# Exercises In Population Genetics

The following exercises are designed to lead you through elementary experiments with some of the evolutionary forces, singly and in combinations. The first part examines fundamental concepts; the other parts use a simulation of the Hardy-Weinberg equilibrium and show how it is affected by varying genotype survival rates, initial allele percentage, and populations size.

## Fundamentals

Questions 1-6 below are intended to help you test your understanding of the fundamentals of the Hardy Weinberg equilibrium and do not require that you make any computer runs.

### A. Initial Population

1. Calculate the number of each genotype in a Hardy-Weinberg equilibrium population of 2000 individuals with a + allele frequency of 0.3; write the number of each genotype in the spaces below:

No. +/+ = ________ No. +/- = ________ No. -/- = ________

2. Consider an initial population of 448 +/+ individuals, 1238 +/- individuals, and 855 -/- individuals.

a. What are the frequencies of the alleles?

Frequency of + = ________ Frequency of - = ________

b. Given the allele frequencies you calculated above, determine the numbers of each of the genotypes you would expect if the population were in Hardy-Weinberg equilibrium:

No. +/+ = ________ No. +/- = ________ No. -/- = ________

c. Is the population in Hardy-Weinberg equilibrium? __________

### B. Survival and Reproductive Rates

For questions 3-6, use the following data. The tables below show possible survival and reproductive rates for five different "runs" of the simulation. Survival rates are measured in terms of percent of each genotype surviving from birth (or hatching, germinating) to reproductive age. Reproductive rates are measured as the average number of young born per individual of each genotype.

 a. Genotype +/+ +/- -/- Phenotype 75% 75% 20%
 b. Genotype +/+ +/- -/- Phenotype 100% 30% 30%
 c. Genotype +/+ +/- -/- Phenotype 40% 40% 60%
 d. Genotype +/+ +/- -/- Phenotype 12% 18% 24%
 e. Genotype +/+ +/- -/- Phenotype 60% 75% 65%
f. none

3. In which of the tables is + dominant for survival rate? a. b. c. d. e. f.

4. In which of the tables is + recessive for survival rates? a. b. c. d. e. f.

5. In which of the tables are + and - heterotic (heterozygous advantage) for survival rate? a. b. c. d. e. f.

6. In which of the tables do the alleles show incomplete dominance for survival rates? a. b. c. d. e. f.

## Hardy-Weinberg Equilibrium

These next exercises will illustrate what is required of you and give you an introduction to the whole process. In particular, note the way the parameter values are set up, and how to examine the graphs of results and the types of questions asked. You may wish to make several runs with each set of parameters. Note that there is to be no gene flow, nor will you need to change parameters during a run. If you are uncertain about allele and genotype frequencies and how to calculate them, read Chapter 24, pages 731-734.

### C. How long does it take to establish Hardy-Weinberg equilibrium starting with a population that is not in equilibrium?

A population in obvious disequilibrium would be one consisting entirely of heterozygotes. There are other ways to set up such an out-of-equilibrium population, can you describe another one?

On the basis of what you know, it would be reasonable to predict that the population would reach Hardy Weinberg equilibrium in one generation. More specifically: the allele and genotype frequencies would remain stable from generation to generation, and within one generation the genotype frequencies would approximate p2 for +/+, 2pq for +/-, and q2 for -/-. Can you think of a situation where the population is in disequilibrium, but does not reach the Hardy Weinberg equilibrium after one generation of random mating?

