Pattern-Oriented Modeling

EES 4760/5760

Agent-Based & Individual-Based Computational Modeling

Jonathan Gilligan

Class #20: Monday, March 26 2018

Pattern-Oriented Modeling

Pattern-Oriented Modeling

pattern

The Modeling Cycle

The Modeling Cycle

The Modeling Cycle

The Modeling Cycle

Validatioon and Verification

Goals of Modeling

  • Goals:
    • Models are “sufficiently good” representations of real counterparts
    • Learn about real world:
      • Capture essential elements of real system’s internal organization
      • Capture generative mechanisms that produce structure and behavior of real systems

Problem: Validation and Verification

  • Version 1:
    • The model mimics the real world well enough for its stated purpose
  • Version 2
    • We can place confidence in inferences about real system based on model results

E.J. Rykiel “Testing ecological models: The meaning of validation” Ecological Modeling 90, 229 (1996)

Starling Flocks

starling flocks

H. Hildenbrandt et al., “Self-organized aerial displays of thousands of starlings: a model,” Behav. Ecol. 21, 1349–-1359 (2010).

Validation of Starling Model

starling validation

H. Hildenbrandt et al., “Self-organized aerial displays of thousands of starlings: a model,” Behav. Ecol. 21, 1349–-1359 (2010).

Fundamental Problem

  • Our model might reproduce the right pattern for the wrong reasons
  • How can we be sure to capture the real generative mechanisms?
  • How can we design models so that we can optimize model complexity?

The Medawar Zone

P. Medawar:

Optimal level of difficulty for a good research problem:

  • Not difficult enough:
    • Result is trivial, uninteresting.
  • Too difficult:
    • Unlikely to solve it

Medawar Zone

P. Medawar, The Art of the Soluble (Oxford, 1967)

Mechanistically Rich Models

  • If model structure is too simple it will not capture essential mechanisms
  • There will be too few ways to test the model
  • Complexity of model is not bad per se and can increase the payoff

D.L. De Angelis and W.M. Mooij, “In Praise of Mechanistically Rich Models,” in C.D. Canham, J.J. Cole, and W.K. Lauenroth (eds.), Models in Ecosystem Science (Princeton, 2003)

Spatial Patterns in Ecology

Spatial Patterns in Ecology

Wave Forest in Newfoundland

http://www.digitalnaturalhistory.com/images/empetrumnigrumlivedeadwaveforestmistakenpoint.jpg

Spatial Patterns in Ecology

Albatross Trajectory

Y. Tremblay, unpublished

What Scientists do with Patterns

Lemon

  • Pattern: Something beyond random variation
  • Pattern contains information about internal organization
  • Develop models that reproduce observed pattern
  • Inference: Real system’s internal mechanisms are like model’s
  • Squeeze the pattern!

Complex Systems

  • A single pattern may not contain enough information
  • Tendency to focus on single patterns observed at one level of observation:
    • Individual Behaviors
    • Population dynamics
    • Community composition

Monoscopic View

Monoscope

Most approaches (and modelers) are not making the best use of available information (lemons)

We Need a Multiscope

Multiscope

Multiscope View

  • Consider multiple patterns
    • Observed at different scales, levels of organization
  • Get model to reproduce multiple patterns simultaneously
  • Use each pattern as a filter to reject faulty submodels or parameterizations
  • Multiple (3 or more) weak patterns may constrain model better than single strong pattern
  • Pattern-Oriented Modeling

Pattern-Oriented Modeling

Pattern-oriented modeling

Three Elements of Pattern-Oriented Modeling

  1. Design: Choose state variables that allow real-world patterns to emerge in models.
  2. Selection: Use multiple patterns to compare & reject submodels
  3. Parameterization: Use multiple patterns to constrain entire sets of unknown parameters (inverse modeling)

From Theories to Models and Back Again

Theory Development Cycle

Example: Vultures and Carcasses

Vultures Feeding at a Carcass

Vultures feeding on carrion

Modeling Vulture Feeding

Model of Vulture Feeding
A. Cortes-Avizanda et al., “Bird sky networks: How do avian scavengers use social information to find carrion?” Ecology 95, 1799–1808 (2014)

Interactions among Vultures

Possible Interactions

Patterns of Feeding

Clusters of Feeders

Model Comparisons

Comparing Models

Impacts of Pesticides on Aquatic Ecosystems

Dynamic Energy Budget Model

  • Daphnia (water flea) population dynamics observed in laboratory
  • Previous models focused on details of each species
  • Dynamic Energy Budget is generic:
    • Calibrate with known species, apply to new (unknown) species

Individual Metabolic Energy Balance

DEB model

Testing the Model

DEB Model Results

Different Environmental Conditions

Model reproduces population density and body size distribution at multiple levels of food supply and toxicant exposure

DEB model results

Dynamical Patterns: Population Cycles

DEB Population Cycles

How Model Fits into Research

Research Framework

Pattern-Oriented Process

Individual-Based Ecology

IBM-Ecology

Phase-1: Conceptualization

  • Define research question(s)
    • Determine whether agent-based/individual-based modeling is the right conceptual framework
  • Identify link between research question and behavioral mechanisms
  • Identify key parameters and processes to represent environment and behavior of the agents (biological species, human actors, etc.)

Phase-2: Implementation

  • Start with proof-of-concept:
  • Program initial model
    • Ideally, starting model should contain little or no code or submodels specific to a single situation
  • Test whether model can produce predictions that are accurate enough to answer research question
  • Run sensitivity analysis of model to determine key parameters and processes and relationship between model complexity and predictive power

Phase-3: Diversification

  • Simplify model as much as possible by removing unnecessary parameters and processes
  • Minimize number of parameters (e.g., global variables) that need to be measured in each new system
    • Derive as many of these as you can from research literature or general relationships
  • Parameterize and test simplified model for a wide range of systems to determine limits of approach
  • Perform meta-analysis of model runs specific to different sites, or situations
  • Use model to test more general theories: gain broadly applicable insights.