1. Evolution & Microevolution Tutorial
Introduction
Microevolution
Hardy Weinberg Equilibrium
Practice!

2. In this tutorial, you will learn:
The difference between macroevolution & microevolution.
How Hardy-Weinberg equilibrium works as well as factors that can upset this equilibrium.
How to use the equation, p2 + 2pq + q2 = 1, to calculate allele frequencies in a population.
Credits:
Figures and images by N. Wheat unless otherwise noted.
Lesser ball python image used with permission from Tim Bailey, Bailey & Bailey Reptiles.
Funded by Title V-STEM grant P031S

3. Introduction
Evolution – includes all of the changes in the characteristics and diversity of life that occur throughout time.
Evolution can occur on both large and small scales.

4. Macroevolution – Evolution on a Large Scale
Macroevolution – evolutionary change on a grand scale.
Origin of novel designs
Evolutionary trends
Adaptive radiation

5. Microevolution – Evolution on a Small Scale
Microevolution - a change in the genetic composition of a population over time.
A change in the frequency of certain alleles in a population over several generations.

6. Polymorphism
Polymorphism occurs when there are different allelic forms of a gene in a population.
Mojave (left) and Lesser (middle) are different alleles of the same gene. Wild type ball python is shown on the right.
Photo courtesy of Bailey & Bailey Reptiles

7. Gene Pool
All of the alleles of all of the genes possessed by all of the members of the population are contained in the gene pool of the population.
We can measure the relative frequency of a particular allele in a population.
Allelic frequency

8. Population Genetics
Population Genetics – the study of how populations change over time.
Dependent on both Darwin’s theory of natural selection and Mendel’s laws of inheritance.
All heritable traits have a genetic basis, some are controlled by multiple genes – not as simple as in Mendel’s studies.

9. Genetic Equilibrium
According to Hardy-Weinberg equilibrium, the hereditary process alone does not produce evolutionary change.
Allelic frequency will remain constant generation to generation unless disturbed by mutation, natural selection, migration, nonrandom mating, or genetic drift.
These are sources of microevolutionary change.

10. Frequency of Alleles
Each allele has a frequency (proportion) in the population.
Example population of 500 wildflowers.
CRCR = red; CRCW = pink; CWCW = white
250 red, 100 pink, 200 white
Frequency of CR =
(250 x 2) / 1000 = 600/1000 =.6 = 60%

11. Frequency of Alleles
p is the frequency of the most common allele (CR in this case).
p = 0.6 or 60%
q is the frequency of the less common allele (CW in this case).
p + q = 1
q = 1- p = 1 – 0.6 = 0.4 or 40%

12. Hardy-Weinberg Theorem
Populations that are not evolving are said to be in Hardy-Weinberg equilibrium.

13. Hardy-Weinberg Theorem
As long as Mendel’s laws are at work, the frequency of alleles will remain unchanged.
Review Punnett squares in the genetics tutorial.

14. Hardy-Weinberg Theorem
The Hardy-Weinberg theorem assumes random mating.
Generation after generation allele frequencies are the same.

15. Hardy-Weinberg Theorem
Conditions required for Hardy-Weinberg equilibrium to hold true:
Very large population
No gene flow into or out of the population
No mutations
Random mating
No natural selection

16. Hardy-Weinberg Theorem
Departure from these conditions results in a change in allele frequencies in the population.
Evolution has occurred!

17. Practice with Hardy Weinberg
Frequency – the proportion of individuals in a category in relation to the total number of individuals.
100 cats, 75 black, 25 white – frequency of black = 75/100 = 0.75, white =0.25.
Two alleles: p is common, q is less common.
p+q = 1

18. The frequency of black cats is:
Question 1
The frequency of black cats is:
0.75 75
0.25 25
100

19. Question 1
Sorry!
That is incorrect.
Try again!

20. Question 1
Congratulations!
You are correct!

21. Question 2
What would the frequency of black cats be if the population size was 80 instead of 100 (still 75 black)?
0.75 75
0.94 (75/80) 1

