This page walks you through the student pages "What does the model look
like?" and "What experiment can I do with the
model?"
The student questions are in red. The answers are provided on this page in blue.
Background
Photo courtesy
http://www.bioimages.org.uk/HTML/P168240.HTM
------------------------------------------------------------------------
The image above is a peppered moth. This is the common form of the moth.
Before the industrial revolution in England most if not all of the peppered
moths looked like this. Near Manchester England in 1848 the first documentation
of a dark peppered moth was reported. Were there
any dark peppered moths in England in the year 1847?
We don't know. If there were there weren't very
many. Scientists find peppered moths in the USA. In polluted areas like
Michigan the percentage of dark to light followed the same pattern found
in England. In non-polluted areas like Southern Appalachia there has been
a fairly constant background level of dark peppered moths of a few percent.
This leads some scientists to think that the dark peppered moths have always
been in the population waiting to breakout.
Mutation
In the 1920's Heslop Harrison thought that
pollution was causing mutations in the moths making them dark. Harrison
decided to test his idea by conducting experiments with moths. He claimed
that feeding polluted leaves to larvae darkened the moths. He didn't use
peppered moths. He used similar moths that like peppered moths appear as
light and dark colored moths. When the pupae (caterpillars) were fed leaves
coated with coal soot the wings of the adults were darker.
------------------------------------------------------------------------
Harrison concluded that the darker moths were
a result of pollution induced mutations in the moths, not natural selection.
------------------------------------------------------------------------
Other scientists tried to replicate Harrison's
experiments using peppered moths. They didn't get the same results. In
their experiments the moths didn't get darker. A few scientists have breed
peppered moths for their experiments. They cross light and dark moths.
The next generation fit the same pattern Mendel found with his peas. One
gene controls whether the moth is light or dark. The dark form "A" is dominant
and the light form "a" is recessive.
------------------------------------------------------------------------
Is it possible that both Harrison and the other
scientists honestly reported their experiments?
Yes.
------------------------------------------------------------------------
How can you explain the different results?
Harrison wasn't experimenting with peppered moths.
The different results may be because the different kinds of moths react
differently to the polluted food.
------------------------------------------------------------------------
A few gray peppered moths have been reported.
These rare gray moths are almost never seen in the industrial areas. Scientists
don't consider these gray moths relevant.
------------------------------------------------------------------------
How would you explain the gray moths?
Answers may vary. Scientists think that there
are other genes that can effect a peppered moth's coloration. One gene
controls the expression of melanic (dark) and typical (light) coloration.
Other genes may cause the rare gray moths.
------------------------------------------------------------------------
Do you agree that the gray moths aren't relevant?
Explain.
Answers may vary. Look for a well-reasoned answer.
------------------------------------------------------------------------
Scientists rejected Harrison's idea that pollution
caused frequent mutations turning the peppered moths dark. As scientist
you need to ask, "What part or part(s) of Harrison's idea were wrong?"
Scientists don't want to, "Throw out the baby with the bath water."
------------------------------------------------------------------------
Harrison's basic idea was that mutations not natural
selection caused the change in peppered moth frequency. A second part of
his idea was that eating polluted leaves causes the mutation. A third part
of the idea was that if one generation did something to acquire a characteristic
they would pass that characteristic on to their descendants. DNA hadn't
been discovered yet so the mechanism for mutations wasn't well understood.
------------------------------------------------------------------------
Which of part(s) of Harrison's idea were shown
to be wrong?
The change in color wasn't caused by eating polluted
leaves. So far we don't have any evidence for or against mutations. We
also don't have evidence regarding the parents passing the trait to their
offspring.
------------------------------------------------------------------------
Scientists wondered if the mutations were caused
by some other factor. Perhaps it was only a coincidence that the moths
changed color as the pollution increased. Back in the twentieth century
scientists couldn't do DNA analysis of the moths in the English countryside.
The DNA analysis that we can do today is limited because almost all of
the peppered moths are white again.
------------------------------------------------------------------------
You can use a computer model to simulate the change
in the population caused by this proposed mutation. You will be using a
Stella model. The model follows the 3 genotypes for the peppered moths:
AA, Aa, and aa. Each type of moth hatches from eggs, lives for a year and
then dies.
------------------------------------------------------------------------
The converter "death natural causes" holds the
death rate for the moths. When you run the model you will be able to adjust
this rate using a slider bar.
