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On the use (and misuse) of models in ecological research
Nicolas Delpierre, ESE (UMR 8079)[email protected] Ecology in English, October 2013
IPCC WG1 – published 2013, Sep. 13th
models +data
models
Models are central in current global change research
A tentative chronology of ecological modelling
Mathematical models are the foundation of modern ecological theory
A tentative chronology of ecological modelling
Mathematical models are the foundation of modern ecological theory
Population ecologyMalthus (1798), Verhulst (1838), Lotka (1925), Leslie (1945)
Biogeography / ecological communities Mc Arthur & Wilson (1967), Hubbel (2001)
Food webs Elton (1927)
Evolutionary ecology Wallace & Darwin (1858)
Ecosystem productivity Lieth (1972)
A tentative chronology of ecological modelling
Mathematical models are the foundation of modern ecological theory
Population ecologyMalthus (1798), Verhulst (1838), Lotka (1925), Leslie (1945)
Biogeography / ecological communities Mc Arthur & Wilson (1967), Hubbel (2001)
Food webs Elton (1927)
Evolutionary ecology Wallace & Darwin (1858)
Ecosystem productivity Lieth (1972)
The complexity of ecological / biological systems prevents the discovery of simple yet powerful models
Different kinds of models
Empirical modelsstatistical
phenomenological
Mechanistic / deterministic modelsbased on the representation of
(known and described) biological / physical processes
Theoretical modelsgeneric, simple
How simple a model needs to be ?
«simple» means « general » means « good »…
William of Ockham 14th c.
How simple a model needs to be ?
«simple» means « general » means « good »… (?)
William of Ockham 14th c.
« some of the theoretical conclusions [from the model] can be pleasingly supported by hard data, while others remain more speculative» (May and Anderson, 1979)
How simple a model needs to be ?
«simple» means « general » means « good »… (?)
William of Ockham 14th c.
« some of the theoretical conclusions [from the model] can be pleasingly supported by hard data, while others remain more speculative» (May and Anderson, 1979)
« The generality of simple models is often superficial because they only demonstrate possible explanations rather than provide actual instances of explanation » (Evans et al., 2013, TREE)
How simple a model needs to be ?
Simple models may sometimes be misleading
Eisinger & Thulke, 2008
Eisinger & Thulke Anderson
Simple model (Eisinger & Thulke 2008):« 70% of the population needs immunization »
Spatially explicit model (Anderson 1981):« 60% …»
A difference of 15 M€ per annuum
How to build a model ?
Knowledge of processesand pre-existing models
Hypotheses
Model
Formulating equations Evaluation
parameterisation
parameterisation
data
Sim
ulati
ons
observations
How to build a model ?
Knowledge of processesand pre-existing models
New hypotheses
Model
Formulating equations Evaluation
parameterisation
parameterisation
data
Sim
ulati
ons
observations
How many processes should i consider ?Is there a limit to the reductionnist approach ?
« We have a tendency to incorporate more and more processes into models to improve fitness between simulated and observed data. »
How many processes should i consider ?Is there a limit to the reductionnist approach ?
« We have a tendency to incorporate more and more processes into models to improve fitness between simulated and observed data.Complicated models may integrate more process knowledge but make more parameters less identifiable given certain data sets. » (Luo, 2009)
IdentifiabilityWhen parameters can be constrained by a set of data with a given model structure, they are identifiable.
Equifinality different models / parameter values of the same model may fit the data equally well
Medlyn et al., 2005, TPBeven, 2006Luo, 2009, Ecol. Appl.
Model 1
Model 1 bis
Model 2
How to parameterize / validate a model ?
A question of (parameters and data) uncertainty…
Parameter uncertainty : different experimental sources report different values for the same parameter
Kattge et al., 2011Hollinger & Richardson, 2005
How to parameterize / validate a model ?
A question of (parameters and data) uncertainty…
Parameter uncertainty : different experimental sources report different values for the same parameter
Data uncertainty:•Sampling error•Measurement precision / accuracy
Kattge et al., 2011Hollinger & Richardson, 2005
These uncertainties must be considered when parameterizing / validating the model
How to parameterize / validate a model ?
An example of data-assimilation techniquesBayesian optimisation approach
posterior parameter distribution
priorparameter distribution
Likelihood function= probability of the data given the model output generated through the
parameter vector q = « measurement of the
prediction error »
DppDp
Van Oijen et al., 2005Martin & Delpierre, 2011Keenan et al., 2012
How to parameterize / validate a model ?