22. Question 2
Sorry!
That is incorrect.
Try again!

23. Question 2
Congratulations!
You are correct!

24. Hardy-Weinberg Theorem
At a locus with two alleles, the three genotypes will appear in the following proportions:
(p + q) x (p + q) = p2 + 2pq + q2 = 1

25. Practice with Hardy Weinberg
(p + q)2 = p pq + q2
Individuals homozygous for allele B
Individuals heterozygous for alleles B & b
Individuals homozygous for allele b

26. Practice with Hardy Weinberg
We will use a population of 100 cats as a practice example.
84 of the 100 cats are black.
16 are white.

27. Practice with Hardy Weinberg
We can use the equation and our color observations to calculate allele frequencies in our population of 100 cats.
p2 + 2pq + q2 = 1
100 = population size

28. Practice with Hardy Weinberg
84 of our 100 cats are black.
Black is the dominant phenotype.
Cats with the genotype Bb or BB will be black.
The frequency of black cats is 84/100, but we can’t yet say anything about the B allele.
See the genetics tutorial to review these terms.

29. Practice with Hardy Weinberg
16 of our 100 cats are white.
White is recessive (bb) and is represented by q2 in our equation: p2 + 2pq + q2 = 1
So, q2 = 16/100 = 0.16
q = square root of 0.16 = 0.40.

30. Practice with Hardy Weinberg
q = square root of 0.16 = 0.40.
Since p + q = 1; p = 1 – q = 0.60.
p2 = 0.36
p2 represents the proportion of individuals in the population with the homozygous dominant phenotype (BB).
Remember population size = 100

31. Question 3
So, the number of cats in our population that have the BB genotype would be:
0.36 cats
0.36 x 100 = 36 cats
0.16 x 100 =16 cats
84 cats

32. Question 3
Sorry!
That is incorrect.
Try again!

33. Question 3
Congratulations!
You are correct!

34. Practice with Hardy Weinberg
Now we know how many of our cats have the BB genotype and the bb genotype.
We can find the number of Bb cats using our equation: p2 + 2pq + q2 = 1.
2pq represents the proportion of cats with Bb.
2 x 0.6(p) x 0.4(q) = 0.48
0.48 x 100 = 48 cats with Bb genotype.

35. Question 4
Let’s try another! In our population of 100 cats, 75 are black & 25 are white. Where do we start?
75 black cats = p2.
75/100 = 0.75 black cats = p2.
25 white cats = q2.
25/100 = 0.25 white cats = q2.
Need more information.

36. Question 4
Sorry!
That is incorrect.
Try again!

37. Question 4
Congratulations!
You are correct!

38. Question 5
If q2 = 0.25, q=
0.05 5
0.5 50

39. Question 5
Sorry!
That is incorrect.
Try again!

40. Question 5
Congratulations!
You are correct!

41. Question 6
If q=0.5, p=
0.5 5
0.6
0.1

42. Question 6
Sorry!
That is incorrect.
Try again!

43. Question 6
Congratulations!
You are correct!

44. So, if p=0.5, and p2=0.25, how many of our cats have the BB genotype?
Question 7
So, if p=0.5, and p2=0.25, how many of our cats have the BB genotype?
0.25 25 50 75

45. Question 7
Sorry!
That is incorrect.
Try again!

46. Question 7
Congratulations!
You are correct!

47. Now, how many of the cats are heterozygous (Bb)?
Question 8
Now, how many of the cats are heterozygous (Bb)? 48
100 .5 50

48. Question 8
Sorry!
That is incorrect.
Try again!

49. Question 8
Congratulations!
You are correct!

50. Question 9
If we measure allele frequency one year at p=0.8 & q=0.2 and then go back 5 generations later to find p=0.5 & q=0.5, what has happened?
The population has remained in Hardy-Weinberg equilibrium.
The population has doubled in size.
There has been a change in allele frequencies: evolution has occurred.
Nothing has changed.

51. Question 9
Sorry!
That is incorrect.
Try again!

52. Question 9
Congratulations!
You are correct!