The Nature of Modeling and Modeling Nature

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The Nature of Modelingand Modeling Nature
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Role Models on the Role of Models

• The sciences do not try to explain, they hardly
  even try to interpret, they mainly make models
  The justification of such a mathematical
  construct is solely and precisely that it is
  expected to workthat is, correctly to describe
  phenomena from a reasonably wide area.
• John Von Neumann

von Neumann
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(No Transcript)
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Models

• What is modeling all about? Is it
• My feeling is no.
• Modeling is about
• abstraction
• simplification
• isomorphism (e.g., being able to envision
  fundamental similarities between different
  systems)
• This need not be mathematical. In a very real
  sense, we all approach our study systems through
  models, as we
• generally work within frameworks of abstracted
  hypothetical mechanisms.
• cannot possibly entertain all details of the
  system.

?
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A Broad Umbrella

• Verbal
• Graphical
• Statistical
• Computer-based
• Mathematical

Competitive Exclusion Principle
Complete competitors cannot coexist (Hardin,
1960)
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How much simplification?
CONTINUUM

• Detail-rich
• Specific in target
• Parameter values (or sensitivities to changes in
  these values) become important
• Predictions are narrow
• Empirical tests can be quantitative

• Highly abstracted
• General in target
• Relations between parameter values take
  precedence over their specific values
• Predictions are broad
• Empirical tests are often qualitative

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Why Toys?
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So, whats the point?

• Must a model make testable predictions in order
  to be valuable?
• Is Hardins competitive exclusion principle (and
  Newtons laws of motion, Hubbells neutral
  theory, etc.) truly untestable?
• Forming a model is very much like creating a
  virtual world.
• Claims made about this virtual world need to
  logically follow from assumptions (mathematics is
  a useful tool here)
• This virtual world in essence becomes an
  experimental system (we ask what happens when we
  wiggle that parameter or fix that variable)
• One concern is whether our virtual world tells us
  useful things about the real world
• Are the assumptions of the model satisfied or
  violated?
• Does the structure of the model reflect (aspects
  of) reality?
• Does the model suggest new empirical directions?
• One might suggest an iterative algorithm when it
  comes to modeling The form of the virtual world
  is dependent on empirical findings and future
  empirical work is informed by this virtual world.

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But why math?

• The major advantages of a mathematical model are
• The virtual world is very well-defined (e.g.,
  Hardins C.E.P. verbal model is ambiguous)
• The assumptions are (at least implicitly) made
  clear
• Mathematical techniques address dynamics that we
  may not be able to intuit (e.g., feedback,
  network behavior, multiple spatial or temporal
  scales, etc.).
• Example (Buss Jackson 1979)
• Buss Jackson claimed that as A grows faster and
  faster, it will exclude B and C
• A mathematical model (Frean Abraham, 2002) of
  an abstracted version of this system shows this
  plausible conclusion to be off the mark. These
  authors find that as A chases B faster, this
  liberates C with a net negative effect on A!
• One intuition (faster growth means better
  competitive ability) is supplanted by another
  (the enemy of my enemy is my friend).
  Mathematics helps tease such intuitions apart.

A
A
C
B
C
B
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Questions

1. What do you think models are?
2. What role do models play in the context of
   science?
3. What role do models play in the context of
   ecology?
4. What role are models likely to play in your own
   research?
5. How central is accurate prediction to the worth
   of a model in your eyes?  Are you convinced that
   models can play other roles (e.g., exploring
   possibilities, forming baselines for more complex
   systems, inspiring empirical/experimental
   directions, and providing explanations for
   phenomena)?
6. In the case of Hardins (1960) essay, if the
   competitive exclusion principle is taken to be a
   verbal model, what do you think its worth is? How
   does it relate to competition in laboratory or
   natural ecosystems? How do you react to Hardins
   statement that the truth of the principle
   cannot be established by empirical facts?  Do you
   think this principle has something to offer those
   studying competition in the field?  Are you
   convinced that the principle uncovers isomorphic
   behavior in a number of different systems
   (ranging from economics to genetics)?