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Article

Regularized Regression: A New Tool for Investigating and Predicting Tree Growth

1
Department of Biology, University of Washington, Seattle, WA 98195, USA
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Institute of Integrative Biology, ETH Zurich, Universitätstrasse 16, 8092 Zürich, Switzerland
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Department of Psychology and eScience Institute, University of Washington, Seattle, WA 98195, USA
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AMAP (botAnique et Modélisation de l’Architecture des Plantes et des Végétations), Université de Montpellier, CIRAD, CNRS, INRAE, IRD, CEDEX 5, 34398 Montpellier, France
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Department of Ecology and Evolutionary Biology, University of California Los Angeles, Los Angeles, CA 90095-1606, USA
*
Author to whom correspondence should be addressed.
Academic Editors: Juan A. Blanco and Yueh-Hsin Lo
Forests 2021, 12(9), 1283; https://doi.org/10.3390/f12091283
Received: 30 August 2021 / Revised: 15 September 2021 / Accepted: 16 September 2021 / Published: 18 September 2021
(This article belongs to the Special Issue Modelling Forest Ecosystems)
Neighborhood models have allowed us to test many hypotheses regarding the drivers of variation in tree growth, but require considerable computation due to the many empirically supported non-linear relationships they include. Regularized regression represents a far more efficient neighborhood modeling method, but it is unclear whether such an ecologically unrealistic model can provide accurate insights on tree growth. Rapid computation is becoming increasingly important as ecological datasets grow in size, and may be essential when using neighborhood models to predict tree growth beyond sample plots or into the future. We built a novel regularized regression model of tree growth and investigated whether it reached the same conclusions as a commonly used neighborhood model, regarding hypotheses of how tree growth is influenced by the species identity of neighboring trees. We also evaluated the ability of both models to interpolate the growth of trees not included in the model fitting dataset. Our regularized regression model replicated most of the classical model’s inferences in a fraction of the time without using high-performance computing resources. We found that both methods could interpolate out-of-sample tree growth, but the method making the most accurate predictions varied among focal species. Regularized regression is particularly efficient for comparing hypotheses because it automates the process of model selection and can handle correlated explanatory variables. This feature means that regularized regression could also be used to select among potential explanatory variables (e.g., climate variables) and thereby streamline the development of a classical neighborhood model. Both regularized regression and classical methods can interpolate out-of-sample tree growth, but future research must determine whether predictions can be extrapolated to trees experiencing novel conditions. Overall, we conclude that regularized regression methods can complement classical methods in the investigation of tree growth drivers and represent a valuable tool for advancing this field toward prediction. View Full-Text
Keywords: forest plot; inference; interpolation; model selection; neighborhood model; regularization; test set validation; tree growth forest plot; inference; interpolation; model selection; neighborhood model; regularization; test set validation; tree growth
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MDPI and ACS Style

Graham, S.I.; Rokem, A.; Fortunel, C.; Kraft, N.J.B.; Hille Ris Lambers, J. Regularized Regression: A New Tool for Investigating and Predicting Tree Growth. Forests 2021, 12, 1283. https://doi.org/10.3390/f12091283

AMA Style

Graham SI, Rokem A, Fortunel C, Kraft NJB, Hille Ris Lambers J. Regularized Regression: A New Tool for Investigating and Predicting Tree Growth. Forests. 2021; 12(9):1283. https://doi.org/10.3390/f12091283

Chicago/Turabian Style

Graham, Stuart I., Ariel Rokem, Claire Fortunel, Nathan J. B. Kraft, and Janneke Hille Ris Lambers. 2021. "Regularized Regression: A New Tool for Investigating and Predicting Tree Growth" Forests 12, no. 9: 1283. https://doi.org/10.3390/f12091283

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