complaint than a fatal criticism, that is, we should be able to model in a contextdependent way when that is needed. We should be able to model in such a way that
the guiding rules in the model shift as the context shifts. We further argue that the
terrific complexity of biological, ecological, and sociological systems can mask the
possibility of simple underlying rules. These rules when used together in a model
might cause the system behavior to appear exceedingly complex. The quest is to
find the underlying rules. Such a quest pushes us well beyond simulation. It is what
we mean by the term “dynamic modeling.”
1.4 Model Components
The most important elements of a system are the state variables. State variables are
indicators of the current status of the system. They are the variables on which all the
other calculations in the model are based. State variables come in two flavors:
conserved and non-conserved. A conserved state variable represents an accumulation or stock of something—water, people, materials, or information. These stocks
are created and destroyed by the results of the control variables in the system. But
non-conserved state variables, such as price and temperature, are also possible.
Clearly, the temperature of a hot body sitting in a cool room will determine the rate
that the body cools. The changing price of a natural resource will signal the changes
in its rate of optimal depletion. To maintain simplicity in the model, strive to
minimize the number of its state variables.
System elements that represent the action or change in a state variable are called
flows or control variables. As a model unfolds in time, control variables update the
state variables at the end of each time step. Examples for control variables are the
rate of flood water inflowing to a reservoir, the rate of water release from that
reservoir, and the rate of water evaporation from its surface—all acting to change
the water contained or “conserved” in the state variable, the reservoir.
The remaining set of variables in any model might be classed as converters or
transforming variables. They take in parameters or perhaps the results of calculations elsewhere in the model and transform these inputs still further. These results
are relayed on to other such transforming variables or to that special class of
transforming variables, the control variables. These interactions in a model are
often classed in terms of feedback—the flow of information from a state variable
through a chain of transforming variables, and ultimately back to the control
variables, change that state variable, and so continue in an ever changing loop,
perhaps finally reaching a steady state or maybe race off to infinity, to zero or to
chaos. The nature of such circulations of information is negative or positive.
Negative feedback tends to force state variables toward goals set up either implicitly or explicitly in the model. Negative feedback leads to balance. Positive feedback tends to do the opposite: it allows variables to reinforce differences rather than
minimize these differences. Positive feedback, as we shall see in the text has some
surprising results. Negative feedback is the basic idea of the controlled dynamic
10
1 Modeling Dynamic Biological Systems
the guiding rules in the model shift as the context shifts. We further argue that the
terrific complexity of biological, ecological, and sociological systems can mask the
possibility of simple underlying rules. These rules when used together in a model
might cause the system behavior to appear exceedingly complex. The quest is to
find the underlying rules. Such a quest pushes us well beyond simulation. It is what
we mean by the term “dynamic modeling.”
1.4 Model Components
The most important elements of a system are the state variables. State variables are
indicators of the current status of the system. They are the variables on which all the
other calculations in the model are based. State variables come in two flavors:
conserved and non-conserved. A conserved state variable represents an accumulation or stock of something—water, people, materials, or information. These stocks
are created and destroyed by the results of the control variables in the system. But
non-conserved state variables, such as price and temperature, are also possible.
Clearly, the temperature of a hot body sitting in a cool room will determine the rate
that the body cools. The changing price of a natural resource will signal the changes
in its rate of optimal depletion. To maintain simplicity in the model, strive to
minimize the number of its state variables.
System elements that represent the action or change in a state variable are called
flows or control variables. As a model unfolds in time, control variables update the
state variables at the end of each time step. Examples for control variables are the
rate of flood water inflowing to a reservoir, the rate of water release from that
reservoir, and the rate of water evaporation from its surface—all acting to change
the water contained or “conserved” in the state variable, the reservoir.
The remaining set of variables in any model might be classed as converters or
transforming variables. They take in parameters or perhaps the results of calculations elsewhere in the model and transform these inputs still further. These results
are relayed on to other such transforming variables or to that special class of
transforming variables, the control variables. These interactions in a model are
often classed in terms of feedback—the flow of information from a state variable
through a chain of transforming variables, and ultimately back to the control
variables, change that state variable, and so continue in an ever changing loop,
perhaps finally reaching a steady state or maybe race off to infinity, to zero or to
chaos. The nature of such circulations of information is negative or positive.
Negative feedback tends to force state variables toward goals set up either implicitly or explicitly in the model. Negative feedback leads to balance. Positive feedback tends to do the opposite: it allows variables to reinforce differences rather than
minimize these differences. Positive feedback, as we shall see in the text has some
surprising results. Negative feedback is the basic idea of the controlled dynamic
10
1 Modeling Dynamic Biological Systems