Wildlife Reserve

In this example we are going to use a fuzzy cognitive map to model the behaviour of a wildlife reserve. This example builds upon the Grazing Fields and the Food, Prey and Predator fuzzy cognitive maps. If you have not already done so, I suggest that you have a look at them before going on with the Wildlife Reserve case.

1. Description of the wildlife reserve

The wildlife reserve is a vast area of land, of which about half is covered by grassland. However, the extension of the reserve occupied by grassland varies, as it depends on the amount of rainfall. When the rain is abundant the coverage of the grassland grows, and in droughts the grassland area shrinks.

In the wildlife reserve there is a colony of zebras that graze on the grassland. The zebras live happily in the reserve, but only to the extent that the lions, which live also in the reserve, leave them in peace. The lions do not leave the zebras in peace because the main ingredient of a lion's diet is zebra meat.

In the outskirts of the wildlife reserve there are farms. The farmers grow crops and, by and large, they do not interfere with the life in the reserve. This is in periods of normal weather. In dry weather things are different. When there is a drought many farmers lose their crops and don't manage to get enough income. In those hard circumstances many of them turn to the wildlife reserve and become poachers. The poachers hunt both zebras and for lions. They sell the zebra meat in the market and sell the lions, dead or alive, to smugglers in the black market.

The number of poachers not only depends on how good or bad the harvest is; it also depends on the population of zebras and lions. When there are many zebras and lions, it is easier to hunt them, and the number of poachers raise. On the other hand, when the population of wildlife is low, the number of poachers decreases.

The wildlife reserve is certainly large, and it can support a small number of poachers without important damage to the population of animals. Nevertheless, to keep the number of poachers at bay the local authorities have set up a small garrison of rangers in the reserve. The rangers patrol the reserve and try to make life difficult for the poachers. The number of rangers is small, and they cannot provide full and continuous coverage of the reserve. However, they manage to prevent the number of poachers raising.

A solution to the problem of illegal hunting would be to recruit the unemployed farmers as rangers. However, the budget of the local authorities is rather tight, so they cannot afford to recruit more rangers.

2. The fuzzy cognitive map for the wildlife reserve system

2.1. Factors in the system

From the description of the system it is quite clear what are the factors involved. These factors are: reserve are:

• The amount of rainfall
• The extension of grassland
• The zebra population
• The lion population
• The number of poachers
• The number of rangers

Therefore we select these six factors to draw the fuzzy cognitive map that models the wildlife reserve.

Once the factors are selected, the next step is to find out how the factors are related to one another.

2.2. The amount of rainfall

The amount of rainfall has an effect on the extension of grassland. The effect is positive because an increase in the amount of rainfall causes an increase in the extension of grassland. And viceversa, a dry period causes a drop in the extension of grassland.

The amount of rainfall also affects the number of poachers. When the rain is plentiful the number of poachers is low, because the harvest is good and the farmers do not need to become poachers. When the rain is scarce the number of poachers raise, out of unemployed farmers. The causality relationship between the rain and the number of poachers is negative.

2.3. The extension of grassland

The extension of grassland only affects the population of zebras, which feed on the grassland. When the extension of grassland is large the zebra population is boosted, and when the grass is scarce the number of zebras decreases. The causality relationship is positive.

2.4. The zebra population

The number of zebras affects the number of lions, because the lions feed on the zebras. If the number of zebras is high the lions thrive, and viceversa. The relationship is positive.

The extension of grassland is affected by the number of zebras. When there are many zebras, they eat too much grass and the grassland extension decreases. And when the number of zebras is low the grassland grows in extension because the zebras do not manage to eat the grass. The relationship is negative.

The number of zebras also affects the number of poachers. The relationship is positive. A large number of zebras encourages the poachers because the zebras are easier to hunt.

2.5. The lion population

The lion population affects the number of zebras because the lions eat the zebras. The relationship is negative: more lions means fewer zebras.

The lion population affects the number of poachers, in the same way as the zebra population does.

2.6. The number of poachers

The number of poachers affects the populations of zebras and lions with negative causality. Poachers kill the animals, so more poachers means fewer animals, and fewer poachers means more animals.

2.7. The number of rangers

The job of the rangers is to chase the poachers, so more rangers implies that there are fewer poachers. This is a negative relationship.

The number of rangers is not affected by any factor in the system. As we said above, the local authorities cannot afford to employ ex-farmers as rangers. The number of rangers is, in principle, constant.

