
Allele Frequencies
Genotype Frequencies
The Hardy-Weinberg Equation

2. Allele Frequency
Allele frequency = number of copies of an allele in a popuation ÷ total number of alleles in a population
Example:
A population of 100 pea plants have the following genotypes
64 tall plants with the genotype TT
32 tall plants with the genotype Tt
4 dwarf plants with the genotype tt
t = (4) ÷ 2 (64) + 2(32) + 2(4)
= 40 ÷ 200 = .2 or 20%

3. Genotype Frequency
Genotype frequency = number of individuals with a particular genotype in a population ÷ total number of individuals in a population
Example:
tt = 4 ÷
= 4 ÷ 100 = .04, or 4%

4. The Hardy Weinberg Equation
Is a way to study whether allele and genotype frequencies will change over the course of many generations.
1908 = Godfrey Harold Hardy and Wilhelm Weinberg independently discovered a mathematical expression that predicted the stability of allele and genotype frequencies from one generation to the next.
Hardy-Weinberg equilibrium = the allele and genotype frequencies do not change over the course of many generations (under a given set of conditions).

5. Factors that cause change in allele and genotype frequencies:
1. Mutation
2. Random Genetic Drift
3. Migration
4. Natural Selection
5. Nonrandom Mating
Assignment: describe each of the above factors on a sheet of paper (pg. 670).

6. Hardy-Weinberg Equation
Example = If a gene exists as 2 different alleles (A and a), then the variable p represents the allele frequency of A and the variable q represents the allele frequency of a.
The following equation shows that the allele frequency of A plus the allele frequency of a equals the 100% of the alleles for a particular gene:
p + q = 1

7. Hardy-Weinberg Equation
p²+ 2pq + q² = 1
p² = the genotype frequency of AA
q² = the genotype frequency of aa
2pq = the genotype frequency of Aa

8. Example If: p = .8 q = .2 Then: AA = p² = (.8)² = .64
Aa = 2pq = 2(.8)(.2) = .32
aa = q² = (.2)² = .04
(In other words, the allele frequency of A = 80% and the allele frequency of a is 20%.)
The genotype frequency of AA is 64 %
The genotype frequency of Aa is 32 %
The genotype frequency of aa is 4%

9. A .8 a .2 AA
(.8) (.8) = .64 Aa
(.8)(.2) = .16
(.2)(.2) = .4 A .8 a .2

10. The African Cheetah
This species has a relatively low level of genetic variation because the population was reduced to a small size approximately 10,000 to 12,000 years ago.