1. Hardy-Weinberg
Part of Chapter 23

2. 5 Agents of Evolutionary Change
Mutation
Gene Flow
Non-random mating
Genetic Drift
Selection

3. Evolution of populations
Evolution = change in allele frequencies in a population
hypothetical: what conditions would cause allele frequencies to not change?
non-evolving population
REMOVE all agents of evolutionary change
very large population size (no genetic drift)
no migration (no gene flow in or out)
no mutation (no genetic change)
random mating (no sexual selection)
no natural selection (everyone is equally fit)

4. Hardy-Weinberg equilibrium
Hypothetical, non-evolving population
preserves allele frequencies
Serves as a model (null hypothesis)
natural populations rarely in H-W equilibrium
useful model to measure if forces are acting on a population
measuring evolutionary change
G.H. Hardy (the English mathematician) and W. Weinberg (the German physician) independently worked out the mathematical basis of population genetics in Their formula predicts the expected genotype frequencies using the allele frequencies in a diploid Mendelian population. They were concerned with questions like "what happens to the frequencies of alleles in a population over time?" and "would you expect to see alleles disappear or become more frequent over time?"
G.H. Hardy
mathematician
W. Weinberg
physician

5. Hardy – Weinberg Theorem
This describes a nonevolving population
States that the frequencies of alleles and genotypes in a population’s gene pool will remain constant over generations.
The shuffling of alleles after meiosis and random fertilization should have no effect on the overall gene pool of a population
Different phenotypic frequencies may appear in future generations but allele frequency should stay the same from generation to generation

6. Hardy-Weinberg theorem
Counting Alleles
assume 2 alleles = B, b
frequency of dominant allele (B) = p
frequency of recessive allele (b) = q
frequencies must add to 1 (100%), so:
p + q = 1 BB Bb bb

7. Hardy-Weinberg theorem
Counting Individuals
frequency of homozygous dominant: p x p = p2
frequency of homozygous recessive: q x q = q2
frequency of heterozygotes: (p x q) + (q x p) = 2pq
frequencies of all individuals must add to 1 (100%), so:
p2 + 2pq + q2 = 1 BB Bb bb

8. H-W formulas B b BB Bb bb BB Bb bb Alleles: p + q = 1
Individuals: p2 + 2pq + q2 = 1 B b BB Bb bb BB Bb bb

9. Using Hardy-Weinberg equation
population: 100 cats
84 black, 16 white
How many of each genotype?
q2 (bb): 16/100 = .16
q (b): √.16 = 0.4
p (B): = 0.6
p2=.36
2pq=.48
q2=.16 BB Bb bb
Must assume population is in H-W equilibrium!

10. Using Hardy-Weinberg Equation
p2=.36
2pq=.48
q2=.16
Assuming H-W equilibrium BB Bb bb
Null hypothesis
p2=.20
p2=.74
2pq=.10
2pq=.64
q2=.16
q2=.16
Sampled data 1:
Hybrids are in some way weaker.
Immigration in from an external population that is predomiantly homozygous B
Non-random mating... white cats tend to mate with white cats and black cats tend to mate with black cats.
Sampled data 2:
Heterozygote advantage.
What’s preventing this population from being in equilibrium. bb Bb BB
Sampled data
How do you explain the data?
How do you explain the data?

11. Application of H-W principle
Sickle cell anemia
inherit a mutation in gene coding for hemoglobin
oxygen-carrying blood protein
recessive allele = HsHs
normal allele = Hb
low oxygen levels causes RBC to sickle
breakdown of RBC
clogging small blood vessels
damage to organs
often lethal

12. Sickle cell frequency High frequency of heterozygotes
1 in 5 in Central Africans = HbHs
unusual for allele with severe detrimental effects in homozygotes
1 in 100 = HsHs
usually die before reproductive age
Sickle Cell:
In tropical Africa, where malaria is common, the sickle-cell allele is both an advantage & disadvantage. Reduces infection by malaria parasite.
Cystic fibrosis:
Cystic fibrosis carriers are thought to be more resistant to cholera:
1:25, or 4% of Caucasians are carriers Cc
Why is the Hs allele maintained at such high levels in African populations?
Suggests some selective advantage of being heterozygous…

13. Malaria
Single-celled eukaryote parasite (Plasmodium) spends part of its life cycle in red blood cells 1 2 3

14. Heterozygote Advantage
In tropical Africa, where malaria is common:
homozygous dominant (normal)
die or reduced reproduction from malaria: HbHb
homozygous recessive
die or reduced reproduction from sickle cell anemia: HsHs
heterozygote carriers are relatively free of both: HbHs
survive & reproduce more, more common in population
Hypothesis:
In malaria-infected cells, the O2 level is lowered enough to cause sickling which kills the cell & destroys the parasite.
Frequency of sickle cell allele & distribution of malaria

15. PKU Example Recessive disorder
About 1 in 10,000 babies born in US has PKU
q2 = .0001
Frequency of recessive allele is the square root of = .01
Frequency of dominant allele is
p = 1- q
p = = .99
Frequency of carriers (heterozygotes) is 2pq =

16. Problems
A lethal recessive condition is responsible for the death of 1 out of every 20,000 babies born in South America.
What is the frequency of homozygous recessive individuals in the population?
What is the frequency of the recessive allele in the population?
How many people, out of 1,000 individuals in this population, would carry the recessive allele?

17. Problems
A lethal recessive condition is responsible for the death of 1 out of every 20,000 babies born in South America.
What is the frequency of homozygous recessive individuals in the population?
q2 = 1/20,000 =
What is the frequency of the recessive allele in the population?
q = sqrt = 0.007
How many people, out of 1,000 individuals in this population, would carry the recessive allele?
p = 1 - q = = 0.993
2pq = 2 x x = 0.014
So: x 1,000 individuals ~ 14 people out of 1,000 carry the recessive allele

18. In snapdragons, R is dominant for red flowers and r is recessive for white flowers. Snapdragons exhibit incomplete dominance. In a population of 100 snapdragons, 50 have pink flowers and 25 have white flowers.
What is the frequency of heterozygous individuals?
What is the frequency of the dominant allele in the population?
What is the frequency of the recessive allele in the population?
What is the frequency of homozygous recessive individuals in the population?
What is the frequency of homozygous dominant individuals in the population?

19. In snapdragons, R is dominant for red flowers and r is recessive for white flowers. Snapdragons exhibit incomplete dominance. In a population of 100 snapdragons, 50 have pink flowers and 25 have white flowers.
What is the frequency of heterozygous individuals?
2pq= 50/100 = ½ or 0.5
What is the frequency of the dominant allele in the population?
p2 = 25/100 = 0.25
p = sqrt 0.25 = 0.5
What is the frequency of the recessive allele in the population?
q = 1 – p = 1 – 0.5 = 0.5
What is the frequency of homozygous recessive individuals in the population?
q2 = 0.25
What is the frequency of homozygous dominant individuals in the population?
p2 = 0.52 = 0.25