Supercomputer Applications

Gypsy Moth Simulation

1.0 Introduction

Another example we have used at Jefferson involves population dynamics of the Gypsy moth caterpillar, an extremely damaging pest of forests in the eastern United States.[8][12] In 1869, Gypsy moths used in a scientific experiment escaped from a laboratory in Massachusetts, and since there are no natural predators here, successive generations have been ravaging forests in the northeast ever since.

2.0 Model Parameters

As with the trajectory model, there are certain equations and parameters which control the basic functioning of Gypsy moth ecology. For instance, a female moth can lay between 400 to 1000 eggs in a single season. When these eggs hatch the next spring, the tiny caterpillars crawl up to the top of forest trees and start eating leaves. There is little damage at first, but as the caterpillars grow in size, each one can eventually consume up to three square feet of leaf surface every day. Caterpillars hatch in early spring, feed until mid summer when they develop into pupae, and after a short time, emerge from the pupae as adult moths. In the moth stage they do not eat leaves anymore but just mate, lay eggs, and die. Fortunately, there is only one generation per year.

Gypsy moths spread by several methods. Because females contain so many eggs, adult moths are too heavy to fly although they are able to crawl. Adults often lay egg masses on moveable objects such as automobiles or campers which then travel to other regions of the country. When these eggs hatch, a new infestation site becomes established.

At first, the young larva are quite small and can be blown by the wind on silk threads for distances up to ten miles. As caterpillars become larger, they can no longer travel by that method but will crawl to adjacent forest regions in search of food.

During severe infestations, trees can become completely defoliated very rapidly. Most trees will die after one or two defoliations, thus eliminating a potential food supply for the growing moth population. Caterpillars seem to like certain trees better than others; oak trees are a preferred food but the caterpillars rarely ever eat tulip poplar trees.

Gypsy moth caterpillars are not affected by many standard predators since the larva usually hide during the day and eat only at night. There are some specific predators which may eventually create a natural balance, but human intervention is an important factor in minimizing primary forest damage in eastern forests. Some human methods of control include destroying egg masses, trapping caterpillars, and spraying trees with biological or chemical controls.

As with any good scientific research, it is important to survey available literature on the subject to review what has been done previously, and to establish precise parameters for an accurate simulation. A more thorough research of Gypsy Moths is recommended before building a realistic model, but the information provided above is probably sufficient to get a prototype started.

3.0 Stages in Prototype Development - Importance of Validation

With a situation as complex as Gypsy moth ecology, it is important to develop the prototype simulation in stages, validating each new characteristic as it is added to the model. To try to put every conceivable aspect of a computer simulation into a model at the beginning and later attempt to validate the result will usually lead to serious difficulties.

A first stage of development in a Gypsy moth simulation would be to model a simple, closed population of moths with a standard birth rate and unlimited food supply. The time step could be done on a daily basis, but probably a yearly summary of Gypsy moth statistics would be sufficient since the desired outcome of this project is to show the qualitative behavior of a population over a long period of time. The expected behavior of this first stage would be to make certain that the model shows a typical exponential growth curve such as that shown in Figure #4. Gradually, other characteristics should be added, and the accuracy checked each time against expected behavior of the population. Figure #5 shows a repeated collapse of the Gypsy moth population due to overpopulation and starvation when all of the food supply is consumed.
Figure 4
Figure #4: Exponential Curve

Figure 5
Figure #5: Oscillating Growth

There are always random factors which affect such simulations, but it is important to avoid adding random occurrences until all aspects of the model have been validated. Early introduction of random numbers to make things "interesting" should definitely be avoided. It is usually very difficult to determine whether the behavior of a model is the result of the randomness, or the result of complex interactions among other factors in the simulation. Constant values within an expected range should be used initially to prove the model is working correctly. Random numbers can always be added later.

4.0 Expanding the Model

The prototype for a sample population will usually become quite involved as various aspects of a realistic simulation are included. Even so, this simulation could still be handled quite easily by a standard PC. The need for a supercomputer becomes apparent when a much larger region is modeled using many different "cells", all running in parallel. This modeling technique is often referred to as a cellular automaton.[9] Each cell would carry the fundamental rules of the initial prototype, but now migration of caterpillars and moths into adjacent cells can be included in order to look at the overall dynamics of Gypsy moths spreading into new forest areas.

It will be necessary to maintain much information about each of the cells, such as the number of caterpillars, birth rates, death rates, food supply, types of trees, history of past defoliations, the existence of predators, and spraying programs. Huge arrays of data will be required to keep track of all the important information available for a large number of cells.

This problem could now become too large for a typical supercomputer run if the same graphics visualization technique used in the trajectory model is applied here. To use every pixel on the screen as a separate cell would require extensive amounts of memory which might not be practical. A better approach in this case would be to divide the screen into small squares or other geometric shapes where each polygon stands for the status of a small segment of the overall population. With fewer cells and lower data requirements, it might be possible to accumulate information for successive years and display results as an animation over time.

Figures #6, #7, and #8 show various stages of the cellular automaton approach to the simulation. The darker the color within a cell, the greater the number of Gypsy moths in that region.

Figure 6
Figure #6: Intitial Gypsy Moth Population

Figure 7
Figure #7: Expanding Population

Figure 8
Figure #8: Collapsing Population

5.0 Suggestions for Future Projects

The cellular automaton approach can be useful in studying the global effects of individuals interacting in a larger population or a variety of other simulations where the behavior of individual components can be defined, but the overall behavior of the system is not so easy to predict, or other projects involving the concepts of granular physics.

Some possible projects for investigation include:

6.0 Bibliography