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Fishy Frequencies

(or How Selection Affects the Hardy-Weinberg Equilibrium)



Introduction:

Understanding natural selection can be confusing and difficult. People often think that animals consciously adapt to their environments -ó that the peppered moth can change its color, the giraffe can permanently stretch its neck, the polar bear can turn itself white - all so that they can better survive in their environments.

In this lab you will use fish crackers to help further your understanding of natural selection and the role of genetics and gene frequencies in evolution.

Background: Facts about the 'Fish'

  1. These little fish are the natural prey of the terrible fish-eating sharks - YOU!

  2. Fish come with two phenotypes ó gold and brown:
    1. gold: this is a recessive trait (f); these fish taste yummy and are easy to catch.
    2. brown: this is a dominant trait (F); these fish taste salty, are sneaky and hard to catch.

  3. You, the terrible fish-eating sharks, much prefer to eat the yummy gold fish; you eat ONLY gold fish unless none are available in which case you resort to eating brown fish in order to stay alive.

  4. New fish are born every 'year'; the birth rate equals the death rate. You simulate births by reaching into the container of 'spare fish' and selecting randomly.

  5. Since the gold trait is recessive, the gold fish are homozygous recessive (ff). Because the brown trait is dominant, the brown fish are either homozygous or heterozygous dominant (FF or Ff).


Hardy-Weinberg:

G. H. Hardy, an English mathematician, and W.R. Weinberg, a German physician, independently worked out the effects of random mating in successive generations on the frequencies of alleles in a population. This is important for biologists because it is the basis of hypothetical stability from which real change can be measured.

For fish crackers, you assume that in the total population, you have the following genotypes, FF, Ff, and ff. You also assume that mating is random so that ff could mate with ff, Ff, or FF; or Ff could mate with ff, Ff, or FF, etc. In addition, you assume that for the gold and brown traits there are only two alleles in the population - F and f. If you counted all the alleles for these traits, the fraction of 'f' alleles plus the fraction of 'F' alleles would add up to 1.

The Hardy-Weinberg equation states that: p2 + 2pq + q2 = 1

This means that the fraction of pp (or FF) individuals plus the fraction of pq (or Ff) individuals plus the fraction of qq (ff) individuals equals 1. The pq is multiplied by 2 because there are two ways to get that combination. You can get F from the male and f from the female OR f from the male and F from female.

If you know that you have 16% recessive fish (ff), then your qq or q2 value is .16 and q = the square root of .16 or .4; thus the frequency of your f allele is .4 and since the sum of the f and F alleles must be 1, the frequency of your F allele must be .6 Using Hardy Weinberg, you can assume that in your population you have .36 FF (.6 x .6) and .48 Ff (2 x .4 x .6) as well as the original .16 ff that you counted.

Procedure:

  1. Get a random population of 10 fish from the 'ocean.'

  2. Count gold and brown fish and record in your chart; you can calculate frequencies later.

  3. Eat 3 gold fish; if you do not have 3 gold fish, fill in the missing number by eating brown fish.

  4. Add 3 fish from the 'ocean.' (One fish for each one that died.) Be random. Do NOT use artificial selection.

  5. Record the number of gold and brown fish.

  6. Again eat 3 fish, all gold if possible.

  7. Add 3 randomly selected fish, one for each death.

  8. Count and record.

  9. Repeat steps 6, 7, and 8 two more times.

  10. Fill in the class results on your chart.

  11. Fill in your data chart and calculation, prepare your graph, and answer the questions.


CHART: (Partners)

generation
gold
brown
q2
q
p
p2
2pq

1

2

3

4

5



CHART: Class

generation
gold
brown
q2
q
p
p2
2pq

1

2

3

4

5

Analysis:

  1. Prepare a graph of your data and the class results. On the 'x' axis put generations 1-5 and on the 'y' axis put frequency (0-1). Plot both the q and p for your data and for the class data. Use one color for your data and another color for class data. What generalizations would you make about your results? How do they compare to the class results?

  2. According to Hardy-Weinberg, what conditions would have to exist for the gene frequencies to stay the same over time?

  3. Why is it important to collect class data?

  4. Explain which phenotype is NOT favorable to the fish and why?

  5. What happens to the genotypic frequencies from generation 1 to generation 5?

  6. What process is occurring when there is a change in genotypic frequencies over a long period of time?

  7. What would happen if it were more advantageous to be heterozygous (Ff)? Would there still be homozygous fish? Explain.

  8. What happens to the recessive genes over successive generations and why?

  9. Why doesn't the recessive gene disappear from the population?

  10. Explain what would happen if selective pressure changed and the recessive gene was selected for.


For Further Investigation:

Design an experiment to show how one of the following affects allele frequencies over several generations:

  1. migration
  2. isolation
  3. no selection
  4. no random mating
  5. very small population
  6. mutations



Lab: How to Find Gene Frequencies in a Wild Population

Hardy-Weinberg Equilibrium Introduction

Woodrow Wilson Index

Activities Exchange Index

 
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