1. The evolution of populations & Hardy-Weinberg Equilibrium
Friday, September 5, 2014

2. Warm-up
What do you think is the most important component in order for evolution to occur? (Hint: think about the definition of evolution).

3. Homework Be a leader assignment… due Monday, September 8!
Directions: Solve your problem on a separate sheet of paper and staple it to your given worksheet slip. Hand it in on Monday.
Be prepared to show your group how you solved the problem!

4. Inheritance of acquired characteristics
Lamarck vs. Darwin
Inheritance of acquired characteristics
Natural selection

6. Evolution is change in the genetic composition of a population from generation to generation

7. Evolution is the change in allele frequencies over time
But what is a more concise definition for evolution that will help us determine quantitatively if evolution is occurring??
Evolution is the change in allele frequencies over time
How can we measure allele frequencies?
How can we track changes in allele frequencies over time?

8. Genetic variation exists in the population (this is key for evolution to occur!)
Certain alleles produce traits that are more adaptive, i.e., promote greater survival and reproduction
These alleles get passed on to the next generation

9. Evolution is the change in allele frequencies in a population over generations
Population: group of individuals of the same species that live in the same area and interbreed, producing fertile offspring.
Gene pool: genetic makeup of a population

10. Evolution is the change in allele frequencies in a population over generations
Mechanisms that cause allele frequency change:
Natural selection
Genetic drift
Gene flow
Mutation
Non-random mating
Only natural selection causes adaptive evolution

11. Mini genetics review Alleles are different versions of that gene
Example:

12. Combinations of alleles
Example for a population in which alleles for a gene are ‘R’ or ‘r’
Homozygous recessive: rr
Homozygous dominant: RR
Heterozygous: Rr
Skittles gene pool

13. Now, how do we measure changes in allele frequencies in populations over time?

14. First, we must know the starting point
What are the allele frequencies in the population right now?
We cannot measure change unless we know the initial state.

15. Use Hardy-Weinberg Principle to quantify evolution
Godfrey Harold "G. H." Hardy
Wilhelm Weinberg

16. The idea is to track allele frequenciesAA Aa aa
What is the frequency of allele A?
What is the frequency of allele a?

17. The idea is to track allele frequenciesAA Aa aa
The frequency for allele A = 13/20 or 0.65
The frequency for allele a = 7/20 or 0.35

18. AA Aa aa ?
Generation 1
Generation 2

19. Hardy-Weinberg Principle
Allele frequencies of alleles and genotypes in a population will remain constant from generation to generation if all assumptions are met
A gene pool that remains constant is said to be in Hardy- Weinberg equilibrium

20. AA Aa aa ?
Generation 1
Generation 2

21. A a Generation 1 Generation 2 Aa aa AA AA 0.42 Aa 0.23 aa 0.12 0.65
0.35 AA
0.42 Aa
0.23 aa
0.12
Generation 1
Generation 2

22. A a f(A) = 0.65 f(a) = 0.35 f(A) = ? f(a) = ? Aa aa AA AA 0.42 Aa 0.23
0.12
f(A) = 0.65 f(a) = 0.35
f(A) = ? f(a) = ?

23. Allele frequencies did not change, thus no evolution.AA Aa aa A
0.65 a
0.35 AA
0.42 Aa
0.23 aa
0.12
f(A) = 0.65 f(a) = 0.35
f(A) = 0.65 f(a) = 0.35
Allele frequencies did not change, thus no evolution.

24. The Hardy-Weinberg Principle
Allele frequencies in a population will remain constant if ALL of the following conditions are met:
The population is infinitely large
Individuals mate randomly
No gene flow
No natural selection
No mutations
If all conditions are met, then NO evolution. Allele frequencies will remain constant. This is the null hypothesis.

25. The Hardy-Weinberg equation: p2 + 2pq + q2 = 1
0.65 a
0.35 AA
0.42 Aa
0.23 aa
0.12

26. Understanding the equation
p2 + 2pq + q2 = 1
p is the frequency of the dominant allele (A) = 0.65
q is the frequency of the recessive allele (a) = 0.35 AA Aa aa

27. Understanding the equation
p2 + 2pq + q2 = 1
p is the frequency of the dominant allele (A) = 0.65
q is the frequency of the recessive allele (a) = 0.35
p = f(AA) + ½ f(Aa)
p = ½ 0.3 = 0.65
q = f(aa) + ½ f(Aa)
q = ½ 0.3 = 0.35 AA Aa aa

28. Using p and q from generation 1, solve for frequencies of predicted genotypes in generation 2 using HW

29. Understanding the equation
p2 + 2pq + q2 = 1
p is the frequency of the dominant allele (A) = 0.65
q is the frequency of the recessive allele (a) = 0.35
p = f(AA) + ½ f(Aa)
p = ½ 0.3 = 0.65
q = f(aa) + ½ f(Aa)
q = ½ 0.3 = 0.35 A
0.65 a
0.35 AA
0.42 Aa
0.23 aa
0.12
Generation 2
p = f(A) = 0.65 q = f(a) = 0.35

