skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.


Title: Regularized Regression: A New Tool for Investigating and Predicting Tree Growth
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.  more » « less
Award ID(s):
2017949
PAR ID:
10353712
Author(s) / Creator(s):
; ; ; ;
Date Published:
Journal Name:
Forests
Volume:
12
Issue:
9
ISSN:
1999-4907
Page Range / eLocation ID:
1283
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Ryan, Michael (Ed.)
    Abstract Increasing evidence suggests that tree growth is sink-limited by environmental and internal controls rather than by carbon availability. However, the mechanisms underlying sink-limitations are not fully understood and thus not represented in large-scale vegetation models. We develop a simple, analytically solved, mechanistic, turgor-driven growth model (TDGM) and a phloem transport model (PTM) to explore the mechanics of phloem transport and evaluate three hypotheses. First, phloem transport must be explicitly considered to accurately predict turgor distributions and thus growth. Second, turgor-limitations can explain growth-scaling with size (metabolic scaling). Third, turgor can explain realistic growth rates and increments. We show that mechanistic, sink-limited growth schemes based on plant turgor limitations are feasible for large-scale model implementations with minimal computational demands. Our PTM predicted nearly uniform sugar concentrations along the phloem transport path regardless of phloem conductance, stem water potential gradients and the strength of sink-demands contrary to our first hypothesis, suggesting that phloem transport is not limited generally by phloem transport capacity per se but rather by carbon demand for growth and respiration. These results enabled TDGM implementation without explicit coupling to the PTM, further simplifying computation. We test the TDGM by comparing predictions of whole-tree growth rate to well-established observations (site indices) and allometric theory. Our simple TDGM predicts realistic tree heights, growth rates and metabolic scaling over decadal to centurial timescales, suggesting that tree growth is generally sink and turgor limited. Like observed trees, our TDGM captures tree-size- and resource-based deviations from the classical ¾ power-law metabolic scaling for which turgor is responsible. 
    more » « less
  2. Context: Growth releases of individuals that survive disturbances are important compensatory response mechanisms that contribute to ecological resilience. However, the role of fine-scale spatial heterogeneity in shaping compensatory growth responses is poorly understood for many broad-scale disturbances. Objectives: We quantified how fine-scale spatial structure affects individual and aggregate tree growthleading up to and following a severe mountain pine beetle (MPB; Dendroctonus ponderosae) outbreak. We asked: (1) How does individual tree growth vary with tree- and neighborhood-scale characteristics? (2) How do within-stand aggregate growth and overstory recruitment vary with neighborhood-scale characteristics? Methods: We used a spatially explicit long-term monitoring dataset of a subalpine lodgepole pine (Pinus contorta var. latifolia) forest (in Colorado, USA) in which every tree ≥ 5 cm diameter was measured and mapped prior to (1989, 2004) and following (2018) a severe MPB outbreak (2003–2011). We used spatial regression to characterize drivers of growth. Results: Overall, we found strong evidence for post-outbreak compensatory responses across spatial scales. Neighborhood characteristics shaped both individual and aggregate growth, with the magnitude of growth strongly mediated by pre-outbreak neighborhood structure and neighborhood mortality. Variation in tree-scale growth, combined with the spatial arrangement of surviving trees, resulted in highly variable emergent patterns of aggregate growth and recruitment. Conclusion: Our findings highlight the importance of fine-scale landscape configuration in shaping forest resilience. Quantifying compensatory responses in a spatially explicit framework at different scales is critical for modeling post-disturbance forest dynamics, which is increasingly important as climate warms and forest disturbance regimes change. 
    more » « less
  3. Abstract Just exactly which tree(s) should we assume when testing evolutionary hypotheses? This question has plagued comparative biologists for decades. Though all phylogenetic comparative methods require input trees, we seldom know with certainty whether even a perfectly estimated tree (if this is possible in practice) is appropriate for our studied traits. Yet, we also know that phylogenetic conflict is ubiquitous in modern comparative biology, and we are still learning about its dangers when testing evolutionary hypotheses. Here, we investigate the consequences of tree-trait mismatch for phylogenetic regression in the presence of gene tree–species tree conflict. Our simulation experiments reveal excessively high false positive rates for mismatched models with both small and large trees, simple and complex traits, and known and estimated phylogenies. In some cases, we find evidence of a directionality of error: assuming a species tree for traits that evolved according to a gene tree sometimes fares worse than the opposite. We also explored the impacts of tree choice using an expansive, cross-species gene expression dataset as an arguably “best-case” scenario in which one may have a better chance of matching tree with trait. Offering a potential path forward, we found promise in the application of a robust estimator as a potential, albeit imperfect, solution to some issues raised by tree mismatch. Collectively, our results emphasize the importance of careful study design for comparative methods, highlighting the need to fully appreciate the role of accurate and thoughtful phylogenetic modeling. 