### D. Neutral Genetic Drift.

For the following exercises we will use a population genetics simulator at the University of Chicago. At their web page you determine the starting parameters for the simulation and a computer program simulate what would happen in a real population from one generation to the next. The parameters that you can control are the population size (Population), the initial allele frequencies (Initial + Frequency) [the frequency of the - allele is whatever it would take to add up to 100], The percent survival for each of the genotypes (+/+ Survival Percentage, etc.) and the number of generations (Generations) that you want the simulator to run. When all of the parameters are set you click in the Simulate box and the computer runs the simulation and returns a graph of the + allele frequency after each generation. Go to the University of Chicago Population Genetics Simulator (http://http.bsd.uchicago.edu/hgd-sad/HWSimulator/sim.cgi ) now and run the default simulation (pop = 100, generations = 100, all survivals =100, + = 50%). What was the final allele frequency? (read it off of the graph)

Go back to the simulator and run the same simulation again. Did you get the same result?

Go back to the simulator and change the number of Runs to 5. Run the simulation and look at the five graphs that are produced. Are they very different or are they all the same?

Why do you think you got this result?

Go back to the simulator, change the population size to 1000 and run the five simulations again. Is there a difference between this result and what you found with the smaller population?

Explain this result.

### E. Natural Selection

As natural selection is the evolutionary force that produces adaptation, let's look at the effect of selection on the allele frequencies.

#### What effect does increasing the strength of selection have on the evolution of an advantageous, dominant allele?

Prediction: Do you expect that evolution (that is, change in allele and genotype frequencies) proceeds more rapidly when the selection is stronger (differences in survival between the genotypes are larger)?

#### Weak selection for a dominant trait:

Number of Generations: 200; Population: 1000; Initial + Frequency: 1%;
Survival of +/+: 100, Survival of +/-: 100, Survival of -/-: 80; Runs: 1

How many generations did it take for the + allele frequency to reach 50%? 90%? 100%?

Describe the pattern of change of the + allele frequency.

#### Strong selection for a dominant trait:

Number of Generations: 200; Population: 1000; Initial + Frequency: 1%;
Survival of +/+: 100, Survival of +/-: 100, Survival of -/-: 20; Runs: 1

How many generations did it take for the + allele frequency to reach 50%? 90%? 100%?

Describe the pattern of change of the + allele frequency.

Try again with a survival of -/- of 0%. This would be the case for a recessive lethal allele. Why do you think it takes so long to get rid of the deleterious recessive allele, even when the selection against the allele is as strong as possible?

### What effect does dominance have on the evolution of an advantageous allele?

Prediction: Do you expect that evolution (that is, change in allele and genotype frequencies) proceeds more rapidly when the selection is for a dominant trait or for a recessive trait? Why?

#### Strong selection for a recessive trait:

Number of Generations: 200; Population: 1000; Initial + Frequency: 1%;
Survival of +/+: 100, Survival of +/-: 20, Survival of -/-: 20; Runs: 1

How many generations did it take for the + allele frequency to reach 50%? 90%? 100%?

Describe the pattern of change of the + allele frequency.

Compare this result to the one you got with the strong selection for a dominant trait. Was your prediction about the effect of dominance on the rate of evolution correct? Why or why not?

### What effect does population size have on the evolution of an advantageous allele?

#### Strong selection for a recessive trait in a small population:

Number of Generations: 200; Population: 100; Initial + Frequency: 1%;
Survival of +/+: 100, Survival of +/-: 20, Survival of -/-: 20; Runs: 5

Are the results of the different runs similar or very different?

What do you think is going on here? Would the effect be the same if the trait was dominant? (Try it and see).

### What happens if there is heterozygous advantage (heterozygotes are selected over either of the homozygotes)?

#### Strong selection for heterozygotes:

Number of Generations: 100; Population: 1000; Initial + Frequency: 1%;
Survival of +/+: 60, Survival of +/-: 100, Survival of -/-: 20; Runs: 1

Describe the pattern of change of the + allele frequency.

What was the final value for the frequency of the + allele?

If you change the starting allele frequency do you get a different result for the ending allele frequency (try some other values besides 1%)? Why or why not?

If you change the survival values (always leaving the +/- with the highest value), does that cause a change in the final allele frequency?

Can you figure out what the final allele frequency will be before you run the simulation?

If so, how?