Is it Modeling or Modelling

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Introduction to Ecological modelling

• Is it Modeling or Modelling ??
• Google (an empirical approach to correct
  spelling)
• 28,700 hits on Ecological Modeling
• 38,500 hits on Ecological Modelling

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Modelling general
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What is a model?

• a relationship between variables
• an abstraction of reality
• expression of essential elements of a problem in
  mathematical terms
• terms model, prediction, theory, statistics often
  used interchangeablyappropriately?

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You model every day!
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or you are exposed to models every day

• predicting the presidential favorite is based on
  a representative sample or model of the
  entire population
• the food pyramid is a model of good nutrition
  (though not a very good one)
• As you leave this building, think about your
  actions how they are really based on our
  intuitive models of the world built from
  experience.
• For example, we cross the street at intersections
  when opposing traffic is supposed to stop - a
  good model most of the time. If it wasnt a
  model, if our decisions were based on complete
  information about our world, people would never
  get hit by cars. (And cars would never hit
  people.)
• Jaywalking is a more complex intuitive model,
  more variables than waiting at the intersection
• whether or not to jaywalk subconsciously, our
  minds do the math

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Jaywalking
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Jaywalking (cont)
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Jaywalking (cont)
So what? 1. Models are all around us 2. Models
can always be more detailed 3. Models can never
be perfected (always make assumptions) 4.
Insights often come from mathematical
representations
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Why do we model?

• Because its impossible to know everything about
  a system

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Why do we model? (cont)

• reduce a complex phenomenon in a way that makes
  it is easier to understand, discuss, and compare
  to others
• identify the most salient parts of the phenomenon
  in question
• describe the important relationships among these
  salient parts
• reveal weaknesses in our knowledge, therefore
  provide mechanism for identifying research
  priorities
• useful in tests of hypotheses

modified from U of Texas, Grad School of Library
Info Science, and Jorgensen and Bendoricchio
(2001)
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Famous models

• spherical earth still modeled today and its
  not round!
• heliocentric solar system Copernicus
• atomic structure Bohr
• general relativity Einsteins theory of
  gravitation
• DNA structure Watson, Crick, Wilkins, Franklin
• standard model many contributors

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Future models

• Protein folding proteins self-assemble almost
  instantaneously from a linear sequence of AA into
  their proper 3D structure. How? What tells this
  string of AAs to form in just the right way?
  (Important for medicine, drug development)
• Theory of everything seeks to explain the four
  primary forces in nature by merging general
  relativity with the standard model of elementary
  particles and their interactions

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Modelling often associated with mathematics or
the act of codifying

• Modelling approach
• the process
• (Whats your question? How do you get there?)

Modelling techniques e.g. individual-based v.
dynamic v. neural networks (varies depending on
the approach)
Modelling tools e.g. statistical / mathematical
software, programming languages (varies
depending on the technique)
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Approach to modeling
Define problem
Conceptual Diagram
Parameterization
Validation
Evaluation
Simplified from Jorgensen and Bendoricchio
Urban
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Modelling techniques

• Mathematical v. verbal v. meso-realistic
• the statement 20 of what politicians say is
  true is a verbal model
• We have a lab meeting in ½ hour. Thats plenty
  of time to read the paper.
• Many classes
• Many approaches

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Many classifications..
Modelling techniques (cont)

• Paired
• Deterministic predicted values computed exactly
• Stochastic predicted values depend on
  probability distribution
• Reductionist includes many (ones hopes relevant)
  details
• Holistic relies on general principles
• Static variables describing the system not
  dependent on time
• Dynamic time dependent
• Distributed parameters considered functions of
  time and space
• Lumped parameters within certain pre-defined
  time and space, constant
• Linear first degree equations are used
  consecutively
• Non-Linear includes non-proportional
  relationships
• Other

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Many approaches.
Modelling techniques (cont)

• Statistical
• Regression
• Analysis of variance
• Mathematical
• Matrix
• Compartment
• Structural equations (SEM)
• Genetic/evolutionary algorithms (GARP)
• Individual-based
• Cellular automata
• Classification and regression tree analysis
  (CART)

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Modelling techniques (cont)

• As a result, models often described as a chain of
  adjectives
• e.g., our model of the onset of migration is a
  stochastic, individual-based, simulation model
• ..of course we can go to far.
• stochastic, dynamic, reductionist, iterative,
  convergent, individual-based, simulation model

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Too many models?

