1. Is the cockroach population evolving?
Population of cockroaches: 5 green, 5 white.
A is the green allele and a is the white allele.
1) Pick up a whiteboard and marker. Split it in half
2) On one half put all the cockroaches. Next to each cockroach put the genotype: AA, Aa or aa. THESE ARE INDIVIDUALS. Yell checkpoint
3) On the other side label gene pool just put alleles individually. THESE ARE ALLELE FREQUENCIES
How many A? Total A/Total
How many a? Total a/Total
4) 100 years later– There are 10/20 As and 10/20 as. Evolved?

2. Symbols
Individuals p2 q2
2pq
Alleles p q

3. The two Hardy-Weinberg formulae allow us to calculate allele frequency:
p2 + 2pq + q2 = 1
p + q = 1

4. 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
What are the genotype frequencies?
Must assume population is in H-W equilibrium! 4

5. Hardy-Weinberg Equation
p=frequency of one allele (A); q=frequency of the other allele (a); p+q= (p=1-q & q=1-p)
p2=frequency of AA genotype; 2pq=frequency of Aa genotype; q2=frequency of aa genotype;
frequencies of all individuals must add to 1 (100%), so: p2 + 2pq + q2 = 1
G.H. Hardy
mathematician
W. Weinberg
physician

6. Hardy Problem
Calculate q2 Count the individuals that are homozygous recessive in the illustration above. Black is recessive to pink. Calculate the percent of the total population they represent. This is q2.
Calculate q
Q2=4/16=0.25
q=0.5
p + q = l. You know q, so what is p, the frequency of the dominant allele?
P=0.5
Find 2pq
2pq = 2(0.5) (0.5) = 0.5 , so 50% of the population is heterozygous.

7. 5 Agents of evolutionary change
Gene Flow
Non-random mating
Genetic Drift
Selection
Mutation 7

8. Hardy-Weinberg=NO EVOLUTION
To see what forces lead to evolutionary change, we must examine the circumstances in which the Hardy-Weinberg law may fail to apply.
There are five must happen:
NO mutation
NO gene flow
NO genetic drift
NO nonrandom mating
NO natural selection

9. Hardy-Weinberg Lab

10. Lab Objectives After doing this laboratory students should be able to
calculate the frequencies of alleles and genotypes in the gene pool of a population using the Hardy-Weinberg formula
discuss natural selection and other causes of microevolution as deviations from the conditions required to maintain Hardy-Weinberg equilibrium

11. Hardy-Weinberg Rule
Establishes allele frequencies at genetic equilibrium (no evolution), under these conditions:
1) No mutations are occurring
2) The population is very, very large
3) The population is isolated from other populations of the same species
4) All members survive, mate, and reproduce (no selection)
5) Mating is random

12. Hardy-Weinberg Rule p = dominant allele q = recessive allele
pq = heterozygote
p + q = all alleles in population
p2+2pq+q2 = all genotypes

13. Allele Frequencies qq pq q pp p
Alleles
GENOTYPES

14. Case 1: Testing An Ideal Population
Each person needs 4 index cards to start—A, A, a, a
Randomly pair off with another student for “breeding.” Any gender works.
Have the cards behind your back. Reveal one card from each partner. That will be the genotype of first offspring.
Reveal another card from each partner. That will be the genotype of second offspring.
Next you and your partner must take on the genotypes of the two offspring you produced. For example if you produced AA and Aa, one of you starts with 4 As and the other with 2As and 2as
Repeat for 5 generations. Recording each time

15. Case 2: Selection
There is 100% selection against homozygous recessive offspring. They won’t live long enough to reach a reproductive age.
Each person needs 4 index cards to start—A, A, a, a
Randomly pair off with another student for “breeding.” Any gender works.
Have the cards behind your back. Reveal one card from each partner. That will be the genotype of first offspring.
Reveal another card from each partner. That will be the genotype of second offspring.
If offspring is aa it dies and you must make 2 surviving offspring
Repeat for 5 generations. Recording each time

16. Case 3: Heterozygous Advantage--malaria
Make a hypothesis
Malaria affects homozygous dominant more severely than heterozygous.