    more » « less
  4. Predicting drought responses of individual trees in tropical forests remains challenging, in part because trees experience drought differently depending on their position in spatially heterogeneous environments. Specifically, topography and the competitive environment can influence the severity of water stress experienced by individual trees, leading to individual-level variation in drought impacts. A drought in 2015 in Puerto Rico provided the opportunity to assess how drought response varies with topography and neighborhood crowding in a tropical forest. In this study, we integrated 3 years of annual census data from the El Yunque Chronosequence plots with measurements of functional traits and LiDAR-derived metrics of microsite topography. We fit hierarchical Bayesian models to examine how drought, microtopography, and neighborhood crowding influence individual tree growth and survival, and the role functional traits play in mediating species’ responses to these drivers. We found that while growth was lower during the drought year, drought had no effect on survival, suggesting that these forests are fairly resilient to a single-year drought. However, growth response to drought, as well as average growth and survival, varied with topography: tree growth in valley-like microsites was more negatively affected by drought, and survival was lower on steeper slopes while growth was higher in valleys. Neighborhood crowding reduced growth and increased survival, but these effects did not vary between drought/non-drought years. Functional traits provided some insight into mechanisms by which drought and topography affected growth and survival. For example, trees with high specific leaf area grew more slowly on steeper slopes, and high wood density trees were less sensitive to drought. However, the relationships between functional traits and response to drought and topography were weak overall. Species sorting across microtopography may drive observed relationships between average performance, drought response, and topography. Our results suggest that understanding species’ responses to drought requires consideration of the microenvironments in which they grow. Complex interactions between regional climate, topography, and traits underlie individual and species variation in drought response. 
    more » « less
  5. null (Ed.)
    Background Ecological communities tend to be spatially structured due to environmental gradients and/or spatially contagious processes such as growth, dispersion and species interactions. Data transformation followed by usage of algorithms such as Redundancy Analysis (RDA) is a fairly common approach in studies searching for spatial structure in ecological communities, despite recent suggestions advocating the use of Generalized Linear Models (GLMs). Here, we compared the performance of GLMs and RDA in describing spatial structure in ecological community composition data. We simulated realistic presence/absence data typical of many β -diversity studies. For model selection we used standard methods commonly used in most studies involving RDA and GLMs. Methods We simulated communities with known spatial structure, based on three real spatial community presence/absence datasets (one terrestrial, one marine and one freshwater). We used spatial eigenvectors as explanatory variables. We varied the number of non-zero coefficients of the spatial variables, and the spatial scales with which these coefficients were associated and then compared the performance of GLMs and RDA frameworks to correctly retrieve the spatial patterns contained in the simulated communities. We used two different methods for model selection, Forward Selection (FW) for RDA and the Akaike Information Criterion (AIC) for GLMs. The performance of each method was assessed by scoring overall accuracy as the proportion of variables whose inclusion/exclusion status was correct, and by distinguishing which kind of error was observed for each method. We also assessed whether errors in variable selection could affect the interpretation of spatial structure. Results Overall GLM with AIC-based model selection (GLM/AIC) performed better than RDA/FW in selecting spatial explanatory variables, although under some simulations the methods performed similarly. In general, RDA/FW performed unpredictably, often retaining too many explanatory variables and selecting variables associated with incorrect spatial scales. The spatial scale of the pattern had a negligible effect on GLM/AIC performance but consistently affected RDA’s error rates under almost all scenarios. Conclusion We encourage the use of GLM/AIC for studies searching for spatial drivers of species presence/absence patterns, since this framework outperformed RDA/FW in situations most likely to be found in natural communities. It is likely that such recommendations might extend to other types of explanatory variables. 
    more » « less