represent as much as possible the reality of the dynamic phenomenon. Some refer to
this form of modeling as the mechanical approach, but this term seems to us too
wooden and likely to leave the impression that we think nature is just another
mechanical process, rather like the engine of an auto. We do not think so.
In systematical modeling, we build into the representation of the phenomenon
that we know actually exists—such as the birth and death processes of populations.
Our systematical alternative therefore starts with an advantage over the purely
statistical or empirical modeling schema. This advantage allows the systematical
model to be used in more related applications than the empirical model—the
systematical model is more transferable to new applications. But the empirical
model does have one advantage: in the process of evaluating the data gathered
about the phenomenon, the mean and standard deviations of the coefficients are
found. The corresponding parameters and initial values in our models are not so
elaborated. Such values are at first usually found or derived from the pertinent
literature, often without a given variation.
Once the systematical model has performed to meet a general sanity test, the
parameters and initial values need to be flexed to determine the sensitivity of the
model results with regard to the choice of parameters and initial conditions. This
process is time consuming and is usually allocated to the drudgery part of modeling.
But it is essential. Just how effective is a model that responds with dramatic
difference when one of its parameters is changed slightly? The point is not whether
sensitivity analysis needs to be done but how can it be done efficiently? Our view is
that STELLA is a very efficient tool for building the structure of the systematical
model and for performing sensitivity analyses.
To conduct a sensitivity analysis, for example on the parameter R of our
population model, choose “Sensi Specs. . .” (Sensitivity Specification) from the
Run pull-down menu, and choose the parameter R—by clicking on it and selecting
it—as the one for which you want to perform a sensitivity analysis. Type in the
dialogue box “# of Runs” 5 to generate five sensitivity runs. Then provide start and
end values for R. If you chose “Incremental” as the variation type, STELLA
calculates the other values from the start and end values that you specified such
that there are equal incremental changes in A from run to run. Plot the five resulting
curves for N in the same graph by choosing the “Graph” option in STELLA II’s
Sensitivity Specs menu. Run the model with the S-Run command and observe the
resulting graph. Here are the results for R varying from run to run incrementally
between 0.05 and 0.15, and a carrying capacity that is specified as
K ¼ 100 þ SINWAVE 10; 12
ð
Þ
ð2:4Þ
The results of this model are shown in Fig. 2.6. Here, we have created one page
in our graph pad that summarizes the five consecutive runs. You can do this by
clicking on the graph that already existed, then selecting a new page for that graph
pad by clicking the triangle that is labeled “New”, and then specifying that this
should serve as a “Comparative” graph (see Fig. 2.7).
34
2 Exploring Dynamic Biological Systems
this form of modeling as the mechanical approach, but this term seems to us too
wooden and likely to leave the impression that we think nature is just another
mechanical process, rather like the engine of an auto. We do not think so.
In systematical modeling, we build into the representation of the phenomenon
that we know actually exists—such as the birth and death processes of populations.
Our systematical alternative therefore starts with an advantage over the purely
statistical or empirical modeling schema. This advantage allows the systematical
model to be used in more related applications than the empirical model—the
systematical model is more transferable to new applications. But the empirical
model does have one advantage: in the process of evaluating the data gathered
about the phenomenon, the mean and standard deviations of the coefficients are
found. The corresponding parameters and initial values in our models are not so
elaborated. Such values are at first usually found or derived from the pertinent
literature, often without a given variation.
Once the systematical model has performed to meet a general sanity test, the
parameters and initial values need to be flexed to determine the sensitivity of the
model results with regard to the choice of parameters and initial conditions. This
process is time consuming and is usually allocated to the drudgery part of modeling.
But it is essential. Just how effective is a model that responds with dramatic
difference when one of its parameters is changed slightly? The point is not whether
sensitivity analysis needs to be done but how can it be done efficiently? Our view is
that STELLA is a very efficient tool for building the structure of the systematical
model and for performing sensitivity analyses.
To conduct a sensitivity analysis, for example on the parameter R of our
population model, choose “Sensi Specs. . .” (Sensitivity Specification) from the
Run pull-down menu, and choose the parameter R—by clicking on it and selecting
it—as the one for which you want to perform a sensitivity analysis. Type in the
dialogue box “# of Runs” 5 to generate five sensitivity runs. Then provide start and
end values for R. If you chose “Incremental” as the variation type, STELLA
calculates the other values from the start and end values that you specified such
that there are equal incremental changes in A from run to run. Plot the five resulting
curves for N in the same graph by choosing the “Graph” option in STELLA II’s
Sensitivity Specs menu. Run the model with the S-Run command and observe the
resulting graph. Here are the results for R varying from run to run incrementally
between 0.05 and 0.15, and a carrying capacity that is specified as
K ¼ 100 þ SINWAVE 10; 12
ð
Þ
ð2:4Þ
The results of this model are shown in Fig. 2.6. Here, we have created one page
in our graph pad that summarizes the five consecutive runs. You can do this by
clicking on the graph that already existed, then selecting a new page for that graph
pad by clicking the triangle that is labeled “New”, and then specifying that this
should serve as a “Comparative” graph (see Fig. 2.7).
34
2 Exploring Dynamic Biological Systems