17. Case 3: Heterozygous Advantage--malaria
Make a hypothesis
Malaria affects homozygous dominant more severely than heterozygous.
Homozygous recessive individuals die from sickle cell.
aa=die from sickle cell
AA=flip a coin
HEADS=death of offspring
TAILS=offspring lives
Aa—survive
Repeat for 5 generations. Recording each time

18. Warm Up Look at the Hardy Weinberg poster headings. What’s different?
Look at A1-A3 Mastery Checklist
Solve Hardy-Weinberg Problem Set

19. Using the Hardy-Weinberg equation to find f (AA), f (Aa) and f (aa):
Step 1: Find q2
Step 4: Find f (aa)
f (aa) = f (q2) = .36
Step 2: Find q
Step 5: Find f (Aa)
f (Aa) = 2pq = 2(.4)(.6) = .48
Step 3: Find p
Step 6: Find f (AA)
f (AA) = f (p2) = .42 = .16

20. Using the Hardy-Weinberg equation to find f (AA), f (Aa) and f (aa):
Step 1: Find q2
Step 4: Find f (aa)
f (q2) = f (white) = = .36 3 8
f (aa) = f (q2) = .36
Step 2: Find q
Step 5: Find f (Aa)
f(q) = f (q2) = = .6
f (Aa) = 2pq = 2(.4)(.6) = .48
Step 3: Find p
Step 6: Find f (AA)
p + q = f (p) =
p = 1 – q f (p) = .4
f (AA) = f (p2) = .42 = .16

21. How to calculate phenotypic frequency in a population:
3 white
5 black
8 total mice
f(white) =
f(black) = 3 8 5 8

22. The Hardy-Weinberg model states that the genetic variation in a population will remain constant from one generation to the next in the absence of disturbing factors.

23. A population (or an allele) is not evolving if it is in Hardy-Weinberg equilibrium.

24. Conditions for an allele to be in Hardy-Weinberg equilibrium:
These conditions are impossible in nature!

25. 1. You have sampled a population in which you know that the percentage of the homozygous recessive genotype (aa) is 36%. Using that 36%, calculate the following:   A. The frequency of the "aa" genotype=.36 B. The frequency of the "a" allele=.6 C. The frequency of the "A" allele=.4 D. The frequencies of the genotypes "AA" and "Aa."  AA= Aa=2pq=.48 E. The frequencies of the two possible phenotypes if "A" is completely dominant over "a.“ AA+Aa= =.64

26. 2. Sickle-cell anemia is an interesting genetic disease
2. Sickle-cell anemia is an interesting genetic disease. Normal homozygous individials (SS) have normal blood cells that are easily infected with the malarial parasite. Thus, many of these individuals become very ill from the parasite and many die. Individuals homozygous for the sickle-cell trait (ss) have red blood cells that readily collapse when deoxygenated. Although malaria cannot grow in these red blood cells, individuals often die because of the genetic defect. However, individuals with the heterozygous condition (Ss) have some sickling of red blood cells, but generally not enough to cause mortality. In addition, malaria cannot survive well within these "partially defective" red blood cells. Thus, heterozygotes tend to survive better than either of the homozygous conditions. If 9% of an African population is born with a severe form of sickle-cell anemia (ss), what percentage of the population will be more resistant to malaria because they are heterozygous (Ss) for the sickle-cell gene?

27. 3. Within a population of butterflies, the color brown (B) is dominant over the color white (b). And, 40% of all butterflies are white. Given this simple information, calculate the following:  A. The percentage of butterflies in the population that are heterozygous.  B. The frequency of homozygous dominant individuals.