2.8. The fuzzy cognitive map

The fuzzy cognitive map for the system is depicted in the figure below:

Causality relationships are indicated with arrows, from the cause to the effect, and the type of relationship (positive or negative) is indicated with a "+" or "-" simbol next to the arrow.

The fuzzy cognitive map for the wildlife reserve is stored in the applet. To load it click the Load System button in the main window of the application. In the popup dialog box select the Wildlife Reserve system and click the Load button. The factors of the system will appear listed in the main window of the application. The factors can be edited and removed using the appropriate buttons in the main window.

3. Levels of factors

Once we have the fuzzy cognitive map loaded in the applet, the next thing to do is to set the parameters for the factors.

Let's suppose that the local authorities have determined that, under normal circumstances, the average rainfall is 700 mm/year, the grassland covers half of the area of the reserve, the population of zebras is 10 zebras per square kilometer of grassland and the ratio of lions and zebras is 20:1. There are four rangers in the reserve, and the number of poachers is estimated to be six. These poachers are endemic: they are a permanent fixture of the park, and their presence is not due to poor crop harvest. Nevertheless, the park can bear the activities of the poachers and the the four rangers manage to keep the number of poachers down to about six. Therefore, it is expected that under normal circumstances and if the rainfall is as expected, the state of the system is steady and the extension of grassland, number of animals and number of poachers remains pretty much constant.

In our fuzzy cognitive map we can represent the expected average levels of the factors with a value of 50 out of 100. Therefore, the levels are as follows:

Each causality relationship in the fuzzy cognitive map has an associated intensity of effect, that may take any value between 0 and 100. For the moment we leave all the intensities of effect at 50. We may modify these values later on if we want to fine-tune the model.

4. Running the simulation

To run the simulation, select Run until convergence and then click the Run simulation button in the main window of the applet.

In the popup window that shows the results of the simulation we can see that the system is stable. After a few iterations there is no change in the levels of the system and the simulation stops. This is what we expected, as we said that the levels of 50 for the factors represent a sustainable state of the system.

5. Effect of the amount of rainfall

Now we can start exploring the effect of variations of the levels of the factors on the global balance of the system. The first factor that we are going to alter is the amount of rainfall.

5.1. Low level of rainfall

We can try and see the effect of setting the rainfall level at values of 40, 30, 20, 10 and 0. That is, from lower than average rainfall down to extreme drought. The levels of all the other factor remain at 50.

For rainfall levels of 40, 30 and 20 we see that the simulation runs to the maximum number of cycles allowed (5000) without reaching convergence. Initially, the extension of grassland and the population of zebras decreases. This causes a drop in the number of lions, but an increase of the number of poachers. Then the system oscillates, as high and low factors tend to compensate one another. The conclusion is that the low rainfall certainly disrupts the balance of the system, but is not enough to make it collapse.

For a rainfall level of 10 the simulation reaches convergence after 66 iterations. The final levels in the final steady state are:

The levels of rangers and rainfall are of course the same as in the initial situation, as these factors are not affected by other factors in the system. The levels of lion population and grassland extension are low and the levels of zebra population and poachers are very low.

We might try to guess correspondences between these fuzzy cognitive map levels and actual levels in the wildlife reserve system. We could assume that the results mean a grassland extension of about 1/3 of the area of the reserve, a zebra population of about 2 animals/km², a lion population of about 0.25 animals/km² and 1 or 2 poachers.

For a rainfall level of 0 (extreme drought) the simulation reaches convergence as well, but the results are different. The extension of grassland decreases quickly. This is followed by a decrease in the number of zebras and, in turn, by a decrease in the number of lions. The number of poachers initially raises, because the drought forces the farmers to become poachers. The higher number of poachers taxes the animal population further. Eventually the grassland disappear, the zebras become extint, the lions die and, finally, the poachers go. Only the rangers remain (rather bored, I guess).

5.2. High level of rainfall

In order to see the effect of a high level of rainfall we run simulations with rain levels of 60, 70, 80, 90 and 100. The levels of other factors are kept at 50.

For levels of rainfall of 60, 70 and 80 the simulation does not reach convergence. It seems that the abundant rainfall disrupts the balance in such a way that it can not settle in an steady state. The system oscillates between different states. It would be interesting to plot the results and see if the oscillations are periodic or random. Unfortunately the applet does not allow to plot the results (yet!).

