Here are the steps to solve this problem using Hardy-Weinberg equilibrium: 1) The frequency of the "aa" genotype is given as 0.36 2) Set up the Hardy-Weinberg equation: p2 + 2pq + q2 = 1 3) We are given q2 (frequency of "aa" genotype) = 0.36 So q = √0.36 = 0.6 4) p + q = 1 So p = 1 - 0.6 = 0.4 5) Frequency of "a" allele = 2q = 2 * 0.6 = 0.6 6) Frequency of "A" allele = 2

1. The Hardy-Weinberg Principle

2. Think. Pair. Share.
Solve for p or q in each of the following:
108 – q = 80 q=?
q = 28
p + 30 = 65 p=?
p = 35
52 - 420 + q2 = 5 q=?
q = 20

3. The Hardy-Weinberg Principle
Godfrey Hardy and Wilhelm Weinberg developed a
mathematical equation to predict allele frequencies in
populations: The Hardy-Weinberg Principle.
Played cricket with his Independently developed the
friend Reginald Punnett. principal at the same time.

4. The Hardy-Weinberg Principle
The Hardy-Weinberg Principle is used to predict allele
distribution and frequencies within a population.
Not always accurate.

5. Think. Pair. Share.
Recall what the following genetics terms mean:
Genotype
Phenotype
Allele
Recessive
Dominant
Homozygous
Heterozygous

6. The Hardy-Weinberg Principle
Suppose a population has only 2 eye colour alleles:
Brown (B)(dominant) and blue (b)(recessive).
BB Bb
bb bb
bb

7. The Hardy-Weinberg Principle
p+q=1
Where:
p is the percentage of dominant alleles in the population
q is the percentage of recessive alleles in the population

8. The Hardy-Weinberg Principle
Percentage of alleles means that 2 alleles were counted
for each person, then added up:
BB Bb
bb bb
bb

9. The Hardy-Weinberg Principle
Alleles present:
3 brown alleles (B)
7 blue alleles (b)
Thus:
p = 3 / (3 + 7)
= 0.30
= 30%
q = 7 / (3 + 7)
= 0.70
= 70%

10. The Hardy-Weinberg Principle
p = 30% means 30% of the alleles in the population are B
q = 70% means 70% of the alleles in the population are b
Check:
p+q=1

11. The Hardy-Weinberg Principle
Now we know
p+q=1
What if we do
(p + q)2 = 12
?

12. Hardy-Weinberg Equilibrium
p2 + 2pq + q 2 =1
Where:
p2 is the percentage of homozygous dominant organisms
Ex. (BB) – person has brown eyes

13. Hardy-Weinberg Equilibrium
p2 + 2pq + q 2 =1
Where:
2pq is the percentage of heterozygous organisms
Ex. (Bb) – person has brown eyes

14. Hardy-Weinberg Equilibrium
p2 + 2pq + q 2 =1
Where:
q2 is the percentage of homozygous recessive organisms
Ex. (bb) – person has blue eyes

15. Think. Pair. Share.
Do the math. Is this population in a Hardy-Weinberg
equilibrium (does the population match p2 + 2pq + q2 = 1)?
BB Bb
bb bb
bb

16. Hardy-Weinberg Equilibrium
Allele distribution in a population can only be predicted if
it is not changing (or evolving).

17. Hardy-Weinberg Equilibrium
The Hardy-Weinberg Principle is only accurate if:
1) no mutations occur.
2) no selection occurs.
3) there is no immigration or emigration.
4) the population is large enough to avoid genetic drift.
5) there is no horizontal gene transfer (bacteria).
6) all mating is random.

18. Hardy-Weinberg Equilibrium
Practice:
1) You have sampled a population in which you know
that the percentage of the homozygous recessive ("aa")
genotype is 36%. Find the following:
A) The frequency of the "aa" genotype
B) The frequency of the "a" allele
C) The frequency of the "A" allele
D) The frequencies of the genotypes "AA" and "Aa"
E) The frequencies of the two possible phenotypes if
"A" is completely dominant over "a"