------------------------------------------------------------------------
The flows "death1", "death2" and "death3" subtract
moths from each of the stocks to simulate the moth's deaths by natural
causes. The number of moths subtracted = the number of moths in the stock
times the rate in "death natural causes."
------------------------------------------------------------------------
The algorithm for the moths that hatch is derived
from a mathematical expression developed by the researchers G.H. Hardy
and W. Weinberg . Hardy and Weinberg's mathematical expression describe
the equilibrium of the genotype frequencies, which occur under random sexual
mating. The mathematical expression assumes a large population size, no
mutation, no migration, and no natural selection. (p2 + 2pq + q2 = 1) where
p2 is the frequency of AA , 2pq is the frequency of Aa, and q2 is the frequency
of aa.
------------------------------------------------------------------------
So far the model, like the Hardy Weinberg expression,
assumes no mutation. Two flows are added to adjust the moth population
by mutation. Flow "mutation1" changes Aa moths to AA moths at the rate
set by converter "mutation rate." Flow "mutation2" changes aa moths to
Aa moths by the 2 times the "mutation rate." Each aa moth has two a alleles
that can mutate.
------------------------------------------------------------------------
Open the "mutation1" model. Click the up triangle
in the upper left corner to move to the interface page. You will see a
graph, a run button and one slider. Adjust the "mutation rate" slider to
the mutation that you think will cause the moths to change to 98% dark
in 50 years. Click the "Run" button and watch the moth population change.
Continue adjusting the "mutation rate" and running the model until you
have 98% after 50 years.
------------------------------------------------------------------------
What mutation rate simulated the observed change
in nature?
.038 - .043 or .040 +.003
------------------------------------------------------------------------
What percentage of the aa and Aa moths are mutating
each year?
4% of the Aa moths and 8% of the aa moths. The
aa moths have 2 chances to mutate.
------------------------------------------------------------------------
Scientists have found that mutations occur less
than .005% of the time. Consider the rate
at which mutations occur and the rate you have found necessary to replicate
the change from light to dark moths. What can you conclude about the idea
that mutations are responsible for the change in moth color?
We would need to multiply the maximum observed
rate of mutation .005 by 1,000 to get a rate of 4% or 8%. Put another way,
the observed rate of mutation is 1,000 times less likely than the rate
needed to cause the shift from white to dark. It isn't reasonable to conclude
that mutations are the cause of the shift from white to dark.
------------------------------------------------------------------------
In the 1950s England and the United States enacted
legislation to reduce air pollution. In the last 50 years the frequency
of dark and white peppered moths in both England and the U.S. have returned
to almost all white peppered moths. Could
the mutation explain this two-direction change?
No. Imagine one mutation that breaks the gene
and causes a deletion. This mutated gene with a missing piece results in
a dark moth. A second mutation mechanism is needed to reinsert the missing
piece back into the gene. Further the pressure that caused the original
gene to break at a weak point and lose a piece is still in place. The new
pressure to reinsert the missing piece is undone by the original mutation
mechanism. The mutation to fix the gene would have to occur at twice the
rate of the original mutation.
------------------------------------------------------------------------
In the 1950s B. Kettlewell did a series of experiments
to see if Tutt's idea of natural selection was reasonable. First Kettlewell
wanted to see and document how well peppered moths are camouflaged on polluted
and non-polluted trees. Kettlewell asked a nature photographer to help
him take pictures of peppered moths on different trees. Peppered moths
are so rare that scientists often only see one or two peppered moths per
year in their natural hiding places. The nature photographer took dark
and light colored peppered moths and placed them side-by-side on tree trunks
to get his photographs.
------------------------------------------------------------------------
Can you find both the dark and light peppered
moth in these photographs?
It is easy to find one moth in each picture.
The students need to look closer to find the second moth. The other moth
is below the obvious moth in each picture.
------------------------------------------------------------------------
Can you conclude that the peppered moths have
effective camouflage?
Answers may vary. Most scientists conclude that
to the human eye the moths are well camouflaged. There is some evidence
that some birds see some ultraviolet frequencies that people can't. This
may or may not have an impact of the bird's ability to see the birds.
------------------------------------------------------------------------
Some of the scientists of the time criticized
Tutt's idea of natural selection by bird predation. One criticism was that
no one had ever seen a bird eat a peppered moth. For that matter very few
peppered moths are seen in the wild. Scientists think that there are fewer
than 100 peppered moths per square kilometer. The best way to find peppered
moths is at night, using a light trap.
