Evolution is often defined as change over time, usually in response to a change in the environment. What this means is that the gene pool of a population shifts as time passes.

What is a gene pool? It is simply the collection of all the available alleles of all the genes on all the chromosomes in the population. What’s a population? It is the group of individuals that have geographic and behavioral mating access to each other. Geographic access is obvious; the dandelions in a yard in Virginia are not in the same gene pool as those in a yard in Pennsylvania, even if they are the same species. They could mate if they were brought together, but dandelion pollen doesn’t blow that far, so they are geographically isolated. Behavioral mating access can be less obvious; one example would be a stag that keeps all other males out of his territory and mates with all the does. The other stags are not allowed to mate, so their genes are not in the pool.

A great deal of the time for most species, evolution is not occurring. The gene pool stays the same, because the environmental situation is not changing. In the early days of population genetics, people argued over whether dominant alleles could “take over” a gene pool without any selection. Two mathematicians, Hardy and Weinberg, showed that this would not happen.

The basis of their argument is that the gene pool will not change, and the frequency of the various alleles will stay the same if the following conditions are met:

· The population is large.

· The population is freely interbreeding at random (this excludes the stag and the does).

· No individuals are taking their alleles out of the population (emigrating) or adding their alleles to the population (immigrating), so the percentages of the alleles can’t change because of migration.

· There are no mutations, so no new alleles appear.

· None of the alleles has a selective advantage (in other words, there aren’t any combinations of alleles that give some individuals a better chance of surviving that anyone else).

Here is the mathematical basis of their argument:

Imagine a simple situation in which a gene has only two alleles, A and a, and A is dominant. Let the frequency of A, expressed as a decimal with a value less than one, be p, and let the frequency of a, expressed as a decimal with a value less than one, be q. Because there are only two alleles, every allele must be either A or a, so,

p + q = 1

By definition, pand qare also the frequencies of the alleles in the eggs and sperm produced by this species. These sperm and eggs can come together in four ways when random mating occurs.

1. The chance that a male p sperm will meet a female p egg is p x p, or p2. The children produced by this cross will be genetically AA and express the dominant allele; they will have the A phenotype.

2. The chance that a male p sperm will meet a female q egg is p x q, or pq. The children produced by this cross will be genetically Aa and express the dominant allele; they will also have the A phenotype.

3. The chance that a male q sperm will meet a female p egg is alsop x q, or pq. The children produced by this cross will also be genetically Aa and express the dominant allele; they will also have the A phenotype.

4. The chance that a male q sperm will meet a female q egg is q x q, or q2. The children produced by this cross will be genetically aa and express the recessive allele; they will have the a phenotype.

These four situations are the only possibilities, so

p2 + pq + pq + q2 = 1 (1.0 represents 100% of all possible events in a mating)

When we combine the middle two terms, we get

p2 + 2pq + q2 = 1

These two formulas,

p + q = 1

p2 + 2pq + q2 = 1

summarize what is known as the Hardy-Weinberg Law.

However, usually we don’t know the frequency of the alleles in a population; in most cases, we can’t even see the gametes! If we want to know what the frequencies of the alleles are, we have to use these two formulas to figure it out.

The most important things to remember are the two formulas above. In these formulas,

· p = the frequency of the dominant allele

· q = the frequency of the recessive allele

· p2 = the frequency of individuals in the population who are homozygous dominant

· 2pq = the frequency of individuals in the population who are heterozygous

· q2 = the frequency of individuals in the population who are homozygous recessive

Materials

· Three colours of beans (chili, pinto and navy are good, but any three contrasting objects will do – M&Ms, coins, beads, etc).

· Two bowls

· A pocket calculator (MS Windows has one too)

Procedure

Two alleles which control hair texture are incompletely dominant to each other, and the phenotypic expression of hair texture is a function of which alleles are present. The genotypes and phenotypes are:

Genotype

Phenotype

C1C1

curly

C1C2

wavy

C2C2

straight

This is where Hardy-Weinberg comes in. Recall:

p2 + 2pq + q2 = 1.0

Remember:

p2 = the frequency of the C1C1s

2pq = the frequency of the C1C2s

q2 = the frequency of the C2C2s

These percentages will remain stable through all subsequent rounds of mating of this population.

Please refer to the following table for calculation references. Also, please adjust the calculations for the rest of the tables.

Please submit this Lab Report Sheet in Webtycho in the Assignments folder.

Data Sheet – Sample table and calculations:

Student answers to questions

1. In the absence of selection, what happens to gene frequencies in a population?

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2. What have you learned about population genetics so far? i.e., what do these results tell you about how genes in a gene pool behave under tightly controlled (i.e., artificial/hypothetical) circumstances?

