Comparing simple ecosystem models in state space

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Comparing simple ecosystem models in state space

• Nicky Grigg, CLW
• Fabio Boschetti, CMAR

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Typical features of aquatic ecosystem models

• Dynamic
• Track the flow of nutrients through sediment and
  water column processes
• Nonlinear interactions, feedbacks, hysteretic
  responses

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Typical uses of aquatic ecosystem models

• Seek inconsistencies between system understanding
  and observations
• Inform monitoring strategies
• Identify system vulnerabilities
• Investigate ecosystem responses to changed forcing

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How to fit a wrong model?

• All models are wrong.
• A good model captures system characteristics of
  interest.
• Dynamics process models dynamical behaviour is
  important?
• Aggregate, statistical quantities in model
  validation and sensitivity analyses throw away
  information about the system dynamics .
• Given a wrong model for a system, what criteria
  can we use to characterise and compare the
  dynamics of the two systems?

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Toy example stochastically forced food chain
qZn
Zooplankton mortality Linear mortality (n 1)
only one basin of attraction Quadratic mortality
(n 2) alternative basins of attraction, and
large flips between basins possible.
Source Edwards and Brindley (1999)
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Given observations from quadratic mortality
system Aim model the dynamics with a linear
mortality model
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Parameter search resultleast squares fit
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Is this a good fit?
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Comparisons in reconstructed state space
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Fitting in state space how?
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Density estimation
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?
Joint Probability Density

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Evaluate joint pdf for set of points
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Estimating probability densityCluster-weighted
modelling
Reference Gershenfeld (1999)
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Why?

• Model-data comparisons
• Parameter sensitivity analysis
• Sensitivity to choice of model structure
• Identifying appropriate simpler or
  lower-dimensional models (including how to lump
  foodwebs and other networks)

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Extrapolating with ensembles of acceptable
models

• Typical justification for using dynamic process
  models their ability to extrapolate and make
  predictions outside the calibration conditions.
• Toy example find an ensemble of acceptable
  models given observations from one basin of
  attraction. Test the fitted models ability to
  extrapolate given novel forcing.

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NPZ model withdifferent nutrient loads
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Best fit to low-nutrient case using the 2D
parameter search and the wrong model
Best time domain fit
Best state-space fit
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Extrapolating high-nutrient response using the
best fits
Extrapolating with model fitted in state space
Extrapolating with model fitted in time domain
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Food Webs
Source Neo Martinez, http//online.sfsu.edu/webh
ead/
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Food web questions

• Can we lump a food web to retain dynamic
  characteristics?
• Can we find relationships between network
  properties and dynamic characteristics?
• Relative importance of network properties vs
  functional form of the links between species?

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Effect of changing one link strength on two
fitness measures
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Pros and cons?

• A single measure which captures many
  characteristics of the time series simultaneously
  aggregate statistical measures, frequency
  information and geometry of state space
  trajectories.
• Suitable for non-stationary, stochastically
  forced and chaotic systems.
• Assumes there is a useful geometrical structure
  in reconstructed state space.
• Faced with numerical searches through
  high-dimensional space.

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Conclusions

• Can characterise non-stationary time series from
  forced dynamical systems in a way that allows
  quantitative comparison between systems
• Currently applying these techniques to NPZ and
  low-dimensional foodweb models
• Need to move beyond toy systems and look at more
  realistic ecosystem models and higher-dimensional
  foodwebs