• May end up with many competing model solutions to
  one modelling problem
• Which model is best? How do you choose?
• AIC
• Akaikes information criterion
• from information theory
• method for selecting among competing models
• has become very popular in recent years

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Modeling tools

• Virtually any software that aids in calculation
• Vary in specificity for modeling
• Generalized software
• Greater flexibility, higher learning curve
  (more complicated syntax), faster, closer to the
  math
• High level languages (C, C, Java)
• Statistical packages (SPSS, SAS, S)
• Math oriented (MATLAB, Mathematica)
• Specialized software
• Less flexible, lower learning curve (no or
  little coding), slower, further from the math
  (graphical representation of relationships)
• Stella
• Madonna (Mac)
• Simile
• Vortex

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Ecological Modelling
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• Is there a father of ecological modelling?
• Not really, but it turns out Eugene P. Odum has a
  brother
• Howard T. Odum
• widely respected among ecological modelers
• Died in 2002 tribute in 2004
• International Society for Ecological Modelling
  (http//www.isemna.org/)
• and related journal Ecological Modelling
• mediocre

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Why do we model in ecology?

• Todays computing allows it
• .. but mostly..
• To gain insights into complex systems and
  behavior.
• species conservation (extinction probabilities)
• wildlife management (setting harvest limits)
• human impacts (disease transmission - WNV)
• basic ecology (scaling, predation, competition)
• Just one of many useful tools, so beware.
• When you have a new hammer, everything looks like
  a nail.
• - old Russian proverb

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The very definition of ecology evokes a
complexity that is poorly understood
Ecology the study of how organisms interact with
each other and their environments
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Trophic relationships

• How strong are the
• interactions between
• these species?
• How do these interactions
• change if we remove/add a
• species? (Do species
• matter?)
• How do these interactions
• change as species vary in
• number?
• Ecologists use highly simplified model food webs
  to study these questions.
• Many say too simplified.

Aquatic food web
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We often use model systems in ecology

• Mesocosms simplified or model ecosystems that,
  when used in scientific experimentation, allow
  greater control and understanding of ecological
  relationships
• e.g., the classic tribolium beetle experiment
• studies of ecosystem function, the role of
  biological diversity, understanding species
  interactions

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Approach to modeling (revised)
Define problem
Conceptual Diagram
Mathematical formulation
Parameterization
Verification
Sensitivity analysis
Calibration
Validation
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Systems approach

• get mind around the big picture and work in
• all models have bounds
• relationships between organisms are so numerous
  and poorly understood, models must be bounded for
  simplicity
• e.g.
• Spatially this landscape only, please
• Temporally spring
• limit number of interactions one predator, two
  prey
• limit to first order effects ignore indirect
  effects?
• more complex models get divided into logical
  subsystems
• e.g.
• the animal dispersal subsystem
• foraging subsystem

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Parsimony?

• Defined simplest assumption in the formulation
  of a theory or in the interpretation of data
• Does Ockhams razor apply to model development?
• Is always unexplained variation
• Adding complexity with the goal of explaining
  additional variation is justified
• However....
• tend to work from the top down, beginning with
  variables that explain the greatest variance
• We may not have detailed knowledge of variables
  that explain less variation (more obscure
  variables are likely supported by less data)
• All parameters have error therefore more
  parameters increases model uncertainty by
  contributing to error propagation
• Diminishing returns variance explained may be
  small relative to uncertainty in estimates
• In principle, should have data for state
  variables success of later stages of model
  development linked to data quality

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Jorgensen decomposes the math of environmental
modelling into 5 elements

