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Volume 88, Issue 4 p. 485-504
Review

Model averaging in ecology: a review of Bayesian, information-theoretic, and tactical approaches for predictive inference

Carsten F. Dormann

Corresponding Author

Carsten F. Dormann

Biometry and Environmental System Analysis, University of Freiburg, Tennenbacher Str. 4, 79106 Freiburg, Germany

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Justin M. Calabrese

Justin M. Calabrese

Conservation Ecology Center, Smithsonian Conservation Biology Institute, 1500 Remount Road, Front Royal, Virginia, 22630 USA

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Gurutzeta Guillera-Arroita

Gurutzeta Guillera-Arroita

School of BioSciences, University of Melbourne, Royal Parade, Parkville, Melbourne, Victoria, 3052 Australia

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Eleni Matechou

Eleni Matechou

School of Mathematics, Statistics and Actuarial Science, University of Kent, Parkwood Road, Canterbury, CT2 7FS UK

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Volker Bahn

Volker Bahn

Department of Biological Sciences, Wright State University, 3640 Colonel Glenn Hwy., Dayton, Ohio, 45435 USA

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Kamil Bartoń

Kamil Bartoń

Institute of Nature Conservation, Polish Academy of Sciences, al. A. Mickiewicza 33, 31-120 Kraków, Poland

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Colin M. Beale

Colin M. Beale

Department of Biology, University of York, Wentworth Way, York, YO10 5DD UK

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Simone Ciuti

Simone Ciuti

Biometry and Environmental System Analysis, University of Freiburg, Tennenbacher Str. 4, 79106 Freiburg, Germany

Laboratory of Wildlife Ecology and Behaviour, School of Biology and Environmental Science, University College Dublin, Belfield D4, Dublin, Ireland

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Jane Elith

Jane Elith

School of BioSciences, University of Melbourne, Royal Parade, Parkville, Melbourne, Victoria, 3052 Australia

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Katharina Gerstner

Katharina Gerstner

Computational Landscape Ecology, Helmholtz Centre for Environmental Research-UFZ, Permoser Str. 15, 04318 Leipzig, Germany

German Centre for Integrative Biodiversity Research (iDiv) Halle-Jena-Leipzig, Deutscher Platz 5E, 04103 Leipzig, Germany

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Jérôme Guelat

Jérôme Guelat

Swiss Ornithological Institute, Seerose 1, 6204 Sempach, Switzerland

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Petr Keil

Petr Keil

German Centre for Integrative Biodiversity Research (iDiv) Halle-Jena-Leipzig, Deutscher Platz 5E, 04103 Leipzig, Germany

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José J. Lahoz-Monfort

José J. Lahoz-Monfort

School of BioSciences, University of Melbourne, Royal Parade, Parkville, Melbourne, Victoria, 3052 Australia

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Laura J. Pollock

Laura J. Pollock

Univ. Grenoble Alpes, CNRS, Univ. Savoie Mont Blanc, Laboratoire d'Ecologie Alpine (LECA), Grenoble, 38000 France

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Björn Reineking

Björn Reineking

University Grenoble Alpes, Irstea, UR LESSEM, F-38402 St-Martin-d'Hères, Grenoble, France

Biogeographical Modelling, Bayreuth Center of Ecology and Environmental Research BayCEER, University of Bayreuth, Dr. Hans-Frisch-Straße 1-3, 95448 Bayreuth, Germany

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David R. Roberts

David R. Roberts

Biometry and Environmental System Analysis, University of Freiburg, Tennenbacher Str. 4, 79106 Freiburg, Germany

Department of Geography, University of Calgary, 2500 University Dr. NW, Calgary, Alberta, T2N 1N4 Canada

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Boris Schröder

Boris Schröder

Landscape Ecology and Environmental Systems Analysis, Institute of Geoecology, Technische Universität Braunschweig, Langer Kamp 19c, 38106 Braunschweig, Germany

Berlin-Brandenburg Institute of Advanced Biodiversity Research (BBIB), Altensteinstr. 34, 14195 Berlin, Germany

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Wilfried Thuiller

Wilfried Thuiller

Univ. Grenoble Alpes, CNRS, Univ. Savoie Mont Blanc, Laboratoire d'Ecologie Alpine (LECA), Grenoble, 38000 France

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David I. Warton

David I. Warton

School of Mathematics and Statistics, Evolution and Ecology Research Centre, University of New South Wales, Sydney, New South Wales, 2052 Australia

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Brendan A. Wintle

Brendan A. Wintle

School of BioSciences, University of Melbourne, Royal Parade, Parkville, Melbourne, Victoria, 3052 Australia

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Simon N. Wood

Simon N. Wood

School of Mathematics, Bristol University, Tyndall Avenue, Bristol, BS8 1TW UK

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Rafael O. Wüest

Rafael O. Wüest

Univ. Grenoble Alpes, CNRS, Univ. Savoie Mont Blanc, Laboratoire d'Ecologie Alpine (LECA), Grenoble, 38000 France

Swiss Federal Institute for Forest, Snow and Landscape Research WSL, Zürcherstrasse 111, 8903 Birmensdorf, Switzerland

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Florian Hartig

Florian Hartig

Biometry and Environmental System Analysis, University of Freiburg, Tennenbacher Str. 4, 79106 Freiburg, Germany

Theoretical Ecology, University of Regensburg, Universitätsstr. 31, 93053 Regensburg, Germany

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First published: 02 May 2018
Citations: 250
Corresponding Editor: Perry de Valpine.

Abstract

In ecology, the true causal structure for a given problem is often not known, and several plausible models and thus model predictions exist. It has been claimed that using weighted averages of these models can reduce prediction error, as well as better reflect model selection uncertainty. These claims, however, are often demonstrated by isolated examples. Analysts must better understand under which conditions model averaging can improve predictions and their uncertainty estimates. Moreover, a large range of different model averaging methods exists, raising the question of how they differ in their behaviour and performance. Here, we review the mathematical foundations of model averaging along with the diversity of approaches available. We explain that the error in model-averaged predictions depends on each model's predictive bias and variance, as well as the covariance in predictions between models, and uncertainty about model weights. We show that model averaging is particularly useful if the predictive error of contributing model predictions is dominated by variance, and if the covariance between models is low. For noisy data, which predominate in ecology, these conditions will often be met. Many different methods to derive averaging weights exist, from Bayesian over information-theoretical to cross-validation optimized and resampling approaches. A general recommendation is difficult, because the performance of methods is often context dependent. Importantly, estimating weights creates some additional uncertainty. As a result, estimated model weights may not always outperform arbitrary fixed weights, such as equal weights for all models. When averaging a set of models with many inadequate models, however, estimating model weights will typically be superior to equal weights. We also investigate the quality of the confidence intervals calculated for model-averaged predictions, showing that they differ greatly in behaviour and seldom manage to achieve nominal coverage. Our overall recommendations stress the importance of non-parametric methods such as cross-validation for a reliable uncertainty quantification of model-averaged predictions.