Definition of the cost function
DppDp
Van Oijen et al., 2005Martin & Delpierre, 2011Keenan et al., 2012
An example of data-assimilation techniquesBayesian optimisation approach
How to parameterize / validate a model ?
posterior parameter distribution
priorparameter distribution
DppDp
Parameter value
Simulations + uncertainty
Van Oijen et al., 2005Martin & Delpierre, 2011Keenan et al., 2012
An example of data-assimilation techniquesBayesian optimisation approach
Kuppel, 2013, PhD Thesis
How to parameterize / validate a model ?
The more correlated… the less identifiable
How to parameterize / validate a model ?
Keenan et al., 2013, Ecol. Appl.
Beware of relying completely on the model !
Solar radiation
temperature
Radiation interceptionGlobal PAR
Photosynthesis
Carbon AllocationC leaves
C coarse roots
C fine roots
Growth Respiration
C litter
C surface
C deep
HeterotrophicRespiration
CO2
Stomatal Cond.
GPP
Reco
C aerial wood
C reserves Maintenance Respiration
Föobar model
Keenan et al., unpubl.
Need for considering uncertainty in projected trends
Assimilating more data reduces the uncertainty of projections
Keenan et al., 2012
Need for considering uncertainty in projected trends
Alternative model formulations…yield different trajectories in future projections
Vitasse et al., 2011, AFM
How to identify the « best » of 2 (n) models ?
William of Ockham 14th c.
Hirotugu Akaike1973
Use the Akaike information criterion !
The lowest the AIC, the best accuracy-parsimony trade-off
How to identify the « best » of 2 (n) models ?
William of Ockham 14th c.
Hirotugu Akaike1973
Use the Akaike information criterion !
The lowest the AIC, the best accuracy-parsimony trade-off
Slide from Chris Yesson (Zoological Society of London)
My model can say many things… depending on what i ask !
Principles of niche modelling
Slide from Chris Yesson (Zoological Society of London)
My model can say many things… depending on what i ask !
Principles of niche modelling
Slide from Chris Yesson (Zoological Society of London)
My model can say many things… depending on what i ask !
Principles of niche modelling
Slide from Chris Yesson (Zoological Society of London)
My model can say many things… depending on what i ask !
Principles of niche modelling
Slide from Chris Yesson (Zoological Society of London)
My model can say many things… depending on what i ask !
Principles of niche modelling
Slide from Chris Yesson (Zoological Society of London)
My model can say many things… depending on what i ask !
Principles of niche modelling
My model can say many things… depending on what i ask !
Objective of the paper :
to assign species to extinction risk categories based on projected declines in population size.
Under a time scale of 80 years
My model can say many things… depending on what i ask !
Thuiller et al., 1005, PNASAkçakaya et al., 2006, GCB
What’s the problem with that ?
My model can say many things… depending on what i ask !
200000 400000 600000 800000 1000000 1200000
1600000
1800000
2000000
2200000
2400000
2600000
50km_ResRU50.txt
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100
150
200
200000 400000 600000 800000 1000000 1200000
1600000
1800000
2000000
2200000
2400000
2600000
8km_ResRU8.txt
0
50
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Simulation of Oak productivity depends on the resolution of climate forcings
Martin et al., unpublished results
Take home ideas
• However detailed, models are idealized representations of the world
• Simple models are most of the time general… and not so good
• Complex models may not be parameterizable (… however complicated the data assimilation technique)
• Model forecasts are conditional on:model structure and parameters (and uncertainties)model forcings
• Models can only answer questions that one asks
On the use and misuse of models in ecological / global change research
Keenan et al. rate my data, validation GCB (fails)Medlyn et al. 2005 perils and pitfallsEvans et al. 2013 « Simple means general means good»
What is a model?What is it used for?How valid are inferences from model simulations ?
Plan
Models are central in current global change researchExamples last ipcc reportExamples spp extinction from pereira et al. 2011Used for projections of what may happenRaises the question of reliability of the models… and of their uncertainties
What is a model ? (we’re not going to center on statistical models)How simple needs a model to be ? Does simple mean general mean true ? (Evans)I’m a researcher : how can i build my model ? (where do i start from ?)The question / problem of parameterisation. Data also are uncertain !Dealing with multiple uncertainties : MDF frameworksMy model is built. How can i check that its predictions are reliable?
Future trends : what do i need for running my model ?How accurate are the input data (Zhao, Nico + Evea)Simulations in a future / modified climate : what indexes of changes should i use (Akcakaya)
What a model can’t do : rate my data…