• An abstraction or simplification of reality
 
• A description of the essential elements of a problem and their relationships
 
• A reconstruction of nature for the purpose of study (Levins 1968)
 
• "A model is a caricature of nature ...... the simpliest version of nature can be perturbed numerically with its responses being indications of the directions nature may take" (Scavia, Lang and Kitchell 1988).
 

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Reality vs. Abstraction/Simplification

2. WHAT IS A SYSTEM? 

• An organized collection of interrelated physical components characterized by a boundary and functional unity
 
• A collection of "communicating" materials and processes that together perform some set of functions
 
• An interlocking complex of processes characterized by many reciprocal cause-effect pathways
 
• Any collection of interacting objects or processes
 
• Any phenomenon, either structural or fuctional, having at least 2 separable components and some interaction between these components
 

3. TYPES OF MODELS 

1) Physical vs. Symbolic (or abstract) Models
 
Physical: a scaled-down (or, less frequently, scaled-up) physical replicas of a real system

Symbolic: verbal, written language, or mathematical 

2) Dynamic vs. Static Models


Dynamic: with time varying variables

Static: time invariant 

3) Empirical (Correlative) vs. Mechanistic (Explanatory) Models


Empirical: without internal dynamics; descriptive; prediction

Mechanistic: with internal dynamics; explanatory; understanding/prediction

Whether a model is empirical or mechanistic is often relative, depending on the level of detail or the scale of observation. 

4) Deterministic vs. Stochastic Models


Deterministic: with no random variables; point estimation of parameters

Stochastic: with one or more random variables; estimation of parameter variations (e.g., mean, variance, distribution)   

5) Simulation vs. Analytical Models


Analytic models: pencil and paper; solvable in closed form analytically; relatively complicated mathematics; greater mathematical power and usually higher generality

Simulation models: use of computers; relatively simpler mathematics; usually less generality and more realism

  

4. WHY MODELS?

• Prediction
 
• Understanding
 
• Generate and test hypotheses
 
• Synthesis
 
• Identify areas of ignorance
 
• Serve as management tools 

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"The basic unit of theoretical investigation is the model" (Levins 1968).

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Different from the traditional reality-model-reality cycle view, Levin asserted that theoretical ecology and empirical ecology draw strength and inspiration from each other, but develop with some degree of independence. Theoretical investigation and observation should be considered equally important as intellectual exercises, but the bridges between them are imperative for either of them to be fruitful.


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Four Phases in Ecological Modeling

Phase 1: Conceptual model formulation
 
• Define the problem
• Specify model objectives
• Delineate system boundaries
• Construct causal diagrams
• Understand feedback loop structure

Phase 2: Quantitative model specification 


• Select general quantitative structure for the model
• Choose basic time step for simulations
• Identify functional forms of model equations
• Estimate parameters of model equations
• Code model equations for the computer
• Execute baseline simulation
• Present model equations 

Phase 3: Model evaluation

• Components of model evaluation
• Model verification
• Model validation 

Phase 4: Model application


• Develop and execute experimental design for simulations
• Analyze and interpret simulation results
• Examine additional types of management policies or environmental situations
• Communicate simulation results 

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An Example: Human Population Dynamics

• Problem: Human population explosion
 
• Objective: To predict world population growth in the next 50 years
 
• Data available (1994):
• World population in 1994 = 5.6 billion
• Global annual birth rate = 2.5% (= 0.025)
• Global annual death rate = 0.9% (= 0.009)
• Global annual growth rate = 0.016
 
• Model assumptions:
• Unlimited resources
• Equal distribution of resources
• The same growth rate will continue...
 
• Model construction and evaluation:
• Analytical vs. Simulation Models
• Doubling Time
• Why populations behave the way as they do?
• Genral population patterns
• Historical record

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• Exponential Growth Model

• Mathematical model
• Behavior
 
• Logistic Growth Model
 
• Competition Models
 

• Predator-Prey Models
 
• Ecosystem Models
• Phytosynthesis
• Nutrient cycling
• Energy flow
• Silver Spring ecosystem model
• STELLA version
 
• Landscape Models
• Spatial modeling
• What is GIS?
• View
• Overlay
• Applications: Land use planning
• Forestry / Ecosystem Management
• Environmental Management