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On the use (and misuse) of models in ecological research Nicolas Delpierre, ESE (UMR 8079) nicolas.delpierre@u-psud.fr Ecology in English, October 2013

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IPCC WG1 – published 2013, Sep. 13 th models + data models Models are central in current global change research

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Pereira et al., 2010, Science Models are central in current global change research data models

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A tentative chronology of ecological modelling Mathematical models are the foundation of modern ecological theory

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A tentative chronology of ecological modelling Mathematical models are the foundation of modern ecological theory Population ecology Malthus (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)

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A tentative chronology of ecological modelling Mathematical models are the foundation of modern ecological theory Population ecology Malthus (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

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Different kinds of models Bolker, 2008 : ecological models and data in R

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Different kinds of models Empirical models Mechanistic / deterministic models Theoretical models

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Different kinds of models Empirical models statistical phenomenological Mechanistic / deterministic models based on the representation of (known and described) biological / physical processes Theoretical models generic, simple

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How simple a model needs to be ? «simple» means « general » means « good »… William of Ockham 14 th c.

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How simple a model needs to be ? «simple» means « general » means « good »… (?) William of Ockham 14 th 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)

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How simple a model needs to be ? «simple» means « general » means « good »… (?) William of Ockham 14 th 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)

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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

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How to build a model ?

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Knowledge of processes and pre-existing models Hypotheses Model Formulating equations Evaluation parameterisation data Simulations observations

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How to build a model ? Knowledge of processes and pre-existing models New hypotheses Model Formulating equations Evaluation parameterisation data Simulations observations

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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. »

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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) Identifiability When 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, TP Beven, 2006 Luo, 2009, Ecol. Appl. Model 1 Model 1 bis Model 2

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How to parameterize / validate a model ?

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How to parameterize / validate a model ? A question of (parameters and data) uncertainty…

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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., 2011 Hollinger & Richardson, 2005

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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., 2011 Hollinger & Richardson, 2005 These uncertainties must be considered when parameterizing / validating the model

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How to parameterize / validate a model ? An example of data-assimilation techniques Bayesian optimisation approach posterior parameter distribution prior parameter distribution Likelihood function = probability of the data given the model output generated through the parameter vector = « measurement of the prediction error » Van Oijen et al., 2005 Martin & Delpierre, 2011 Keenan et al., 2012

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How to parameterize / validate a model ? Definition of the cost function Van Oijen et al., 2005 Martin & Delpierre, 2011 Keenan et al., 2012 An example of data-assimilation techniques Bayesian optimisation approach

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How to parameterize / validate a model ? posterior parameter distribution prior parameter distribution Parameter value Simulations + uncertainty Van Oijen et al., 2005 Martin & Delpierre, 2011 Keenan et al., 2012 An example of data-assimilation techniques Bayesian optimisation approach

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Kuppel, 2013, PhD Thesis How to parameterize / validate a model ? The more correlated… the less identifiable

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How to parameterize / validate a model ? How many data do i need ? Keenan et al., 2013, Ecol. Appl.

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How to parameterize / validate a model ? Keenan et al., 2013, Ecol. Appl. Beware of relying completely on the model !

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Solar radiation temperature Radiation interception GlobalPAR Photosynthesis Carbon Allocation C leaves C coarse roots C fine roots Growth Respiration C litter C surface C deep Heterotrophic Respiration CO 2 Stomatal Cond. GPP Reco C aerial wood C reserves Maintenance Respiration Föobar model Keenan et al., unpubl.

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Need for considering uncertainty in projected trends Assimilating more data reduces the uncertainty of projections Keenan et al., 2012

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Need for considering uncertainty in projected trends Alternative model formulations… yield different trajectories in future projections Vitasse et al., 2011, AFM

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How to identify the « best » of 2 (n) models ? William of Ockham 14 th c. Hirotugu Akaike 1973 Use the Akaike information criterion ! The lowest the AIC, the best accuracy-parsimony trade-off

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How to identify the « best » of 2 (n) models ? William of Ockham 14 th c. Hirotugu Akaike 1973 Use the Akaike information criterion ! The lowest the AIC, the best accuracy-parsimony trade-off

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What a dataset will not tell…

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Do experiments provide reliable data for informing my model ? Wolkovich et al., 2012, Nature

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Can model parameters be treated as constants ? acclimation processes Wythers et al., 2005, GCB

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Using a model for prospective studies

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Slide from Chris Yesson (Zoological Society of London) My model can say many things… depending on what i ask ! Principles of niche modelling

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Slide from Chris Yesson (Zoological Society of London) My model can say many things… depending on what i ask ! Principles of niche modelling

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Slide from Chris Yesson (Zoological Society of London) My model can say many things… depending on what i ask ! Principles of niche modelling

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Slide from Chris Yesson (Zoological Society of London) My model can say many things… depending on what i ask ! Principles of niche modelling

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Slide from Chris Yesson (Zoological Society of London) My model can say many things… depending on what i ask ! Principles of niche modelling

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Slide from Chris Yesson (Zoological Society of London) My model can say many things… depending on what i ask ! Principles of niche modelling

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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

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My model can say many things… depending on what i ask ! Thuiller et al., 1005, PNAS Akçakaya et al., 2006, GCB What’s the problem with that ?

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My model can say many things… depending on what i ask ! Simulation of Oak productivity depends on the resolution of climate forcings Martin et al., unpublished results

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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

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Supplementary material

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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 pitfalls Evans et al. 2013 « Simple means general means good» What is a model? What is it used for? How valid are inferences from model simulations ?

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Plan Models are central in current global change research Examples last ipcc report Examples spp extinction from pereira et al. 2011 Used for projections of what may happen Raises 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 frameworks My 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…

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