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You’ll use your three colours of beans (or any 3 objects of your choice), from this point on, to represent the individuals in your population. The red (chili) beans represent the homozygous dominants (C1C1 – curlies), the mottled (pinto) beans the heterozygotes (C1C2 – wavies), and the white (navy) beans the homozygous recessives (C2C2 – straights).

Pick the beans (objects) two at a time and record your results here. Use the example above (page 6) to help you in your calculations).

Experiment 1

In this first exercise, you are going to determine what happens when you allow your population of 80 to interbreed freely.

In a bowl, place the correct numbers of the three colours of beans to represent the population of 80 people. For 20 C1C1s, 40 C1C2‘s, and 20 C2C2’s, you would choose 20 red beans, 40 pinto beans, and 20 white beans (or any three different objects you chose). Mix them thoroughly and then, without peeking (i.e., at random), withdraw two beans (or two objects). Record the genotypes represented by the two beans.

Example: if you withdraw a white bean and a pinto bean the first time, then you will record one (1) C2C2 x C1C2; you have mated one pair.

Put your first two beans in the second bowl and continue to draw pairs of beans from the first bowl until you have withdrawn all 40 pairs. Your records will now show a series of 80 random matings from this population.

There are six possible combinations:

1. C1C1 x C1C1 (two chili beans),

2. C1C1 x C1C2 (one chili, one pinto),

3. C1C1 x C2C2 (one chili, one navy),

4. C1C2 x C1C2 (two pintos),

5. C1C2 x C2C2 (one pinto, one navy), and

6. C2C2 x C2C2 (two navies).

Record the total number for each of the six matings.

Data sheet (fill in the BLUE and YELLOW areas).

(see page 6 for detailed calculation help).

MATINGS

OFFSPRING = Matings x 4

C1S

C2S

C1C1

X

C1C1

C1C1

X

C1C2

C1C1

X

C2C2

C1C2

X

C1C2

C1C2

X

C2C2

C2C2

X

C2C2

total

P=

Frequency of C1 =

Q=

Frequency of C2 =

3. How do these compare with the parental generation?

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4. What principle have you demonstrated with this exercise?

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Experiment 2

Put your beans back in the bowl. This time, withdraw only 20 pairs(= 20 random matings), and record the results as you did in Task 1.

Next, calculate the offspring of this generation: again, assume 4 offspring per mating. Total the numbers of C1C1s, C1C2s and C2C2s. and then calculate the allele frequencies. Finally, determine the genotypic frequencies.

Data sheet (fill in the BLUE and YELLOW areas).

(see page 6 for detailed calculation help).

MATINGS

OFFSPRING = Matings x 4

C1S

C2S

C1C1

X

C1C1

C1C1

X

C1C2

C1C1

X

C2C2

C1C2

X

C1C2

C1C2

X

C2C2

C2C2

X

C2C2

total

P=

Frequency of C1 =

Q=

Frequency of C2 =

5. How do these last P and Q (frequencies) compare with the P (parental) generation (Experiment 1)?

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6. If you repeated this experiment (i.e., you selected another 20 pairs from the bowl) would you expect to get the same result? Why or why not?

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7. What principle have you illustrated this time?

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Experiment 3

Now you are going to assume that your population has been invaded by an ET which is a human predator. It particularly fancies people with curly hair – eats them preferentially – and when it moves on (looking for more of its favourite lunch), your population has been denuded of curlies (C1C1).

Set up your new population in the bowl, and go through the mating (bean picking/ withdrawal) procedure again, recording your results. Again, assume that each mating produces four offspring.

(see page 6 for detailed calculation help).

MATINGS

OFFSPRING = Matings x 4

C1S

C2S

C1C2

X

C1C2

C1C2

X

C2C2

C2C2

X

C2C2

total

P=

Frequency of C1 =

Q=

Frequency of C2 =

8. What is going on?

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9. How have the relative proportions of C1s and C2s changed?

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10. What principle have you demonstrated here?

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Experiment 4

Go back to your population in Experiment 3. This time, assume that through some further natural disaster which has discriminated against people with wavy hair, half the wavieshave also been lost. Allow this population to breed at random and determine the outcome of the next generation.

(see page 6 for detailed calculation help).

MATINGS

OFFSPRING = Matings x 4

C1S

C2S

C1C2

X

C1C2

C1C2

X

C2C2

C2C2

X

C2C2

total

P=

Frequency of C1 =

Q=

Frequency of C2 =

13. What is going on this time?

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14. What if this trend continues?

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SUMMARY

15. Summarize what you have learned from this lab about the principles of evolution.

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Define (one short sentence each):

1) Evolution

2) Microevolution

3) Macroevolution

4) Genetic Drift

5) Natural selection

What did you learn about or in each of the following?

a) The Hardy-Weinberg Equilibrium

b) Experiment 1

c) Experiment 2

d) Experiment 3

e) Experiment 4

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