question at hand. The assumptions, form, and outcomes of the model need
to be realistic for the situation and clearly communicated to the user. Based
upon his experience in using models in courtroom situations, Swartzman
(1996) points out several elements of a mathematical model that allow
effective communication with decision makers.
• The model must make common sense. For example, a Leslie matrix
model (Leslie 1945) is commonly used to analyze population dynamics but
can project infinite growth. To avoid this unbelievable possibility being
discussed in the courtroom, Swartzman (1996) introduced a densitydependent fecundity term into the model.
• A model must be simple enough for the judges, lawyers, and jury
members to understand.
• Jargon must be avoided.
• The model and its projections must be clearly described; simple
illustrative graphics are helpful.
These lessons are general enough to be applicable to mathematical models
that might be applied to environmental decisions. The act of modeling is
often called an art because there are many ways to express observed
relationships using mathematics, and it takes experience, expertise, and
creativity to appropriately capture complex interactions. Because of the
wider use and range of applicability of mathematical models, they are the
focus of this volume.
1.2.2 General Characteristics of Models
Models are a valuable tool for increasing understanding about environmental interactions. They are quantitative and, when run in a deterministic
mode, are repeatable. They are able to integrate known information from
a number of different sources. They can also be adjusted to a desired spatial
and temporal resolution (e.g., a particular locality). However, the sophistication of numerical models often leads to a false sense of confidence and
may inhibit people from questioning the results. In addition, the use of such
models may be costly, time consuming, or require special expertise. Models
need to be validated by comparing projections to field data or historical
conditions, but such a comparison is not always done and may be infeasible in some cases. Backcasting and comparing model results to historical
conditions sometimes offers a useful way to validate a model.
The ability to simulate conditions without disturbing the situation makes
models particularly useful. Although the high variability of natural settings
can confound the interpretation of model results, much of the variability
can be controlled in their use, which enhances the potential for model
experiments and the testing of hypotheses.
Ecological models can be applied to a broad range of spatial and
temporal scales. The specific environmental management issue focuses the
8
Virginia H. Dale
to be realistic for the situation and clearly communicated to the user. Based
upon his experience in using models in courtroom situations, Swartzman
(1996) points out several elements of a mathematical model that allow
effective communication with decision makers.
• The model must make common sense. For example, a Leslie matrix
model (Leslie 1945) is commonly used to analyze population dynamics but
can project infinite growth. To avoid this unbelievable possibility being
discussed in the courtroom, Swartzman (1996) introduced a densitydependent fecundity term into the model.
• A model must be simple enough for the judges, lawyers, and jury
members to understand.
• Jargon must be avoided.
• The model and its projections must be clearly described; simple
illustrative graphics are helpful.
These lessons are general enough to be applicable to mathematical models
that might be applied to environmental decisions. The act of modeling is
often called an art because there are many ways to express observed
relationships using mathematics, and it takes experience, expertise, and
creativity to appropriately capture complex interactions. Because of the
wider use and range of applicability of mathematical models, they are the
focus of this volume.
1.2.2 General Characteristics of Models
Models are a valuable tool for increasing understanding about environmental interactions. They are quantitative and, when run in a deterministic
mode, are repeatable. They are able to integrate known information from
a number of different sources. They can also be adjusted to a desired spatial
and temporal resolution (e.g., a particular locality). However, the sophistication of numerical models often leads to a false sense of confidence and
may inhibit people from questioning the results. In addition, the use of such
models may be costly, time consuming, or require special expertise. Models
need to be validated by comparing projections to field data or historical
conditions, but such a comparison is not always done and may be infeasible in some cases. Backcasting and comparing model results to historical
conditions sometimes offers a useful way to validate a model.
The ability to simulate conditions without disturbing the situation makes
models particularly useful. Although the high variability of natural settings
can confound the interpretation of model results, much of the variability
can be controlled in their use, which enhances the potential for model
experiments and the testing of hypotheses.
Ecological models can be applied to a broad range of spatial and
temporal scales. The specific environmental management issue focuses the
8
Virginia H. Dale