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

Abstract

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.

forestexplorR: an R package for the exploration and analysis of stem‐mapped forest stand data

“…Widespread use of stem-mapped forest stand datasets is currently hampered by the high programming and computational demands involved, particularly in the quantitative description of neighborhoods, selecting an appropriate neighborhood size and fitting neighborhood models of tree performance. forestexplorR removes these barriers by providing flexible and user-friendly functions for describing neighborhoods, selecting neighborhood size and implementing a rapid-fitting neighborhood model of tree growth or mortality (Graham et al 2021) that can be used to investigate species interactions. Moreover, by requiring only the data types common to all stem-mapped forest stands (species identity, location, DBH measurements), forestexplorR is compatible with all rectangular stem-mapped forest stand datasets.…”

“…These transformed growth rate variables partially account for the non‐linear relationship between tree size and growth rate and tend to more closely follow a normal distribution than raw growth rates, thereby enabling linear modeling of tree growth (Graham et al 2021). The detailed_growth function works similarly to growth_summary but instead returns separate growth rates for each tree between each pair of consecutive stand censuses.…”

“…This means that such models take a long time to fit and their use is therefore restricted to research teams with access to high‐performance computing resources. To encourage broader use of neighborhood models, the forestexplorR functions growth_model and mortality_model implement a new regularized regression model of tree growth and mortality, respectively, that can be run in minutes on a personal laptop (Graham et al 2021); less than 1% of the time required to fit other neighborhood models (Uriarte et al 2004).…”

“…This means that our neighborhood metrics cannot represent the empirically‐supported non‐linear relationships underlying tree performance (e.g. the relationship between neighbor distance and the competitive effect on focal growth), but despite this simplification, these linear models have been shown to predict tree growth rates with accuracy (Graham et al 2021). This simplification does not prevent all exploration of density metrics and neighborhood_summary provides several options for how densities can be computed.…”

“…forestexplorR provides functions for calculating common neighborhood metrics, and creates clean visualizations for data exploration. In addition, it allows the user to implement a new, efficient neighborhood model of tree growth or mortality (Graham et al 2021) that can be used to select an appropriate neighborhood size, guide the development of a more mechanistic model (Uriarte et al 2004), and test ecological hypotheses. forestexplorR will most significantly increase the utility of distributed networks of stem‐mapped forest stands because it provides user‐friendly tools for combining data from multiple stands into a single neighborhood analysis, thereby enabling users to test hypotheses on how forest processes vary between biomes and across environmental gradients.…”