28. 4. A population cats have 396 white bodies and 557 black
4. A population cats have 396 white bodies and 557 black. Assume that white is totally recessive. Please calculate the following:  A. The allele frequencies of each allele.  B. The expected genotype frequencies.  C. The number of heterozygous individuals that you would predict to be in this population.  D. The expected phenotype frequencies.  E. In the next generation, 1,245 mice are produced. Assuming that all of the Hardy-Weinberg conditions are met, how many of these would you expect to be white and how many black?

29. 5. A very large population of randomly-mating laboratory mice contains 35% white mice. White coloring is caused by the double recessive genotype, "aa". Calculate allelic and genotypic frequencies for this population

30. 6. After graduation, you and 19 of your closest friends (lets say 10 males and 10 females) charter a plane to go on a round-the-world tour. Unfortunately, you all crash land (safely) on a deserted island. No one finds you and you start a new population totally isolated from the rest of the world. Two of your friends carry (i.e. are heterozygous for) the recessive cystic fibrosis allele (c). Assuming that the frequency of this allele does not change as the population grows, what will be the incidence of cystic fibrosis on your island?

31. 7. Cystic fibrosis is a recessive condition that affects about 1 in 2,500 babies in the Caucasian population of the United States. Please calculate the following.  A. The frequency of the recessive allele in the population.  B. The frequency of the dominant allele in the population.  C. The percentage of heterozygous individuals (carriers) in the population

32. Case 4: Genetic Drift
Small populations have a much greater potential for genetic drift
You will form 3 groups of 10.
Make a hypothesis

33. Case 4: Genetic Drift
Small populations have a much greater potential for genetic drift
You will form 3 groups of 10.
Make a hypothesis
Do same as ideal population in your small groups

34. Hardy-Weinberg Rule
Establishes allele frequencies at genetic equilibrium (no evolution), under these conditions:
1) No mutations are occurring
2) The population is very, very large
3) The population is isolated from other populations of the same species
4) All members survive, mate, and reproduce (no selection)
5) Mating is random

35. 5 Agents of evolutionary change
Gene Flow
Non-random mating
Genetic Drift
Selection
Mutation 35

38. Gizmo

39.  How could mutations affect the fitness of an organism?
Discussion questions ( 15 – 30 minutes)
As students are working or just after they are done, discuss the following questions:
 Do you think the fittest individuals always survive and reproduce? Why might some of the fittest individuals not survive?
 How do you think changing the mutation rate would change how quickly a population evolved? [If time allows, have students use the Gizmo to test their predictions.]
 How could mutations affect the fitness of an organism?
 Do populations evolve on purpose?

40. Problem 1
In a certain population of 1000 fruit flies, 640 have red eyes while the remainder have sepia eyes. The sepia eye trait is recessive to red eyes. How many individuals would you expect to be homozygous for red eye color?
Hint: The first step is always to calculate q2! Start by determining the number of fruit flies that are homozygous recessive. If you need help doing the calculation, look back at the Hardy-Weinberg equation.

41. Dispatch—Pick up Oct calendar and review guide. Solve the problem below

42. Problem 2
The Hardy-Weinberg equation is useful for predicting the percent of a human population that may be heterozygous carriers of recessive alleles for certain genetic diseases. Phenylketonuria (PKU) is a human metabolic disorder that results in mental retardation if it is untreated in infancy. In the United States, one out of approximately 10,000 babies is born with the disorder.
Approximately what percent of the population are heterozygous carriers of the recessive PKU allele?

43. Natural selection NOT in Hardy-Weinberg
Fitness: contribution an individual makes to the gene pool of the next generation
3 types:
A. Directional
B. Diversifying
C. Stabilizing

45. Effects of Selection Changes in the average trait of a population
DIRECTIONAL SELECTION
STABILIZING SELECTION
DISRUPTIVE SELECTION
giraffe neck
horse size
human birth weight
rock pocket mice 45