• Forcing functions
• External variables that influence ecosystems
• E.g. climate, weather
• State variables
• Describe the ecosystem
• E.g. if were modelling the effects of
  agricultural runoff on trophic relationships in
  aquatic systems, state variables would be the
  species at different trophic levels and nutrient
  concentration
• Mathematical equations
• Represent the biological and physical processes
• can describe the relationship between external
  forcings and state variables
• E.g. nutrient load per unit volume in water, Nc,
  in aquatic systems is proportional to rain
  accumulation, R,
• Nc R (I dont have a proportional to symbol
  so we go with )

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Five elements (cont)

• Parameters
• Coefficients in the mathematical representations
  of processes
• they may be constants within specific ecosystems
• e.g. proportion of rain water, p, entering
  aquatic systems (aka runoff accumulation) is
  f(slope, distance from water, soil type, etc) and
  nutrient load per unit volume of runoff, Nr, is
  f(agricultural treatment, nutrient saturation of
  the soil, etc),
• Nc NrpR
• Constants
• Universal constants
• E.g. speed of light, atomic weights (none of
  these in our example), so we get,
• Nc NrpR / (Vw pR), where Vw is the volume
  of the body of water

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Example genetic structure in jack pine (for
context, see Young and Merriam 1994, Young et al.
1993)

• How does forest fragmentation influence
  relatedness among conspecifics of Pinus banksiana
  (jack pine)?
• gametes disperse via seed and pollen
• cones serotinous, short dispersal
• pollen annual, abundant, wind dispersed
• greatest potential to project genetic material
  long distances
• Does fragmentation facilitate or inhibit the
  movement of pollen?

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Pollen density model - linear, no feedback -

• Does fragmentation facilitate or inhibit the
  movement of pollen?
• compare pollen dispersal through fragmented and
  unfragmented landscape matrices

Continuously forested
Fragmented
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Pollen density model - linear, no feedback -

• map pattern of fragments to nearby continuous
  forest
• some proportion of wind dispersed pollen that
  leaves patch A will arrive in the area of patch B
• if pollen movement through landscape matrices
  differs, so should this proportion
• so at patch B, we want to model the density of
  pollen from patch A

B
B
A
A
Continuously forested
Fragmented
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Pollen density model - linear, no feedback -
Environmental/forcing variables
State variables
Process variables (parameters)
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Pollen density model (cont)
Specifying the model
Source stem density, age, etc
Source airborne pollen density
Target airborne pollen density
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Pollen density model (cont)
Bounding the system - in retrospect -
Source pollen production
Source airborne pollen density
Target airborne pollen density

• Already bounded in space (previous figure)
• Interested in movement of pollen between habitats
• We need to know source airborne pollen density
• Do we need to model source pollen production or
  the mechanisms of pollen release?
• Production can be measured directly in the field
• Model development is an
  iterative process !

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Pollen density model (cont)
Dispersal sub-model
Pollen proportion to distance
Prevailing wind speed
Target patch distance
Pollen settling rate
Pollen dispersal
Landscape matrix
Pollen proportion in direction
Prevailing wind direction
Target patch direction
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Pollen density model (cont)
Weaknesses? Assumptions?
Pollen proportion to distance
Prevailing wind speed
Target patch distance
Pollen settling rate
Pollen dispersal
Landscape matrix
Pollen proportion in direction
Prevailing wind direction
Target patch direction
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Pollen density model (cont)

• How do we verify airborne pollen density at the
  target location?
• genetic studies (enough generations?)
• How do we calculate
• pollen release?
• possible to build empirical relationships
• settling rate?
• Topographic relief
• Sources differ in pollen
• Competing hyhpothses

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For next class.

• outline a research question that frames a good
  modelling problem use own research
• Candidate ecological models have many of the
  following characteristics
• Good question The scientific question the model
  seeks to address remains unanswered or poorly
  addressed in the literature
• Sufficient data There is sufficient data on the
  biology supporting the model so as to minimize
  assumptions
• Sound ecology Potential ecological mechanisms
  and relationships are known (e.g. gape limitation
  in fish predation)
• Best approach Addressing the question by other
  means (e.g. field research) is impractical
  financially, logistically, etc. or is a successor
  to modelling
• construct a conceptual diagram of the ecological
  relationships in your candidate model
• this lecture will be on the web if needed
• We will discuss in 2 weeks