------------------------------------------------------------------------
Kettlewell wanted to see if birds would eat peppered
moths. He collected some moths and took them to an aviary. When he released
the moths in the aviary the birds flew up and ate the moths. This showed
that captive birds would eat peppered moths.
------------------------------------------------------------------------
Based on Kettelwell's first experiment would you
conclude that A) Wild birds will eat peppered moths. B) Wild birds won't
eat peppered moths. C) You don't have enough information to draw a conclusion.
C. You don't have enough information to draw
a conclusion. We know that caged birds will eat peppered moths that are
released and fly in the daylight. Wild peppered moths don't fly during
the day. Caged birds may be different than wild birds. Maybe they aren't
as picky about what live bugs they eat. This experiment establishes that
it is possible that wild birds may eat peppered moths but it doesn't prove
it.
------------------------------------------------------------------------
Some scientists weren't convinced. These scientists
thought that wild birds and captive birds might act differently. They didn't
know that wild birds would act differently. The scientists didn't have
evidence that wild and caged birds would act the same.
Staged
Kettlewell also wanted to find evidence that
wild birds ate peppered moths. He also wanted to show that wild birds would
eat more white moths on polluted trees. Kettlewell set up an experiment
to see if this was true.
------------------------------------------------------------------------
Kettlewell collected equal numbers of white and dark peppered moths. He went to a non-polluted forest and set up a blind to hide from the birds. He stuck these dead white and dark moths on trees beside his blind. He watched to see if the birds ate more white or dark moths. He repeated this experiment in a polluted forest. This is his data:
------------------------------------------------------------------------
In a non-polluted forest Kettlewell expected more
dark moths to be eaten. Does his data support
that prediction?
Yes. Almost 6 times more dark moths were eaten.
------------------------------------------------------------------------
In a polluted forest Kettlewell expected more
white moths to be eaten. Does his data support
that prediction?
Yes about 3 times more white moths were eaten.
------------------------------------------------------------------------
Kettlewell place the moths on tree trunks where
they were easy for him to observe. Some scientists criticized this choice
of location. Kettlewell didn't provide evidence that peppered moths spent
the day on tree trunks. The criticizing scientists didn't know where moths
hide. The scientists thought that moths might hide under branch or places
where their camouflage wasn't important.
------------------------------------------------------------------------
A scientist named, M. E. N. Majerus spent 40 years looking for and studying peppered moths. During his 40 years of searching the woods of England for peppered moths he found only 47 moths in the wild. That is a little over one each year. The following table shows where he found them.
------------------------------------------------------------------------
The most common resting place for a peppered moth
was the trunk/branch junction. This is on the trunk and a few inches under
a branch. What percentage of wild moths were
found resting on tree trunks?
68.1% or 68.2% If you add the moths found on
trunks you get 68.2%. If you subtract moths found in trees but not on the
trunk you get 68.1%.
------------------------------------------------------------------------
As a scientist do you feel that this data supports
Kettlewell's experiment of placing moths on tree trunks? Does the data
cause you to totally support the theory of natural selection as the cause
for the increase in dark moths? Does the data cause you to totally reject
the theory? Does the data provide a little more support for the theory?
Does the data provide a little more evidence against the theory?
Since more than
2/3 of the peppered moths were found on tree trunks, Kettlewell's placement
of moths on tree trunks is reasonable. This additional support for the
theory of natural selection but it doesn't prove it was the causal factor
in this case or any other case.
Recapture
Kettlewell wanted to see if wild birds would
preferentially eat live peppered moths depending on the amount of pollution
in the area. He knew that it was very hard to observe wild peppered moths
in the countryside. He also needed to work with a few hundred moths so
his results would be significant.
------------------------------------------------------------------------
He decided to catch moths with a light trap. He
put a paint mark on the underside of each moth's wing. Moths land on trees
and lie flat all day so birds wouldn't be able to see the paint mark. He
counted the number of light and dark moths that he had marked. At dawn
he released the moths in a polluted forest. The moths flew up into the
trees and waited for the next night.
------------------------------------------------------------------------
For the next few nights Kettlewell set up his light trap and recaptured the moths. He recorded the number of marked moths that he recaptured.
------------------------------------------------------------------------
As scientists we need to analyze this data. In
this polluted forest, which did Kettlewell recapture more, white or dark
moths?
Dark. 205 dark and 34 light.
------------------------------------------------------------------------
Was it a fair trial? Did Kettlewell release the
same number of dark and white moths?
No. Kettlewell released 3 times as many dark
moths as light moths.
------------------------------------------------------------------------
How can the percent recaptured be used to overcome
the unfairness of the experiment?