30. Understanding the equation
p2 + 2pq + q2 = 1
p is the frequency of the dominant allele (A) = 0.65
q is the frequency of the recessive allele (a) = 0.35
p = f(AA) + ½ f(Aa)
p = ½ 0.3 = 0.65
q = f(aa) + ½ f(Aa)
q = ½ 0.3 = 0.35 A
0.65 a
0.35 AA
0.42 Aa
0.23 aa
0.12
p2 = the predicted frequency of genotype AA = 0.42
2pq = the predicted frequency of genotype Aa = 0.46
q2 = the predicted frequency of genotype aa = 0.12
Generation 2
p = f(A) = 0.65 q = f(a) = 0.35

32. The Hardy-Weinberg equation: p2 + 2pq + q2 = 1
What is the frequency of alleles B and b?

33. Allele Frequencies
Red short-horned cattle are homozygous for the red allele, white cattle are homozygous for the white allele, and roan cattle are heterozygotes. Population A consists of 36% red, 16% white, and 48% roan cattle. What are the allele frequencies?
red = 0.36, white = 0.16
red = 0.6, white = 0.4
red = 0.5, white = 0.5
Allele frequencies cannot be determined unless the population is in equilibrium.
Answer: b 33

34. Allele Frequencies
Red short-horned cattle are homozygous for the red allele, white cattle are homozygous for the white allele, and roan cattle are heterozygotes. Population A consists of 36% red, 16% white, and 48% roan cattle. What are the allele frequencies?
red = 0.36, white = 0.16
red = 0.6, white = 0.4
red = 0.5, white = 0.5
Allele frequencies cannot be determined unless the population is in equilibrium.
Answer: b 34

35. Let’s see another example
We sampled 200 individuals from a population:
128 individuals have the AA genotype
53 individuals have the Aa genotype
19 individuals have the aa genotype
What are the genotype frequencies?

36. Let’s see another example
We sampled 200 individuals from a population:
128 individuals have the AA genotype (0.64)
53 individuals have the Aa genotype (0.26)
19 individuals have the aa genotype (0.10)
What are the allele frequencies?
Genotype frequencies

37. Let’s see another example
We sampled 200 individuals from a population:
128 individuals have the AA genotype (0.64)
53 individuals have the Aa genotype (0.26)
19 individuals have the aa genotype (0.10)
p = AA + ½(Aa) = ½(0.26) = 0.77
q = aa + ½(Aa) = ½(0.26) = 0.23
Genotype frequencies
Allele frequencies

38. Let’s see another example
We sampled 200 individuals from a population:
128 individuals have the AA genotype (0.64)
53 individuals have the Aa genotype (0.26)
19 individuals have the aa genotype (0.10)
p = AA + ½(Aa) = ½(0.26) = 0.77
q = aa + ½(Aa) = ½(0.26) = 0.23
p + q = = 1.0
p2 + 2pq + q2 = (0.77)2 + 2(0.77)(0.23) + (0.23)2 = 1.0
Genotype frequencies
Allele frequencies

39. Let’s work through another example
Albinism (aa) occurs on average 1 in 20,000 individuals in North America.
What is the frequency of the A and a allele in this population?

40. Let’s work through another example
Albinism (aa) occurs on average 1 in 20,000 individuals in North America.
 What is the frequency of the A and a allele in this population?
The Hardy-Weinberg equation: p2 + 2pq + q2 = 1
q2 = f(aa) = 1/20,000 =
√ q2 = √
q = (frequency of a in the population)
p = 1 – q
p = 1 – 0.007
p = (frequency A in the population)
p2 + 2pq + q2
(0.993)2 + 2(0.993)(0.007) + (0.007)2 = 1.0
p2 = 98.6% (AA)
2pq = 1.4% (Aa)
q2 = 0.005% (aa)

41. The Hardy-Weinberg Principle
Allele frequencies in a population will remain constant if ALL of the following conditions are met:
The population is infinitely large
Individuals mate randomly
No genetic migration and mutation
No natural selection
No mutation
If ALL conditions are met, then there’s NO evolution. Allele frequencies will remain constant.
The Hardy-Weinberg equation: p2 + 2pq + q2 = 1

42. A a Aa aa AA What will happen if these assumptions are not met?
0.65 a
0.35 AA
0.42 Aa
0.23 aa
0.12
f(A) = 0.65 f(a) = 0.35
f(A) = 0.65 f(a) = 0.35
What will happen if these assumptions are not met?
The population is infinitely large
Individuals mate randomly
No genetic migration and mutation
No natural selection

43. Exit Ticket
What is the Hardy-Weinberg formula, and what does each component represent?

44. Work on Clover Study