Predator-Prey Dynamics with Emphasis on Refugia
Rene" Salinas and Florencia Campon
Background
Predator-prey dynamics have been extensively studies most of this century. The effects of predation on the population dynamics of the predator and its prey present different dynamics that range from extinction of the prey and a consequent extinction of the predator to coexistence of both population at a certain equilibrium. There have been series of models developed as attempts to understand prey-predator dynamics. The simplest differential equation model is known by the name of its originators: Lotka-Volterra. In this models it is assumed that in the absence of predators the prey population increases exponentially. But when predators occur the prey individuals are removed, and this occurs at a rate that depends on the frequency of the predator-prey encounters. These will increase as any of the populations (prey or predator) increase. This simple form of the Lotka-Volterra model can further be elaborated by including heterogeneity in the habitat, particularly refugia. Predators have no access or chances of settling in these refuges and thus maintain a portion of the prey population under no risk of predation. This Lab has two separate Ecobeaker Situation Files, one for the situation with refuges and one for the situation in which the spatial heterogeneity does not act as a refuge. You willfind the latter one of these (No Refuges) to be useful, but it is not referenced directly in the lab below.you You will have to open each Situation file in the appropriate section below.
Lab Outline
The lab will begin with an example of the basic Lotka-Volterra predator-prey oscillations so you can understand what can happens when a predator exploits all of its food resource. The predator and prey have different immigration and growth rates. Because of the sensitivity of the model to immigration, we will keep it constant. The growth rate, however, will be varied to analyze the dynamics. The habitat includes an area in which the predator and prey have an equal chance of traveling around and settling. You will then add refugia to the landscape to give the prey a place to hide from the predator. This allows the populations to stabilize and coexist. You will also develop an understanding of how the refugia size and number affect the population sizes of the predator and prey. This Lab has two separate Ecobeaker Situation Files, one for the situation with refuges and one for the situation in which the spatial heterogeneity does not act as a refuge. You will have to open each Situation file in the appropriate section below.
The Lab
1. Run EcoBeaker (double-click on its icon).
2. Open the Refuge Situation File (use the OPEN command in the File menu). The window at the top left is the habitat grid. The next window to the right is the bar graph representation of the Predator and prey. The next is a line graph representation. The Change Parameter window will allow you to change the necessary parameters to perform the lab. Below the habitat grid is the Control Panel. This allows you to start, stop and restart the model.
3. Press the GO button on the control panel.
In the habitat grid, you should see green (prey) and blue (predator) dots, these represent the movement of the organisms. The red circles represent habitat patches that are not advantageous to either organism. If you look at the line graph you will see the oscillations of the prey and predator populations. Notice that the predator population stops increasing when the prey population reaches zero. Notice that the growth rates for each are different (Prey = 0.04, Predator = 0.03). Change the growth rates of each to see how it affects the dynamics. Which of the growth rates do you think has a greater effect on the system? How?
NOTE:
If at some point you run the model and the prey population overruns the whole grid, just press STOP, RESET, and GO again. Due to the sensitivity of the model to parameters, this does sometimes happen. The program requires an immigration term for each organism. This is why there is sometimes a delay in the model when you start it.
NOTE:
If the axis on the graphs ever get too big so making it hard to see the
plots, double-click on the graph (even in the middle of running the
model) and click on the SCALES button. Change the maximum value
to 1000 and click OK to get back to the model (You will have to click
on OK again in the next menu).
Press STOP. In the Change Parameter window, change the radius and number of
circles to 5 and 3, respectively. Click on the CHANGE button to make the changes
effective. Press RESET and then GO in the Control Window and let the model run
until the populations have come close reaching an equilibrium (about 1200 time steps).
Reset the scale to 1000 (while the model is running), return to the model and estimate
the predator and prey values and fill in table 1 below. Do this for the rest of the data
in the table.
NOTE:
The radius and circumference values present the situation in which the
total area is about the same for each, but there is more surface area
(circumference) as you go down the table. The ratios will not be
exactly the write since sometimes the refugia overlap, but it for our
purposes just assume they are correct.
TABLE 1
What can you conclude about the results in the table?
Radius/Number
Area:Circumference.
Prey #
Predator #
Difference
5/3
2.5 : 1
4/5
2 : 1
2/20
1 : 1
Repeat the last exercise with the following table in which we have different total
areas. (This will be done by keeping a constant radius and varying the number of
refugia.)
TABLE 2
Plot the graph of Area vs. Prey # and Area vs. Predator #. What can you say about
their relationship?
Notes and Comments
In this lab you should have seen how refugia affects predator-prey dynamics. You should
have also seen how different sizes and number of refugia can regulate population levels. This
tradeoff of number and size of refugia comes up frequently when conservation biologists are
trying to set aside land for reserves.
Radius/Number
Area
Prey #
Predator #
5/2
156
5/4
312
5/6
468
5/8
624
5/10
780