For the rainfall level of 90 the simulation reaches convergence. The final levels are:

That is, the grassland abound and zebra population grows as much as poachers do. Lions thrive after the zebras, but not as much. We might expect that the rainfall would keep the number of poachers down, because the farmers do not need to become poachers, but it seems that despite the abundant rainfall the number of poachers raised pulled by the high number of animals in the reserve. As we did before, we might try to convert the fuzzy cognitive map levels into actual levels of factors in the real system.

The results of a simulation run with a rainfall level of 100 shows that the grassland extension raises quickly, and with it the populations of zebras and lions. The number of poachers initially drops quite low, but then raises due to the high levels of the animal population. Eventually, the levels of all factors raise as much as possible (except for the number of rangers, which is fixed). The abundant rainfall is not enough to keep the number of poachers low when the animal population is high.

6. Effect of changes in the ranger recruitment policy

In the description of the wildlife reserve above we said that the local authories could not afford to recruit unemployed farmers and train them as rangers. Nevertheless, with the fuzzy cognitive map we can explore what would happen if the local authorities decide to change this recruitment policy.

There are two ways of modelling a change in the recruitment policy for the rangers. The first way is to modify the levels of rainfall and rangers simultaneously. The second way is to add a causal link from the rainfall factor to the ranger factor and modify the level of rainfall. Each way models a different kind of recruitment policy.

6.1. Simultaneous variation of rainfall and rangers factor levels

In the description of the wildlife reserve we said that, under normal circumstances, there are four rangers in the reserve. This is represented with a factor level of 50 in the fuzzy cognitive map. We may suppose that the local authorities are ready to recruit unemployed farmers as rangers in periods of dry wheather, but that they do not intend to reduce the number of rangers below their usual number of four when the rainfall is abundant and the crop harvest is good. In the fuzzy cognitive map we can mimic this policy by modifying simultaneously the initial levels of rainfall and rangers.

We are interested to see what happens when the wheather is dry and the local authorities are forced to recruit more rangers. Therefore we run five simulations using the following initial values for the levels of rainfall and rangers, where the rainfall level is lower than the average and the number of rangers is higher than the average.

In the simulations for the three first situations -values of (40, 60), (30, 70) and (20, 80)- convergence is not reached. The system alternates between states. A plot of the results would show if the oscillations are periodic or not, and whether the system oscillates in the same way for the three initial conditions.

The simulation for the initial conditions (10, 90) reaches convergence after 66 iterations. The final levels of the factors are shown in the following table.

Surprinsingly, the results are the same as those shown in Section 5.1 above, where we ran a simulation for very dry weather (level 10) but there was no additional recruitment of rangers. The conclusion is that, when the weather is dry, it does not matter if the local authorities recruit more rangers or not. The effect on the grassland extension and the population of animals is the same. Recruiting more rangers may relieve the families of the unemployed farmers, but will not affect life in the wildlife reserve.

The result of the last simulation, with initial levels of 0 and 100 for rainfall and rangers, also finishes in a steady state: the grassland and wildlife disappears and only the rangers are left.

6.2. Causal relationship between rainfall and rangers

In the previous section we have assumed that the local authorities would recruit unemployed farmers as rangers in dry weather, but they would not dismiss the core of four rangers of the reserve when the rainfall is above the average level.

Now we assume that the number of rangers is strictly dependent on the amount of the rainfall: when the weather is dry the authorities will recruit more rangers, but when the weather is wet the number of rangers will fall below the average (maybe because the rangers resign and become farmers).

To represent this situation we need to add a negative causal relationship between the fainfall factor and the number of rangers factor. The fuzzy cognitive map that results is shown in the figure below.

To add this new causal relationship in the fuzzy cognitive map applet we click in the Rangers factor to select it in the main window of the applet. Then we click the Edit button. In the popup Factor Editor window, we select the Rain factor in the list of possible causes. We set the effect on factor as Negative and the intensity of effect at level 50. Finally, we click OK to accept the changes.

We can run simulations for dry weather (for example, with leves 40, 30, 20, 10 and 0) and for wet weather (levels 60, 70, 80, 90 and 100). The levels of the remaining factors, including the rangers, should be all at 50 initially.

The simulation for initial level of rainfall at 0 shows that there is extintion of animals and grassland and no poachers. The number of rangers is maximum, though.

The simulation for initial levels of rainfall at 10 and 20 reach convergence. The final results are shown in the table below:

The simulation for rainfall level at 10 shows the same final results as we saw above, when there was no causal link between rainfall and rangers and the level of rangers was kept at 50. This seems to indicate that there is no much point in recruiting more rangers: at the end the result is the same. On the other hand, the simulation for rainfall level at 20 suggest that by recruiting more rangers when the weather is rather dry (but not too dry) it is possible to maintain the reserve in relative good health -only the zebra population is below the average level.