Percent means per 100. If we look at the percent
recaptured we are looking at the number that would have been recaptured
if he had released 100 of each. So for each 100 released 16 white and 34
dark moths were recaptured. Or about twice as many dark survived and were
recaptured.
------------------------------------------------------------------------
Kettlewell wanted to show that in a polluted forest
more white moths would be eaten. Are there
other explanations that could explain why more dark moths were recaptured?
Answers will vary. For all the students know
white and dark moths may not act the same. They may fly or hide differently.
Scientists looked into this. They put moths in a container with white and
black surfaces and shook them up. Then the scientists recorded which color
they landed on. They both landed randomly. Scientists haven't noticed any
differences in white and dark moths except their color.
------------------------------------------------------------------------
The next year he repeated the experiment but this time he released the moths in a forest that wasn't polluted.
Table Unpolluted forest
------------------------------------------------------------------------Was this a fair trial? Did Kettlewell start with
the same number of dark and white moths?
No, but their numbers were close to the same.
They are only off by about 4%
------------------------------------------------------------------------
Which kind of moth was more likely to be recaptured
in the non-polluted forest?
The white moths.
------------------------------------------------------------------------
In the polluted forest, how much more likely is
it that the dark moths will survive and be recaptured?
The dark moths are twice as likely to survive
and be recaptured in a polluted forest.
------------------------------------------------------------------------
In the non-polluted forest, how much more likely
is it that the white moths will survive and be recaptured?
In a non-polluted forest the white moths are
twice as likely to survive and be recaptured.
------------------------------------------------------------------------
When you compare the two experiments do you see
evidence that one kind of moth is better able to avoid recapture because
they are stronger, smarter, weaker, etc?
No.
------------------------------------------------------------------------
Kettlewell acknowledged that some of the moths
might have flown out of the area and weren't recaptured. He also realized
that some of the moths may have died of natural causes. Peppered moths
only live as moths for a few days. Some of the released moths may have
been 4 or 5 days old and died that day of old age.
------------------------------------------------------------------------
Kettlewell assumed that these other reasons for
not recapturing some of the moths would have affected both dark and white
moths the same. The same percent (5%, 25% or 50%) of both dark and white
moths would be lost. Kettlewell didn't know the percent lost but if he
used the percent recaptured that would make the experiment fair.
------------------------------------------------------------------------
Kettlewell analyzed the percent recaptured and
concluded that twice as many dark moths were recaptured in a polluted forest
so twice as many white moths were eaten by birds. In an unpolluted forest
he found the opposite results. Twice as many white moths were recaptured.
Kettlewell concluded that in an unpolluted forest the birds ate twice as
may dark moths as white moths.
------------------------------------------------------------------------
As scientists you need to analyze both Kettlewell's
experiment and his conclusions. You can check the accuracy of his conclusion
by building a spreadsheet. Set up the first 5 rows of your spreadsheet
by entering the text as seen in the image below.
------------------------------------------------------------------------
In cells A6 through A15 enter 0, 0.1, 0.2, 0.3...
0.9.
------------------------------------------------------------------------
In cell B6 you will calculate the rate at which
the moths were eaten if none were lost. B3/B2 gives you the rate that the
moths were recaptured. If none of the moths were lost every moth that wasn't
recaptured was eaten. The number of moths released minus the number recaptured
equals the number eaten. In rates that is 1-B3/B2. Put this in cell B6.
Remember to start the equation with "=" so the spreadsheet will know it
is a formula not text.
------------------------------------------------------------------------
In cell B7 you will calculate the rate at which
the moths were eaten if 10% were lost. Again it will be 1 minus the number
of moths released divided by the number eaten. Start with =1-B$3/. The
$ in front of the 3 tells Excel not to change the 3 if the cell is copied.
You will want Excel to do an absolute reference to B2 and B3 when you copy
the cell for all of the other emigration rates.
------------------------------------------------------------------------
B$3 is divided by the number of moths eaten. The
number eaten is the number released minus the number that were lost. The
number lost is the emigration rate times the number released or B$2-A7
* B$2. Notice that A7 doesn't have a $. That is because as you copy down,
you want to also use the rate as you go down.
------------------------------------------------------------------------
Copy cell B7 down to cell B15. This will give
you the predation rates for the white moths.
------------------------------------------------------------------------
Repeat these procedures for the dark moths using
the appropriate relative and absolute references.
