As mentioned in a previous post, variables may be considered those things
that change over time. They can therefore be plotted during a typical SD
simulation. Some of these will be of immediate interest and will be the
main focus of the inquiry. Others may occur in the background and do not
need to be followed in detail during each simulation. Of course, it would
be a good idea to examine _all_ of them occassionally to be sure they are
behaving as expected.
True constants would _never_ change from one simulation to another. The
speed of light might be an example. I would say the acceleration of gravity
comes close to being such an example, unless very precise dynamics are
involved that would vary in Death Valley, Mt. Everest, the N. Pole, or the
equator. Or if you are on the moon, or on Mars. (Perhaps NASA needs to look
more closely at this issue . . . ?)
Parameters are variables which are held constant within a given simulation.
For example, a rabbit population model contains a number of "constants"
such as birth rate and death rate. The simulation runs and the population
(variable) is plotted as a function of time. In reality, the birth rate and
death rate is not constant, it is just held constant for each particular
simulation. Parameters can be changed systematically from one simulation to
the next to determine the influence of one parameter at a time, or several
parameters in relation to each other, on the final variable of interest, in
this case population.
In fact, not only _can_ parameters be examined in this way, they should be
examined _intensively_ in this way! One of the major hurdles I find with
beginners is convincing them how important this is, and how much they
should do it. (Of course Im a simulation junkie; I LOVE this part of SD!)
Try low birth rates, zero birth rates, moderate birth rates, high birth
rates. Try low, zero, moderate, death rates. Try low birth rates with high
death rates, low birth rates with low death rates, etc. etc. etc.; you get
the idea.
There is a real art and science to sensivity testing beyond just mindless
combinations of every combination, which soon becomes impossible anyway
with more complex models. But this is another topic altogether.
When does a parameter become a variable?
After a basic understanding of birth and death rates, and their
interactions is obtained, it may be time to add some complexity (realism?)
to the model. (Again, always consistent with the purpose of the model . . .
).
Perhaps you have evidence that population density increases; i.e. the
growing population is limited to some finite environment. Food becomes
scarce as population density increases, and food shortages lead to
progressively lower birth rates.
Keeping in mind that our initial variable of interest was (and still is)
population, now we have several new variables to examine. One is population
density (which in this case is not too interesting since it will be
directly proportional to population), and the other is birth rate. What was
once a parameter (fixed birth rate) is now a variable, dependent upon
population.
Aha, the plot thickens! Now the model begins to exhibit S-shaped growth!
Shifting loop dominance! And so on . . .
I hope this helps any beginners out there, and Id be happy to receive
comments or corrections about these issues from the experts.
"True" constants (speed of light)
"Almost true" constants (acceleration of gravity on earth)
"Constant variables" (i.e. parameters; what would otherwise be variables,
but are fixed for now)
Variables, which can be plotted as functions of time
Ed Gallaher, PhD
From: Ed Gallaher <
gallaher@mail.teleport.com>
VA Research Pharmacologist
Associate Professor
Behavioral Neuroscience and Physiology/Pharmacology
Oregon Health Sciences University
Portland, OR 97201