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3.2. Modeling
3.2.1. Definition of a model
3.2.1.1. Abstract representation of a real system
  • A simplification of a real system

  • Is itself a system

  • Behaves like a real system in certain respects

  • Features depend on objectives

  • Infinite number of valid models for same system

  • Form may be 3-dimensional physical model, graph, flow chart, equation, or computer model
3.2.1.2. In pest management a model is generally a quantitative representation of the real system (an hypothesis about the behavior of the system expressed mathematically)
  • Analytical vs. simulation (numerical)

  • Descriptive vs. mechanistic (explanatory)

  • Static vs. dynamic

  • Deterministic vs. stochastic
3.2.1.3. Level of organization
(e.g. biosphere: ecosystem: population: organism: organ: tissue: cell: organelle)
3.2.2. Reasons for modeling
3.2.2.1. Organizational
  • Helps to identify the components of a complex system and clarify their relationships

  • Helps to identify missing or inadequate information

  • Sensitivity analysis -- look at changes in behavior of model resulting from small adjustments of parameters or changes in structure

  • Helps set research priorities
3.2.2.2. Emergent properties (not predictable from understanding separate components)
  • Examine specific responses to stimuli never observed before

  • Model failure leads us to question our assumptions

  • Can compress time

  • Can conduct "experiments" that would be illegal, immoral, impractical, or impossible with a real system
3.2.3. Steps in computer simulation modeling (follow same steps as in systems analysis)
3.2.3.1. Define the system
  1. Identify components, interactions, constraints

  2. Determine variables--uncontrollable or controllable? If controllable, controlled or uncontrolled? Internal or external variables? (endogenous or exogenous)
3.2.3.2. Define the objectives
  1. Since the structure of the model depends on its objectives, it is important to explicitly state the objectives at the outset

  2. The objectives must take account of the use of the model and its users
3.2.3.3. Create a conceptual model
  1. Identify the important components of the system that must be included in the model

  2. Determine how these components interact (the structure of the model)

  3. Diagram the model structure -- this serves to clarify the modeler's ideas for the modeler herself/himself as well as to communicate them to others
3.2.3.4. Develop mathematical models to describe the interactions of the major components
3.2.3.5. Write the computer program
  1. The program steps through time, changing the values of the state variables with each step

  2. The mathematical equations are translated into algorithms in a high-level programming language, such as BASIC, Fortran, Pascal, or C. Recently, new modeling tools have been developed that do not require learning a programming language. (e.g., "SIMULINK," "Modelmaker," and "Prophesy!" for the PC and "Stella" for the Macintosh)

  3. There is a state equation for each state variable, describing how its state changes with each time step

  4. Rate equations describe the flows of material and of information in the system

  5. The program includes a user interface that controls the input and output of the model
3.2.3.6. Model validation (performance evaluation)
  • Before it can be trusted as a research or management tool, a model must be validated

  • Validation is the comparison of the behavior of the model with the behavior of the real system under the same conditions

  • The data set used for validation must be different from the one used for model construction and parameterization

  • Validation can be a simple visual comparison of the predicted and observed values (do they rise and fall together?) or a more rigorous statistical test, such as the regression of predicted values versus observed values (a straight line with a slope of 1.0)
3.3. Computer simulations in pest management

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