------------------------------------------------------------------------
Column E calculates the ratio of white predation
rate divided by dark predation rate. For cell E6 that is =B6/D6. Again
these are relative references. Copy this down for all of the emigration
rates.
------------------------------------------------------------------------
Column F is the additional predation. Think about
the ratio of white predation to dark predation. For no emigration the ratio
or dark to dark is 1 and the ratio of white to dark is 1.26. The additional
predation on the white is the difference between 1 and 1.26 or 1.26-1.
In cell F6 enter =E6-1. again relative reference. Copy this down for all
emigration rates. Set the format to percent.
------------------------------------------------------------------------
Repeat these steps to set up the calculations
for the Non-Polluted forest. Depending on where you set up the cells you
will have to be sure to reference the correct cells.
------------------------------------------------------------------------
What does it mean when the predation rate is negative?
Could the emigration rate be 90%?
For the predation rate to be negative birds would
have to be making new moths. That can't happen. Emigration rates that result
in negative predation rates aren't reasonable. No, an emigration rate of
90% results in negative predation rates.
------------------------------------------------------------------------
Describe how much additional predation was there
on white moths in the polluted forest?
The white moths experienced additional predation
rates of between 26% and 288% as the emigration rate varied from 0% to
60%.
------------------------------------------------------------------------
Describe how much additional predation was there
on dark moths in the non-polluted forest?
The dark moths experienced additional predation
rates of between 7% and 82% as the emigration rate varied from 0% to 80%.
------------------------------------------------------------------------
Kettlewell said that there was twice as much predation
on the white moths in a polluted forest and twice as much predation on
dark moths in a non-polluted forest. Was he: 100% right, 100% wrong, part
right and part wrong?
We don't know exactly what the ratio of predation
rates was. We know a range and can say that the predation rate was higher
for white moths in polluted than dark, and that the opposite was true in
non-polluted forests. It would be tempting to say that the white moths
had about 3 times as much predation as the dark moths in forests where
they didn't match the pollution level. Unfortunately we don't know if the
emigration rate was the same it the two forests, so we can't compare the
predation rates. Kettlewell was part right.
------------------------------------------------------------------------
If he was part right and part wrong, explain where
you agree and disagree with his conclusion.
Kettlewell was correct that there was more predation
on the white moths in a polluted forest and more predation on dark moths
in a non-polluted forest. We can't say what the exact increase in predation
was only a range.
------------------------------------------------------------------------
Kettlewell's overall position was that natural
selection by bird predation on the white colored moths caused the change
in moth ratios from 98% white to 98% dark. Kettlewell based this on his
experiments and his conclusion that the wrong colored moths were eaten
at twice the rate of the camouflaged moths. If
Kettelwell was wrong and it wasn't twice as much predation, should you
conclude that his overall position was wrong?
Our analysis that more predation on the wrong
colored moths happened. This supports Kettlewell's position on natural
selection. We don't have evidence that natural selection wasn't the cause
of the change in moth ratios. The question is if there is enough evidence
to support Kettlewell's position. Each scientist needs to evaluate that
for himself or herself.
Modeling
In the 1950s England and the United States
enacted legislation to reduce air pollution. As the pollution in the countryside
has gone down the ratio of dark to light peppered moths has returned to
pre-industrial levels.
------------------------------------------------------------------------
Scientists did the best experiments they could
think of at the time. No experiment is ever perfect. Scientists always
look back at experiments and think, "If I had done this part a little differently,
the results would have be more convincing or I would have learned more."
When scientists have time they try the experiment again with the changes
to improve their understanding.
------------------------------------------------------------------------
Scientists are running out of time and opportunity
to do more experiments on peppered moths. There are very few dark peppered
moths left to observe. What new experiment can you do to explore the rise
and fall of dark peppered moths?
------------------------------------------------------------------------
You can't repeat these experiments in the classroom.
It takes one year and many hours of collecting and feeding leaves to raise
the caterpillars. You don't see the moths until the second year. The moth
population changed over a period of 50 years. You will all be retiring
in 50 years.
------------------------------------------------------------------------
You can use a computer model to simulate natural
selection through selective predation. Ask your teacher for the Stella
model called "mothimm."
------------------------------------------------------------------------
This model's algorithm is similar to the model
that explored mutation. The mutation flows have been removed and bird predation
has been added.
------------------------------------------------------------------------
The converter pollution 2 is a graph function.
The graph holds the pollution values that simulate pollution levels in
England for the last century and a half. The pollution starts at 1. In
year 74 the pollution starts to fall. After 20 years it reaches 0 and stays
at 0.