The simulations for initial levels of rainfall at 30, 40, 60 and 70 do not converge, so we cannot say much if we do not plot the results.

The simulations for initial levels of rainfall at 80 and 90 the simulations converge to the following levels:

The results show that, without rangers, the poachers thrive. However, thanks to the abundant rainfall the levels of grassland and animal life are next or well above the average level. Again, this suggest that there is not much need of recruiting rangers.

7. Effect of variations in the number of rangers

Some of the simulations that we have tried in the sections above suggest that there is not much difference between having or not having rangers in the reserve. To ascertain what the effect of not having rangers is, we can run simulations with different levels for the ranger factor.

First, we remove the causal relationship between the rain factor and the rangers factor. To do this, we edit the ranger factor. In the Factor Editor window for the ranger factor we select the Rain cause and then set the effect on factor as None.

If we run simulations with initial levels of rangers of 0, 10, 20, 30 and 40, leaving all other levels at 50, we see that the simulations do not reach convergence. This means that the reduction or absence of rangers causes a perturbation in the system, but does not lead it to a collapse. The wildlife reserve is able to survive without rangers, providing that the amount of rainfall is at least at the average.

8. Intensities of effect

In all the simulations we have run so far for the wildlife reserve system all the intensities of effect were set at 50. This may not be very realistic. We could adjust the intensities of effect to reflect better the causality relationships in the real system.

The population of a species is usually more dependent on the availability of food than on the presence of predators. Too many predators are bad, but too little food is worse. We can express this in the fuzzy cognitive map by assigning an intensity of effect of 60 to the dependency on food and an intensity of 40 to the presence of predators. For the zebras the predators are the lions, and for the grassland the predators are the zebras.

We could argue that the presence of zebras or lions does not encourage the poacher to go hunting in the same way. The poachers hunt zebras to sell the meat, but it turns out that the meat of zebra is not very good and they have to sell it cheap. Hunting zebras is not very profitable for poachers. On the other hand, hunting lions is a very profitable business. Lions are expensive and are in high demand. Therefore, the zebra population and the lion population do not have the same effect on the number of poachers. We can then assign an intensity of effect at 20 between zebra population and poachers, and an intensity of effect of 70 between lion population and poachers.

The local authorities have found that the presence of poachers does not cause the same damage to the zebra population as to the lion population. The effect of poachers on the zebra population is, apparently, moderate, so we assign an intensity of effect of 30 to it. On the other hand, the poachers cause great damage to the lion population because they always tend to hunt for the best animals, which taxes the ability of the lion population to breed. We assign an intensity of effect higher than for the zebras, say 50.

The simulations that we run in the previous sections seemed to indicate that the effect of the number of rangers on the wildlife reserve is moderate. Also, we could assume that the effect of the lack or abundance of rainfall has a moderate effect on the number of poachers, because only part of the unemployed farmers become poachers. We assign intensities of effect of 30 to these two relationships.

After setting the new intensities of effect the fuzzy cognitive map is as shown in the figure below:

The intensities of effect are shown between brackets next to the arrows that indicate the causality relationships.

To edit the intensities of effect in the applet, select one or more factors in the main window of the applet and then click the Edit button. In the popup Factor Editor window select the causes in turn and modify the intensity of effect using the scroll bar. Finally, click OK to accept the changes.

9. Validity of the model

We have used a fuzzy cognitive map to model the effect of rainfall in a wildlife reserve. Our fuzzy cognitive map for the reserve is a very simple one, with only six factors. Nevertheless, the simulations we have run have shown some interesting trends and the results we have obtained seem to be reasonable.

To ascertain the validity of our fuzzy cognitive map we would have to compare the outcome of the simulations with the actual effects of rainfall in the reserve.

If the fuzzy cognitive map, as it is, does not prove good enough to predict the behaviour of the actual system then it would be necessary to refine the model. The refinement of the fuzzy map can be done by adding more factors, by rearranging the causality relationships or by modifying the intensities of effect.

10. Feedback

If you have comments, good or bad, about the wildlife reserve fuzzy cognitive map, or you have suggestions on how to improve it, feel free to contact me.

If you have a fuzzy cognitive map that models an ecosystem similar, or not so similar, to the wildlife reserve, please let me know about your experience. What did you use your fuzzy map for? Was your fuzzy map able to model the real system? If you wish, I can add your fuzzy map to the applet (and add your name to the credits too!).