Download Simulation of Natural Selection Using Chi Square Test

Simulation of Natural Selection Using Chi Square Test
Modified from Phyllis Nicholson, Palo Alto High School
Introduction:
Evolution is a process that results in changes in genetic make of POPULATIONS over time, and
these changes can be observed in the changing phenotypes. Natural Selection is the term
designated by Charles Darwin in Origin of Species (1859) as the most important cause of
evolutionary changes. Individuals ability to reproduce depends on its ability to survive; “Survival
of the Fittest.” If all the phenotypes or gene variations were equally capable of surviving and
reproducing then there would never be a change or shift in the population. This experiment
models natural selection on three populations of beans as prey.
Purpose:
This experiment will study three different bean phenotypes in two different habitats and
determine if any type of natural selection occurs in favor of one of the phenotypes through three
generations of predation.
Part 1 Procedure: READ ALL DIRECTIONS BEFORE STARTING
1. Work in groups of two or three people. Count 10 each of Lima, pinto and red kidney beans.
These represent each of the three phenotypes, which we assume are all equal numbers
initially.
2. Choose two habitats and perform the procedure the same way in each one. Choose two from
the lists. If you work outside: sidewalk, asphalt, sand, grass. If you work inside on the lab
tables: use bare lab top, different colors of carpeting. Label your data table with the type you
selected in Habitat #1 and #2. A sample data table is provided for the first trial of Habitat #1,
but you will need to construct a table three times as long to complete the data collection, and
another one just like it for Habitat #2 as well as other data tables as needed for Part 2.
3. Scatter the 30 beans randomly over an area of about one square meter. Do not dump into a
single pile!
4. One person will be the designated “predator” and will “eat” (pick up) EXACTLY 20 beans
total. Try to think like a predator, picking up the first ones you see as quickly as you can.
Put the 20 beans in the plastic bag/cup provided, and leave the rest in the habitat. They
survived, so they will be able to reproduce!!
5. Count the number of beans collected (20) and record the specific numbers of each kid of bean
on line B.
6. Subtract the number of each kind eaten (line B), from the number you started with (line A), to
obtain the number of survivors (line C).
7. Assume that each survivor has two offspring. Record those values on line D. These are the
numbers of each bean that need to be scattered with the survivors to bring the population
back up to exactly 30. Count out and scatter the required number of beans into the same area
as your P1 (First Parent Generation) survivors.
8. Now complete line A for P2 by adding up lines C and D. These are your second generation
populations.
9. Repeat steps 4-7 two more times to complete the table for Habitat #1. Remember the
offspring values tell you how many beans of each type you need to scatter into the predator
foraging area.
10. Pick up all the beans when you are finished and repeat the entire procedure in Habitat #2. Fill
out your data table.
11. Analyze your results using the Chi Square formula outlined below, write a conclusion and
answer the discussion questions.
Fill in habitats you chose below in the blanks.
Be sure to total across to check your math occasionally.
– P1 generation HABITAT #1____________________________________
Lima Beans
Pinto Beans
Kidney Beans
A (P1 initial)30 total 10
10
10
B (eaten) 20 total
C (survivors) A-B
D (reproduced) 2C
(P2 initial) C+D
– P2 generation
Lima Beans
Pinto Beans
Kidney Beans
A (P2 initial)30 total
B (eaten) 20 total
C (survivors) A-B
D (reproduced) 2C
(P3 initial) C+D
– P3 generation
Lima Beans
Pinto Beans
Kidney Beans
A (P3 initial)30 total
B (eaten) 20 total
C (survivors) A-B
D (reproduced) 2C
(final result) C+D
– P1 generation HABITAT #2_____________________________________
Lima Beans
Pinto Beans
Kidney Beans
A (P1 initial)30 total 10
10
10
B (eaten) 20 total
C (survivors) A-B
D (reproduced) 2C
(P2 initial) C+D
– P2 generation
Lima Beans
Pinto Beans
Kidney Beans
A (P2 initial)30 total
B (eaten) 20 total
C (survivors) A-B
D (reproduced) 2C
(P3 initial) C+D
– P3 generation
Lima Beans
Pinto Beans
Kidney Beans
A (P3 initial)30 total
B (eaten) 20 total
C (survivors) A-B
D (reproduced) 2C
(final result) C+D
ANALYSIS OF RESULTS OF PART 1 USING CHI SQUARE
How do we determine if the frequencies of each type of bean after three generations are
significantly different from the initial ones? In other words, how do we know if natural selection
occurred? Using the Chi Square Statistic test (X 2 ) will allow us to determine this.
Chi Square X 2 =  ( o – e ) 2
E
Where o = observed count in a category
E = expected count in that category
 = means to sum for each category
When you calculate the Chi square value, locate it on the table below. The Degrees of
Freedom is always one less than the number of categories. Since we have 3 phenotypic categories
(bean types), there are 2 degrees of freedom.
If you find that the Chi square value at 2 degrees of freedom is less than .05, then there is
less than a 5% chance that the differences between our beginning and ending counts could be due
to random variation. This means that there is a 95% probability that the differences are NOT due
to chance alone or random factors, but that they are they are the result of our experiment.
Any statistic can only test two hypotheses:
H o (The Null Hypothesis): There is NO DIFFERENCE between the initial and
ending counts
H 1 (The Alternative Hypothesis): There is a STATISTICALLY SIGNIFICANT
DIFFERENCE between the initial and ending counts
Remember that in science we can never prove that any hypothesis is true since there is always
more data to gather, so we can only prove a hypothesis to be FALSE!
RESULTS/DISCUSSION QUESTIONS:
1. Show all calculations for your Chi Square data for Habitat #1and Habitat #2.
2. Write a null hypothesis and experimental/alternative hypothesis for this experiment
(remember that the experiment involves the role of predation and habitat in natural selection)
3. How do your results differ for the two habitats?
4. How can you explain your results in terms of the hypotheses?
CONCLUSION:
Write a 1-2 paragraph conclusion for Part 1.
Part 2 Procedure:
1. Design an experiment that will test the effectiveness of different kinds of predators on the
bean-prey you have just used in the above experiment. You may use different kinds of plastic
forks, spoons, knives, or other equipment such as tweezers, clothespins and such to represent
the different predators. Make this experiment similar to the one you just did by using the
same two habitats, but allow two or more “predators” in your group to “forage” for the prey
at the same time. I suggest you limit the foraging time to no more than 30 seconds. Record
the data you collect over three generations of beans (prey) making sure that each survivor
reproduces two offspring before each successive generation. You will also need to eliminate a
predator if he is not able to eat enough. (You decide how much). You might even want to
permit one of the predators to have a disability, such as breaking the tine of a fork, or
blindfolding.
2. Write out your experimental design in a formal lab report format, with all materials and
methods. (intro, materials, procedure, results, analysis/discussion, conclusion)
3. Interpret the results of your experimental design and write a conclusion. How does this
experiment differ from Part 1?
4. Extra credit will be given if you perform Chi Square analysis for each of the different tests
you perform with different predators.