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.

  1. How many frogs are there in the forest at time t = 20 years?
  1. What is the shape of the growth curve?
  1. Explain the growth curve in plain English, taking care to explain what variable is changing with what and how.
  1. Were the conservation measures useful?

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 white-eye 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.

  1. At the end of 5 generation cycles, what is the population size of each fly strain?
  1. Draw a free hand sketch of your graph and explain the growth curves for each fly strain with respect to dependent and independent variables.
  1. What growth rate, value of r, would have produced 500 flies at the end of 5 generation cycles?

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).

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?


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 Zebra-catfish by using the up arrow. At what value does the outcome change? What is the new outcome and why?

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