1. Hardy-Weinberg Principle

2. Hardy-Weinberg Principle
Hardy-Weinberg Principle – enables us
to calculate and predict allelic and
genotypic frequencies
Allelic frequency – the frequency of an
allele in a population
Genotypic frequency – the frequency of
a genotype in a population

3. Hardy-Weinberg
We use p to represent the dominant allele, and q to represent the recessive allele
For allelic frequency: p + q = 1
So if the frequency of the dominant allele (p) is 0.75, then the frequency of the recessive allele (q) is…0.25

4. Hardy-Weinberg For genotypic frequency: p2 + 2pq + q2 = 1 Where:
p2 = frequency of homozygous dominant
2pq = frequency of heterozygous
q2 = frequency of homozygous recessive

6. Hardy-Weinberg
SO…for example, if we know the frequency of the homozygous recessive genotype (q2), we can find the frequency of the recessive allele [√(q2) = q]
THEN…since we know q, we can find p, then p2, then 2pq!

7. Hardy-Weinberg
Hardy-Weinberg predicts that gene frequencies will remain the same from one generation to the next
However, certain conditions must be met

8. Hardy-Weinberg the frequencies of the alleles do not change and
as long as the mating is random, the genotypic frequencies will remain in the proportions p2 (frequency of AA), 2pq (frequency of Aa) and q2 (frequency of aa) where p is the frequency of A and q is the frequency of a
The sum of the genotypic frequencies should be: p2 + 2pq + q2 = 1

9. Hardy-Weinberg Assumptions
1) Large population
2) Random mating
3) No mutation
4) No migration (in or out of population)
5) No selective pressure

10. Brachydactyly and evolutionary change
We know the gene for brachydactyl fingers is dominant to normal fingers
A man named Yule suggested that short-fingered people should become more common through time
Godfrey Hardy showed this inference was wrong
Wilhelm Weinberg derived the same solution to the problem independently

11. The Hardy-Weinberg Law - the most important principle in population genetics
The law is divided into three parts: a set of assumptions and two major results
In an infinitely large, randomly mating population, free from mutation, migration and natural selection (note there are five assumptions here)

12. The Hardy-Weinberg Law - the most important principle in population genetics
The incidence of albinism is remarkably common ( or 13 in every 3000 Hopis)
Assuming Hardy-Weinberg equilibrium, we can calculate q as the square root of = 0.066
p is therefore equal to 0.934
The frequency of heterozygotes in the population is 2pq = 0.123
In other words, 1 in 8 Hopis carries the gene for albinism!
Take-home Lesson: For a rare allele, heterozygotes can be relatively common

13. Albinism in Hopi Native Americans
The incidence of albinism is remarkably common ( or 13 in every 3000 Hopis)
Assuming Hardy-Weinberg equilibrium, we can calculate q as the square root of = 0.066
p is therefore equal to 0.934
The frequency of heterozygotes in the population is 2pq = 0.123
In other words, 1 in 8 Hopis carries the gene for albinism!
Take-home Lesson: For a rare allele, heterozygotes can be relatively common

14. Hardy Weinberg Problem I
Sickle Cell Anemia
– SS = susceptible to malaria but no SCA
– ss = non-susceptible but SCA 􀃆 mortality
– Ss = non-susceptible and no SCA
What do we expect proportions of ss? Ss?
• E.g. 4% ss - what are proportions of Ss
– .04 = ss = q2 􀃆 q = √.04 = .2
– p = 1 - q = = .8
– Ss = 2pq = 2(.8)(.2) = .32

15. Hardy Weinberg Problem II
What would it take to increase Ss
proportion to 50% (from 32%)?
– Ss = 2pq = .5 􀃆 pq = .25
– q = 1 - p 􀃆 p (1-p) = .25 􀃆 p = .5
– Which means
aa goes to .25 from .04, over 6x

16. Hardy Weinberg Problem III
How many of you can roll your tongues?
– A - Yes
– B - N

17. Hardy Weinberg Problem III
What is the percentage of heterozygous
tongue-rollers?
– Yes = p2 + 2pq
– No = q2
– q = √No
– p = 1- q
– Heterozygous = 2pq