Name: _________________________________________
Bio 325 Ecology Recitation
Populus Worksheet
* Go to http://www.cbs.umn.edu/populus/ and download Populus
Density-Independent Geometric growth with discrete generations
1. Consider a population of an endangered frog species living in a tiny forest. It has a per capita
growth rate of 1.2. This species breeds only once a year. Hence discrete cohorts are produced
every year. The forest is surrounded by urbanization and hence there is no immigration into or
emigration from the population. A group of conservationists in the city conduct a study and find
that only 20 individuals of this species are remaining in this forest. They convince the authorities
that this species is dying out and this little forest patch is one of its last few remnant habitats.
Strict measures are taken to prevent disturbance of the forest. Twenty years later the city
authorities decide to review whether the conservation measures were valuable or not. Using
Populus answer the questions below.
Using Populus
1. Open Populus
2. Go to: Model… Single-Species Dynamics…. Density-Independent Growth
3. In the Density-Independent Growth window, click “Discrete”.
4. Set parameter values.
5. Select “N vs t” under Plot types.
6. Click View to update the graph.
a. How many frogs are there in the forest at time t = 20 years?
b. What is the shape of the growth curve?
c. Explain the growth curve in plain English, taking care to explain what variable is changing
with what and how.
d. Were the conservation measures useful?
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Name: _________________________________________
Bio 325 Ecology Recitation
Density-Independent Exponential Growth with Continuous Breeding
2. An introductory biology course was conducting a lab experiment on Mendelian genetics.
Three strains of flies were going to be used – wild type, white-eye, and ebony. About 500 flies of
each strain were required for the experiments. However the lab had only a 100 of each strain. So
they started breeding these in flasks to increase their numbers in time for the lab exercise. A
group of students were assigned to taking care of these flies. But these students were not very
careful, and only the wild type strain had a positive instantaneous growth rate of 0.2. The whiteeye strain and ebony strain flies suffered badly, one having no growth rate at all, and the other
actually having a negative growth rate of –0.5. The experiment, unfortunately, had to be
cancelled. Using Populus answer the questions below.
[
Using Populus:
1. Click “continuous” instead of discrete.
2. In the input window there are 4 colored tabs: A, B, C, D. These allow you to plot more
than one population on the same graph.
3. Set the parameters in each tab, taking care to check the box in each.
4. Click View. You should see 3 curves on the graph. The color of the line corresponds to
the color of the tab A, B, C or D.
a. At the end of 5 generation cycles, what is the population size of each fly strain?
b. Draw a free hand sketch of your graph and explain the growth curves for each fly strain with
respect to dependent and independent variables.
c. What growth rate, value of r, would have produced 500 flies at the end of 5 generation
cycles?
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Name: _________________________________________
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Bio 325 Ecology Recitation
Name: _________________________________________
Bio 325 Ecology Recitation
Density Dependent Growth
3. A local farmer decided to use her 3 farm-ponds for aquaculture of prawns (shrimp). She
purchases 300 egg-laden female prawns and introduces 100 of them to each of her ponds.
Unbeknownst to her, her ponds, which differ in size, also differ in prawn carrying capacities.
Pond A is large, and has a carrying capacity of 500; pond B is medium size and has a K of 100
prawns; and pond C is the smallest and has a K of 50 prawns. If there were no K, prawns have an
r of 0.2.
Using Populus:
1. In Populus, go to Model… Single-Species Dynamics… Density-Dependent Growth.
2. Select “Continuous Logistic”.
3. Set parameter values under tabs A, B, C. Be sure to check the boxes under each tab.
4. Select the correct plot type – which one should it be?
5. Click View.
a. Which pond gave the farmer the highest return on her investment? What happened to the
other 2 ponds?
b. How do the 3 populations change with time? Draw rough sketches of the 3 curves (or paste
the Populus graph into your worksheet) and explain them.
c. As the population size increases, how does the per capita rate of increase (r) change? Why is
this happening? (Hint: r = dN/Ndt).
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Name: _________________________________________
Bio 325 Ecology Recitation
Lotka-Volterra Competition
4. The number of buffalo in a forest in India is 10; and the number of deer is 50. The buffalo
population grows at a rate of 0.9 while the deer population grows at a rate of 0.5. The forest has a
carrying capacity of 500 for the buffalo and 700 for the deer. The deer affect the forest’s carrying
capacity of buffalo by a factor of 0.6, while the buffalo affect the forest’s carrying capacity of
deer by a factor of 0.7. Assuming that conditions remain the same, how might the interaction
between these two species affect their populations? Using Populus answer the questions below.
Using Populus:
1. In Populus, go to Model… Multi-Species Dynamics…. Lotka-Volterra Competition.
2. Set parameter values.
3. Under Termination Conditions, select “Run until steady state”.
4. Click View.
a. Draw a rough sketch of the population curves of the two species changing over time. Does
either species drive the other to extinction? (Draw on next page).
b. Now plot the zero isoclines of the two species against each other. Draw your graph below.
What is the outcome of the interaction? Was your answer in (a) correct?
c. What would happen if you started with 600 buffalo and 50 deer?
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Name: _________________________________________
Bio 325 Ecology Recitation
5. A fish species, Zebra-catfish, lives in a lake in Africa and feeds on bottom dwelling
organisms. Zebra-catfish is not a very “desired” fish by anglers. To increase revenue from
ecotourism, the authorities introduced 10 individuals of a new fish species Hippo-fish into the
lake, which is a very popular game species. Hippo-fish also feeds on bottom dwelling organisms
and became a competitor to Zebra-catfish. At the point of introduction of Hippo-fish, there were
only 10 individuals of Zebra-catfish in the lake. Both Zebra-catfish and Hippo-fish have an
intrinsic growth rate of 0.5, and they each affect the lake’s carrying capacity for the other by a
factor of 0.7. The lake has a carrying capacity of 200 for Zebra-catfish and 400 for Hippo-fish.
Using Populus, answer the questions below.
a. What is the outcome of the interaction at steady state? Explain with respect to the parameter
values - why this outcome?
b. Increase the carrying capacity of Zebra-catfish by clicking the up arrow. At what point does
the outcome change? What were the values of the carrying capacities of the lake for the two
species at that point? Why do you think the outcome changes here?
c. Keep increasing the carrying capacity for Zebra-catfish until the outcome changes again.
What are the values of the carrying capacities at this point?
d. Increase the value of the effect that Hippo-fish has on the lake’s carrying capacity for Zebracatfish by using the up arrow. At what value does the outcome change? What is the new
outcome and why?
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