Population Genetics and Evolution: Bear Frequencies /50
How Selection Affects Hardy-Weinberg Equilibrium
Introduction:
Understanding natural selection can be confusing and difficult. Animals CANNOT
consciously adapt to their environments –i.e. the peppered moth cannot decide to
change its color, the giraffe cannot permanently stretch its neck, the polar bear
cannot turn itself white - all so they can better survive in their environments. Some
other variable is at work – to trigger EVOLUTION.
Objective: Use bear crackers to help further your understanding of natural selection
and the role of genetics and gene frequencies in evolution. Examine genotype
frequencies as a result of selective predation to illustrate natural selection.
Background: Facts about the 'Bear'
1. These little bears are the natural prey of - YOU!
2. Bears come with two phenotypes BROWN and CREAM:
a. CREAM: recessive trait (b); taste yummy and are easy to catch.
b. BROWN: dominant trait (B); taste gamey, are sneaky and hard to catch.
3. You, the hunter, much prefer to eat the yummy cream bears; you eat ONLY
cream unless none are available in which case you resort to eating brown bears
in order to stay alive.
4. New bears are born every 'year'; the birth rate equals the death rate. You
simulate births by reaching into the container of 'spare bears', selecting
randomly.
5. Since the cream trait is recessive, the creams are homozygous recessive (bb).
Because the brown trait is dominant, the brown bears are either homozygous or
heterozygous dominant (BB or Bb).
Procedure:
1. Get a random population of 10 bears from the 'forest.' (bowl) – GENERATION 1
2. Count the # of cream and brown bears, record in your chart; you can calculate frequencies
later.
3. Eat 3 cream bears; if you do not have 3 cream bears, fill in the missing number by eating
brown bears.
4. At random, add 3 bears from the 'forest.' (One bear for each one that died.) Be random. Do
NOT use artificial selection.
5. Record the number of cream and brown bears. – GENERATION 2
6. Again eat 3 bears, all cream if possible.
7. Add 3 randomly selected bears, one for each death.
8. Count and record. –GENERATION 3
9. Repeat steps 6, 7, and 8 SEVEN more times.
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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.
The Hardy-Weinberg rule for a population in genetic equilibrium assumes:
1. No genetic mutation is occurring within the population.
2. The breeding population is large.
3. The population is isolated from other populations of the same species. No
differential migration occurs.
4. All members of the population survive and reproduce. There is no natural selection.
5. Mating is random within the population.
Therefore, for the bear crackers, assume
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No mutations are occurring in the bears phenotype colour
There is a large number of bears reproducing more baby bears (the bowl)
No other alleles affect the cream and brown characteristics (only B and b exist).
In the total population, all three genotypes, BB, Bb, and bb are present.
Mating is random so that bb could mate with bb, Bb, or BB; or Bb could mate
with bb, Bb, or BB, etc.
The Hardy-Weinberg
equation states that:
p2 + 2pq + q2 = 1
p+q=1
The fraction of pp (or BB) individuals plus the fraction
of pq (or Bb) individuals plus the fraction of qq (bb)
individuals equals 1. The pq is multiplied by 2 because
there are two ways to get that combination. You can
get B from the male and b from the female OR b from
the male and B from female
Population genotype frequency in Hardy-Weinberg equilibrium =
p2 (BB) = 0.36
2pq (Bb) = 0.48
q2 (bb) = 0.16
16% of the BEARS in equilibrium population express recessive
allele (bb). The q2 value is 0.16, and q equals the square root of
0.16 (0.4). Thus, the frequency of the b allele is 0.4. Since the
sum of the B and b alleles must be 1, the frequency of the B
allele must be 0.6. Using Hardy-Weinberg, you can assume that
in the population there are 0.36 BB (0.6 x 0.6), 0.48 Bb (2 x 0.4
x 0.6), and 0.16 bb.
Hints for calculating genotype frequencies
If the frequency changes significantly, natural selection is occurring allowing for
evolution to potentially occur. The Hardy-Weinberg rule is an important tool for
detecting changes in the genotype frequencies of a population.
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DATA: (10 marks)
Your Bears’ allele frequency :
generation
cream
brown
q2
q
p
p2
2pq
1
2
3
4
5
6
7
DO NOT CALCULATE
8
9
10
Class allele frequency
generation
cream
brown
q2
q
p
p2
2pq
1
2
3
4
5
10
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Analysis:
Answer either typed or neatly written – though discussion is permitted
THINK FOR YOURSELF!
1. (10) 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.
2. (3) What generalizations would you make about your bears’ results in relation
to selective pressure? How do they compare to the class results?
3. (2) Why is it important to collect class data?
4. (5) According to Hardy-Weinberg, what conditions would have to exist for the
gene frequencies to stay the same over time?
5. (4) Explain which phenotype is NOT favorable to the bear in his environment
and why? Relate to the animal behaviour and predator selection.
6. (6) Using the class data. What happens to the genotypic frequencies (i.e. BB,
Bb, bb) at generation 1; generation 3 and generation 5? (HINT: p2, 2pq, q2).
Show your calculations.
7. (3) What process is occurring when there is a change in genotypic frequencies
over a long period of time? What is the name of the pattern of natural selection
occurring? Show a diagram of the pattern.
8. (5) What would happen if it were more advantageous to be heterozygous (Ff)?
Would there still be homozygous bears? Make up a scenerio and explain.
9. (3) Explain why the recessive gene doesn't disappear from the population?
10. (5) Explain what would happen if selective pressure changed and the dominant
gene was selected for. Refer to phenotype frequency, genotype frequency,
pattern of natural selection, type evolution.
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Population Genetics and Evolution: Bear Frequencies
How Selection Affects Hardy-Weinberg Equilibrium
ANSWERS
1. Title: ______________________________________________________________________
Data Sheet Mark
______/10 Neat an complete
TOTAL= _____________/55
Answer Sheet Marks
1.
2.
3.
4.
5.
6.
7.
8.
9.
______/10Graph
______/3 Generalizations
______/2 Class Data
______/5 Hardy-Weinberg conditions
______/4 phenotype NOT favorable
______/7 generation genotypic frequencies
______/2 process is occurring/ name of pattern/diagram
______/5 favouring heterozygous (Ff)/scenerio
______/3 recessive gene doesn't disappear
10. ______/5 selective pressure changed to the dominant
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