The lower left-hand corner of the graph pad also shows several symbols—a
triangle, which allows you to flip though the pages of a graph pad, assuming there is
more than one graph specified in that pad; a lock, to “freeze” the output from a
model run so it does not lost of the model is run again; a printer symbol to print the
graph; and a dynamite stick to clear the graph. Also, below the graph is the name of
the graph, which we have not specified, but you can do so by double clicking on
“Untitled” and then typing in a name. At the top right-hand corner of the graph pad,
you see a “pin” that can be used—by clicking on it—to affix the graph to the top
layer of your diagram so that it does not go to the background when you, for
example, open or close a stock or other symbol.
What do we really have here in our model? How does STELLA determine the time
path of our state variable? Actually, it is not very difficult. At the beginning of each
time period, starting with time ¼ 0 years (the initial period), STELLA looks at all the
components for the required calculations. The values of the state variables will
probably form the basis for these calculations. Only the variable REPRODUCTION
depends on the state variable FISH. The estimate the value of REPRODUCTION
after the first time period, STELLA multiplies 0.05 by the value FISH (@ time ¼ 0) or
200 (provided by the information arrows) to arrive at 10. From time ¼ 1 to time ¼ 2,
the next DT, STELLA repeats the process and continues through the length of the
model. When you plot you model results in a table you find that, for our simple fish
model, STELLA calculates fractions of fish from time ¼ 1 onward. This problem is
easy to solve for example by having STELLA round the calculated number of fish—
there is a built-in function that can do that—or just by re-interpreting the population
size as “thousands of fish.”
This process of calculating stocks form flows highlights the important role that is
played by the state variable. The computer carries that information—and only that
information—from one DT to the next, which is why it is defined as the variable
that represents the condition of the system.
You can drill down in the STELLA model to see the parameters and equations
that you have specified and how STELLA makes use of them. Click on the Equation
tap on the far right of your STELLA diagram. The equations and parameters of your
models are listed here. Note how the fish population in time period t is calculated
from the population one small time step DT earlier and all the flows that occurred
during a DT.
The model of the fish population dynamics is simple. So simple, in fact, we could
have solved it with pencil and paper, using analytic or symbolic techniques. The
model is also linear and unrealistic. So let us add a dimension of reality, and by
doing so explore some of STELLA’s flexibility. This may be justified by the
observation that, as populations get large, mechanisms set in that influence the
rate of reproduction.
To account for feedback between the size of the fish population and its rate of
reproduction, an information arrow is needed to connect FISH with REPRODUCTION RATE. The connection will cause a question mark to appear in the symbol
for REPRODUCTION RATE (Fig. 1.10). The previous specification is no longer
correct; it now requires FISH as an input.
1.5 Modeling in STELLA
17
triangle, which allows you to flip though the pages of a graph pad, assuming there is
more than one graph specified in that pad; a lock, to “freeze” the output from a
model run so it does not lost of the model is run again; a printer symbol to print the
graph; and a dynamite stick to clear the graph. Also, below the graph is the name of
the graph, which we have not specified, but you can do so by double clicking on
“Untitled” and then typing in a name. At the top right-hand corner of the graph pad,
you see a “pin” that can be used—by clicking on it—to affix the graph to the top
layer of your diagram so that it does not go to the background when you, for
example, open or close a stock or other symbol.
What do we really have here in our model? How does STELLA determine the time
path of our state variable? Actually, it is not very difficult. At the beginning of each
time period, starting with time ¼ 0 years (the initial period), STELLA looks at all the
components for the required calculations. The values of the state variables will
probably form the basis for these calculations. Only the variable REPRODUCTION
depends on the state variable FISH. The estimate the value of REPRODUCTION
after the first time period, STELLA multiplies 0.05 by the value FISH (@ time ¼ 0) or
200 (provided by the information arrows) to arrive at 10. From time ¼ 1 to time ¼ 2,
the next DT, STELLA repeats the process and continues through the length of the
model. When you plot you model results in a table you find that, for our simple fish
model, STELLA calculates fractions of fish from time ¼ 1 onward. This problem is
easy to solve for example by having STELLA round the calculated number of fish—
there is a built-in function that can do that—or just by re-interpreting the population
size as “thousands of fish.”
This process of calculating stocks form flows highlights the important role that is
played by the state variable. The computer carries that information—and only that
information—from one DT to the next, which is why it is defined as the variable
that represents the condition of the system.
You can drill down in the STELLA model to see the parameters and equations
that you have specified and how STELLA makes use of them. Click on the Equation
tap on the far right of your STELLA diagram. The equations and parameters of your
models are listed here. Note how the fish population in time period t is calculated
from the population one small time step DT earlier and all the flows that occurred
during a DT.
The model of the fish population dynamics is simple. So simple, in fact, we could
have solved it with pencil and paper, using analytic or symbolic techniques. The
model is also linear and unrealistic. So let us add a dimension of reality, and by
doing so explore some of STELLA’s flexibility. This may be justified by the
observation that, as populations get large, mechanisms set in that influence the
rate of reproduction.
To account for feedback between the size of the fish population and its rate of
reproduction, an information arrow is needed to connect FISH with REPRODUCTION RATE. The connection will cause a question mark to appear in the symbol
for REPRODUCTION RATE (Fig. 1.10). The previous specification is no longer
correct; it now requires FISH as an input.
1.5 Modeling in STELLA
17