Grazing Fields

Let's suppose that we want to use a fuzzy congnitive map to model the behaviour of a very simple ecosystem formed by grazing fields and by the hervibores (cattle, zebras or whatever) that feed on the fields.

The herbivores of the system feed on the grass, and therefore they will thrive if the grass is abundant. On the other hand, the amount of grassland available will drop when the population of hervibores increases.

The fuzzy conginitive map for this system is represented in the figure below.

The two factors of the system are represented by two labelled boxes in the diagram. The arrows that go from one factor to other factor represent causality. The amount of grassland has an effect on the population of hervibores, and the population of hervibores has an effect of on the amount of grassland.

The "+" and "-" symbols indicate the type of causality that the arrow represents. The "+" symbol represents positive causality and the symbol "-" indicates negative causality.

The "+" arrow that goes from Grassland to Grazing animals indicates that an increase in the extension of grassland will cause an increase in the population of grazing animals. Conversely, a drop in the extension of grassland will cause a reduction in the population of animals.

The "-" arrow that goes from Grazing animals to Grassland indicates that a reduction in the number of grazing animals will allow the extension of grassland to grow larger, and that a raise in the number of animals would reduce the extension of grassland.

1. Loading the system

To load the grassland-hervibores system in the fuzzy cognitive map applet click the Load System button. In the Load System dialog box select the Grazing Fields item and click the Load button. The two factors of the system (Grassland and Grazing animals) will appear in the factors list of the main window of the application.

It is possible to edit the factors of the system by selecting one or more of them and then clicking on the Edit button. In the Factor Editor dialog box the following attributes of a factor can be modified:

• The name of the factor, which must be unique in the system.
• The level of the factor, in the range from 0 to 100. A value of 0 means that the factor is not present, and a value 100 means that the factor is present to the maximum extent possible.
• The intensity and type of effect that other factors play on the factor being edited. The potential factors are listed in the dialog. To modify the effect type and intensity of effect of a cause, select the cause in the list and then use the drop-down list and scrollbar in the window. The intensity of effect ranges from 0 to 100, where 0 means that the cause has no effect on the factor being edited, and 100 means the the effect is as intense as possible. If the effect on factor is none the intensity of effect plays no role.

2. Setting the parameters for the system

Let's suppose that the ecosystem being modelled has an extension of 400 km², of which half are covered by grassland. For the local climate, this grassland coverage is considered by the biologists to be the average. Let's also suppose that the biologists have determined that a sustainable population of hervibores is 10 animals per square kilometer of grassland.

Since we consider that ½ grassland coverage and 10 animals/km² are average and sustainable levels for the factors of the system, we can represent these values with levels of 50 out of 100 in our fuzzy cognitive map. We edit the factors in the applet and set the levels at 50.

For the Grazing animals factor the Grassland cause has positive effect, and for the Grassland factor the Grazing animals cause has negative effect.

We leave the intensities of effects at 50 in both cases.

3. Running the simulation

Once we have set the parameters of the system as indicated above, we run the simulation.

In the main window of the application it is possible to choose a fixed number of iterations of the simulation or to leave it run until convergence is reached.

To run the simulation, we click the Run Simulation button. The results are displayed in a popup window.

We can see that the simulation reaches convergence and that there is no variation in the levels of the factors.

This result is what we expected. The levels of the parameters, set at 50, represent a sustainable situation in which there should not be any variation in the extension of grassland or animal population.

4. Effects of variations of grassland extension

Now we can start playing with the levels of the factors and see what effects the variations have on the balance of the system.

First, we vary the grassland extension level, leaving the animal population level at 50.

Let's suppose that, due to a drought, the extension of grassland drops from ½ to only ¼ of coverage. We can represent this in the fuzzy cognitive map with a level of 25 for the grassland.

If we run the simulation we see that the grassland level diminishes very quickly and eventually becomes 0. The population of animals also diminishes and disappear. The explanation of this result is that, at the initial conditions, the extension of grassland is too low to support an average populatioin of animals. The animals consume the grassland until it disappears, and then the animals disappear because there is not grassland left to feed themselves.

If this is not obvious at first sight, you can run the simulation with a level of 40 for the grassland, rather than 25. The final result is the same, but it takes more iterations to reach it, and the evolution of the levels is clearer.

Now let's suppose that due to abnormal weather conditions the extension of grassland suddenly goes up to 3/4 of coverage of the land. We represent this increase with a level of 75 for the grassland factor in the fuzzy cognitive map. When we run the simulation we see that the population of animals is too low to prevent the extension of grassland to grow further. In absence of enough animals the grassland extension grows fast, and then the population of animals grows as well due to the larger amount of food available.

5. Effect of variations of animal population

Variations in the population of animals also play an effect in the balance of the system.

Let's suppose that, due to an epidemic, the population of animals suddenly drops to a lower than average density that we can represent with a level of 40 in the fuzzy cognitive map. In the results of the simulation we see that, in the long term the epidemic is good for the animals. In absence of enough animals that feed on the grass, the extension of grassland starts increasing, until it reaches the maximum. The population of animals recovers and, due to the higher availability of grassland, it increases above the average and then reaches the maximum.

If, on the other hand, more animals are introduced in the system (say a population of animals at a level of 60 for grassland at an average level of 50), the grassland is not enough to sustain the animal population. The extension of grassland decreases and disappears, and the animals disappear with it.