8.3 Model Implementation
Simulation modeling has traditionally been conducted in the realm of
high-level procedural computer programming, creating programs that can
be difficult to use and that produce complex output. Long time intervals
between the design of a model and its implementation tend to decrease
its relevance and utility. Furthermore, the nature of the code produced
tends to make linking models problematic and prone to error. Emerging
approaches are beginning to overcome limitations in designing, coding, and
linking computer models, allowing more flexible implementation of models
to answer specific questions posed by decision makers.
8.3.1 Approaches and Technologies
8.3.1.1 Markov Models
Markov models represent one widely used approach that underlies many
ecological models. The main advantage (and also the main limitation) of a
Markov model is revealed in the definition of the Markov property: given
the present, the future is independent of the past. In such a model, no information other than the present state is required to predict the future. Markov
models are therefore specified by some initial probability distribution
of states, and a description of the probability of transition from any particular state to some other state at some future time. These transitions are
specified by a transition matrix (for discrete-time models) or a transition
probability-density function (for continuous-state models) of the probabilities of transition from one state to any other state in one time period.
Because Markov models ignore past history, they are relatively easy to
construct from observations of a system. The major limitation is that, in
many cases, history does matter, and projecting the future based solely on
the current state may be quite inaccurate. For example, if a population is
far from demographic equilibrium, then age structure significantly affects
overall population growth rates. The effect of the “baby-boom” generation
(the generation born between 1946 and 1960) on future demographics in
the United States is a good example. Of course, one can extend the state
space of the model by including a sequence of past states within the current
state to make the Markov assumption more appropriate. However, this
greatly increases the dimensionality of the problem and reduces the advantage of the Markov approach.
8.3.1.2 Agent-Based Models
Agent-based models are another class of models related to the Markov
framework. Agent-based approaches simulate the autonomous behavior
of agents (individuals) by constructing rules governing the physiology
and behavior of those individuals. As the agents act according to the rules
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Eric Gustafson et al.
Simulation modeling has traditionally been conducted in the realm of
high-level procedural computer programming, creating programs that can
be difficult to use and that produce complex output. Long time intervals
between the design of a model and its implementation tend to decrease
its relevance and utility. Furthermore, the nature of the code produced
tends to make linking models problematic and prone to error. Emerging
approaches are beginning to overcome limitations in designing, coding, and
linking computer models, allowing more flexible implementation of models
to answer specific questions posed by decision makers.
8.3.1 Approaches and Technologies
8.3.1.1 Markov Models
Markov models represent one widely used approach that underlies many
ecological models. The main advantage (and also the main limitation) of a
Markov model is revealed in the definition of the Markov property: given
the present, the future is independent of the past. In such a model, no information other than the present state is required to predict the future. Markov
models are therefore specified by some initial probability distribution
of states, and a description of the probability of transition from any particular state to some other state at some future time. These transitions are
specified by a transition matrix (for discrete-time models) or a transition
probability-density function (for continuous-state models) of the probabilities of transition from one state to any other state in one time period.
Because Markov models ignore past history, they are relatively easy to
construct from observations of a system. The major limitation is that, in
many cases, history does matter, and projecting the future based solely on
the current state may be quite inaccurate. For example, if a population is
far from demographic equilibrium, then age structure significantly affects
overall population growth rates. The effect of the “baby-boom” generation
(the generation born between 1946 and 1960) on future demographics in
the United States is a good example. Of course, one can extend the state
space of the model by including a sequence of past states within the current
state to make the Markov assumption more appropriate. However, this
greatly increases the dimensionality of the problem and reduces the advantage of the Markov approach.
8.3.1.2 Agent-Based Models
Agent-based models are another class of models related to the Markov
framework. Agent-based approaches simulate the autonomous behavior
of agents (individuals) by constructing rules governing the physiology
and behavior of those individuals. As the agents act according to the rules
140
Eric Gustafson et al.