modeling is to “discover” the hopefully few rather simple underlying principles that
together bring the observed complexity. This is our meaning of simplicity.
Each element of the model is specified by initial conditions and the computer
works out the system’s responses according to the specified relations among the
model elements. The initial conditions may derive from actual measurement, such
as the number of people living on an island, or estimates, such as estimates of the
number of voles living in a specific garden. The estimates, in turn, could be derived
from empirical information or even reasonable guesses by a modeling team. Models
built on such uncertain parameters may still be of great value, providing a picture of
a particular processes, rather than exact information. Documentation of the parameters and assumptions, always necessary at each step in the modeling process, is
important when the modeler’s judgment is used.
In the end, models can be no better than the modelers. Hence the elegant
statement by Botkin [4] is very appropriate,
by operating the model the computer faithfully and faultlessly demonstrates the implications of our assumptions and information. It forces us to see the implications, true or false,
wise or foolish, of the assumptions we have made. It is not so much that we want to believe
everything that the computer tells us, but that we want a tool to confront us with the
implications of what we think we know.
1.3 Analogies, Anomalies, and Reality
For many years, physicists have known of the analogous relations between the
principle variables in the basic equations of hydraulics, electricity, and mechanical
systems. Force, springs, dampers, inertia, velocity, and displacement have their counterparts in voltage, current, resistance, inductance and capacitance and again pressure,
mass flow, frictional loss, and vorticity. Coulomb apparently was convinced that the
attractive force between charged particles was of the same form as the gravitational
attraction between planetary bodies, put forth by Newton centuries before. These
analogies are more than curiosities. They show a common worldview of such important phenomena. As scientists developed each of these disciplines in their turn, they
recognized the heritage of hard-won successes in describing parts of the real world.
Not only were these analogies useful in physics and engineering, but it is well
known that the great economist Walras produced his equations of the economy
from the principles of hydraulics. Before him, the medical doctor and physiocratic
economist Quesnay divined his input–output tables of the French economy from an
analogy with the circulation of blood in the body. Analogy, carried to the right level
of detail, is the cornerstone if not the foundation of the creative enterprise.
Analogies abound between economics, biology, and chemistry. For example, the
most common production functional form used in economics is:
Rate of Production ¼ Q ¼ AL
α K
β
ð1:1Þ
8
1 Modeling Dynamic Biological Systems
together bring the observed complexity. This is our meaning of simplicity.
Each element of the model is specified by initial conditions and the computer
works out the system’s responses according to the specified relations among the
model elements. The initial conditions may derive from actual measurement, such
as the number of people living on an island, or estimates, such as estimates of the
number of voles living in a specific garden. The estimates, in turn, could be derived
from empirical information or even reasonable guesses by a modeling team. Models
built on such uncertain parameters may still be of great value, providing a picture of
a particular processes, rather than exact information. Documentation of the parameters and assumptions, always necessary at each step in the modeling process, is
important when the modeler’s judgment is used.
In the end, models can be no better than the modelers. Hence the elegant
statement by Botkin [4] is very appropriate,
by operating the model the computer faithfully and faultlessly demonstrates the implications of our assumptions and information. It forces us to see the implications, true or false,
wise or foolish, of the assumptions we have made. It is not so much that we want to believe
everything that the computer tells us, but that we want a tool to confront us with the
implications of what we think we know.
1.3 Analogies, Anomalies, and Reality
For many years, physicists have known of the analogous relations between the
principle variables in the basic equations of hydraulics, electricity, and mechanical
systems. Force, springs, dampers, inertia, velocity, and displacement have their counterparts in voltage, current, resistance, inductance and capacitance and again pressure,
mass flow, frictional loss, and vorticity. Coulomb apparently was convinced that the
attractive force between charged particles was of the same form as the gravitational
attraction between planetary bodies, put forth by Newton centuries before. These
analogies are more than curiosities. They show a common worldview of such important phenomena. As scientists developed each of these disciplines in their turn, they
recognized the heritage of hard-won successes in describing parts of the real world.
Not only were these analogies useful in physics and engineering, but it is well
known that the great economist Walras produced his equations of the economy
from the principles of hydraulics. Before him, the medical doctor and physiocratic
economist Quesnay divined his input–output tables of the French economy from an
analogy with the circulation of blood in the body. Analogy, carried to the right level
of detail, is the cornerstone if not the foundation of the creative enterprise.
Analogies abound between economics, biology, and chemistry. For example, the
most common production functional form used in economics is:
Rate of Production ¼ Q ¼ AL
α K
β
ð1:1Þ
8
1 Modeling Dynamic Biological Systems