------------------------------------------------------------------------
The converter "bird predation dark" does the calculation:
bird_pred_rate-(pollution_2*bird_pred_rate). The theory says that it is
harder for birds to find dark moths when there is pollution. The additional
bird predation rate is lower when there is pollution.
------------------------------------------------------------------------
The converter "bird pred light" does the calculation:
pollution_2*bird_pred_rate. When there is pollution (pollution =1) the
additional predation is bird_pred_rate. When there isn't any pollution
(pollution =0) there isn't any extra predation.
------------------------------------------------------------------------
Click the up triangle to go to the interface page.
Set immigration to 0. Click the run button to run the model.
------------------------------------------------------------------------
The graph shows the frequency of the dark moths,
the frequency of the light moths, and the level of pollution. The frequency
of dark and light moths can range from 0 to 1. If the frequency is 1 then
all of the moths are that type. If you drag the mouse onto the graph and
right click numbers appear under the variables: "dark freq", "light freq",
and "pollution'. As you move the mouse left and right across the graph
you can see the values of the variables at different times in the simulation.
------------------------------------------------------------------------
Does the model's results match the data that was
observed in England?
Yes in a general sense. We don't have data for
the elimination of air pollution in England. For that matter we don't know
the relative importance of sulfur versus black particular pollution. The
students don't have access to data for the shape of the curve for moth
frequency change. Some of that data is available in the scientific literature
(See the teacher resource page).
------------------------------------------------------------------------
All of the communities in England didn't see the
same change in peppered moths. Some rural areas had very little change
in phenotype frequency. Even in the industrial areas the phenotype frequencies
varied. Some polluted industrial areas saw a 50% maximum frequency of dark
peppered moths. Others saw a maximum of 75%.
------------------------------------------------------------------------
Scientists need to explain why two polluted areas
can have different phenotype frequencies. Some scientists suggested that
peppered moths immigrated into and out of polluted areas. Depending on
the phenotype ratios in surrounding areas and the amount of immigration
different phenotype frequencies would be observed.
------------------------------------------------------------------------
Scientists know that male peppered moths can fly
a few kilometers each night. Scientists have also observed that peppered
moths make a silk kite after they hatch from an egg. The newly hatched
larva, use these kites to fly across the countryside. Scientists don't
know how far they fly.
------------------------------------------------------------------------
Why can't scientists observe the immigration of
peppered moths?
The male moths fly at night when we can't track
them. The newly hatched larva are so small that as soon as the breeze picks
them up, we loose track of them.
------------------------------------------------------------------------
The model "mothimm." simulates the immigration
of peppered moths. Each of the phenotypes, AA, Aa, and aa, has a flows
that simulates moths immigrating into and emigrating out of the area. The
converter called "immigration" controls the amount of immigration and emigration.
------------------------------------------------------------------------
Adjust the immigration slider. Run the model and
see if the maximum dark frequency changes.
------------------------------------------------------------------------
Continue to adjust the immigration slider. Try
to simulate conditions that result in maximum dark frequencies that range
from 50 to 98%. Record your results in a table.
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------------------------------------------------------------------------
Scientists suggested that the variation in maximum
dark moth frequency could be explained by immigration. Does the results
of your simulation support this suggestion? Does your simulation prove
this suggestion?
The results of the model are consistent with
the observed frequencies. This supports the suggestion that immigration
is a causal factor. It doesn't prove that this is the causal factor. There
may be other factors that contribute with or without immigration.
Agents
As the model runs, the moths act as individual agents. Individual
moths die of natural causes, and predation by birds. If two moths of opposite
sex come together, they can mate and produce eggs. These eggs carry the
genetic material of their parents. The adult moths die and the eggs form
the next generation.
------------------------------------------------------------------------
Run the model.
Do the results approximate the results seen in
the Stella model and England?
Yes. The students may need to change the parameters
several times. The simulation is also an example of a chaotic system. Each
moth individually interacts with other moths and birds and there is a chance
that they will mate or be eaten. Two runs with the same parameter settings
may give different results because of the results of thousands of individual
chance interactions.
------------------------------------------------------------------------
Do the results of your simulations support the theory of natural selection? Explain your answer.
Yes. We can say that the results of our models that used natural selection as the causal factor driving the shift in moth frequencies is consistent with observations in the English country side. This doesn't prove a relationship.
You may find it useful to open the student version of:
in a separate window. This will allow you to toggle between the teacher discussions and the student lesson.
