25. Ecosystem Modeling
proximation and to vary the calculation interval to
optimize computational speed to solve the appropriate and desired accuracy of approximation (see
Patten 1971; Beltrami 1987).
Figure 25.3 illustrates the dynamic response of
the Silver Springs model in Equation 20.20 under
several diagnostic conditions. Figure 3A shows
what is termed the forced response of the system.
In this case, the dynamics of the system is determined for a case in which the initial values or initial
conditions of the compartments are all set to zero.
The inputs of the system or forcings are set to their
normal values. The dynamics that are shown are
analogous to a case in which the material (or energy) going into a system is labeled in some way
from a particular time onward and the dynamics of
this new, labeled material as it replaces the old, unlabeled material is followed.
Figure 25.3B illustrates the free response of the
Silver Springs model. In this case, the compartment
state variables begin the simulation with the values
that one would expect them to have at equilibrium,
and the input terms in the equations are set to zero.
The dynamics are analogous to those expected if
all material in the system were labeled and the rate
at which this labeled material was flushed out of
the system is equaled by the input of new, unlabeled
material. Figure 25.3C is the impulse response of
the system. This response has its analog in a rapid
injection of labeled material into an otherwise unlabeled system.
Compartment models are appealing for ecological studies for several reasons. First, they are mathematically tractable. The procedures for estimating
the parameters for such models are well developed
in several fields (applied mathematics, physics, engineering). Historically, these invited procedures
were transferred to ecosystem studies. Compartment models also appeared to predict certain aspects of ecological systems, particularly the movement of radioactive materials through a variety of
aquatic and terrestrial ecosystems. The development of the atomic bomb, nuclear industry and concern about radioactive pollution inspired considerable interest in the movement of radioisotopes
through ecosystems. The experimental (and in
some cases, accidental) application of isotopes to
laboratory and field systems ("radioecology") was
an important aspect of ecology in the 1950s and
1960s. For materials such as radioisotopes and trace
381
substances of various kinds, compartment models
have proven to have reasonable predictive ability
(given an appropriate parameterization).
Analysis Phase
The analysis phase of ecosystem modeling tends to
focus on two questions:
1. How credible is the model as a representation of
the ecosystem? This leads to issues of model
validation.
2. What do features of the models tell us about the
real system? This leads to considerations of the
theoretical implications of formal analyses of
the models and to application of the models to
predict changes in the system under novel and/or
future conditions.
The complexity of these considerations can be
great, but it is worthwhile to identify some of the
key issues.
Model Validation
In determining model credibility, Mankin et al.
(1977) and Shugart (1984) divided model testing
into two basic types of procedures (verification and
validation) and saw model application as a measure
of a model's usefulness. In verifying a model, the
model is tested on whether it can be made consistent with some set of observations. In validation
procedures, a model is tested on its agreement with
a set of observations independent of those observations used to structure the model and estimate its
parameters. When testing a model, it can be important that it can simulate ecosystem change under
the constraint that all parameters in the model are
realistic (Shugart 1984).
Sensitivity Analysis
The basic aim of sensitivity analysis is to document
the pattern of variation in the state variables or system responses to small changes in the model parameters. The usual objective of sensitivity analysis
is to determine which parameters in a model are
"important" with respect to developing better measurements. Sensitivity analysis also provides insights into theories on system structure and control
proximation and to vary the calculation interval to
optimize computational speed to solve the appropriate and desired accuracy of approximation (see
Patten 1971; Beltrami 1987).
Figure 25.3 illustrates the dynamic response of
the Silver Springs model in Equation 20.20 under
several diagnostic conditions. Figure 3A shows
what is termed the forced response of the system.
In this case, the dynamics of the system is determined for a case in which the initial values or initial
conditions of the compartments are all set to zero.
The inputs of the system or forcings are set to their
normal values. The dynamics that are shown are
analogous to a case in which the material (or energy) going into a system is labeled in some way
from a particular time onward and the dynamics of
this new, labeled material as it replaces the old, unlabeled material is followed.
Figure 25.3B illustrates the free response of the
Silver Springs model. In this case, the compartment
state variables begin the simulation with the values
that one would expect them to have at equilibrium,
and the input terms in the equations are set to zero.
The dynamics are analogous to those expected if
all material in the system were labeled and the rate
at which this labeled material was flushed out of
the system is equaled by the input of new, unlabeled
material. Figure 25.3C is the impulse response of
the system. This response has its analog in a rapid
injection of labeled material into an otherwise unlabeled system.
Compartment models are appealing for ecological studies for several reasons. First, they are mathematically tractable. The procedures for estimating
the parameters for such models are well developed
in several fields (applied mathematics, physics, engineering). Historically, these invited procedures
were transferred to ecosystem studies. Compartment models also appeared to predict certain aspects of ecological systems, particularly the movement of radioactive materials through a variety of
aquatic and terrestrial ecosystems. The development of the atomic bomb, nuclear industry and concern about radioactive pollution inspired considerable interest in the movement of radioisotopes
through ecosystems. The experimental (and in
some cases, accidental) application of isotopes to
laboratory and field systems ("radioecology") was
an important aspect of ecology in the 1950s and
1960s. For materials such as radioisotopes and trace
381
substances of various kinds, compartment models
have proven to have reasonable predictive ability
(given an appropriate parameterization).
Analysis Phase
The analysis phase of ecosystem modeling tends to
focus on two questions:
1. How credible is the model as a representation of
the ecosystem? This leads to issues of model
validation.
2. What do features of the models tell us about the
real system? This leads to considerations of the
theoretical implications of formal analyses of
the models and to application of the models to
predict changes in the system under novel and/or
future conditions.
The complexity of these considerations can be
great, but it is worthwhile to identify some of the
key issues.
Model Validation
In determining model credibility, Mankin et al.
(1977) and Shugart (1984) divided model testing
into two basic types of procedures (verification and
validation) and saw model application as a measure
of a model's usefulness. In verifying a model, the
model is tested on whether it can be made consistent with some set of observations. In validation
procedures, a model is tested on its agreement with
a set of observations independent of those observations used to structure the model and estimate its
parameters. When testing a model, it can be important that it can simulate ecosystem change under
the constraint that all parameters in the model are
realistic (Shugart 1984).
Sensitivity Analysis
The basic aim of sensitivity analysis is to document
the pattern of variation in the state variables or system responses to small changes in the model parameters. The usual objective of sensitivity analysis
is to determine which parameters in a model are
"important" with respect to developing better measurements. Sensitivity analysis also provides insights into theories on system structure and control