skip to main content

Title: Generalized additive models reveal among-stand variation in live tree biomass equations
Accurate estimation of forest biomass is important for scientists and policymakers interested in carbon accounting, nutrient cycling, and forest resilience. Estimates often rely on the allometry of trees; however, limited datasets, uncertainty in model form, and unaccounted for sources of variation warrant a re-examination of allometric relationships using modern statistical techniques. We asked the following questions: (1) Is there among-stand variation in allometric relationships? (2) Is there nonlinearity in allometric relationships? (3) Can among-stand variation or nonlinearities in allometric equations be attributed to differences in stand age? (4) What are the implications for biomass estimation? To answer these questions, we synthesized a dataset of small trees from six different studies in the White Mountains of New Hampshire. We compared the performance of generalized additive models (GAMs) and linear models and found that GAMs consistently outperform linear models. The best-fitting model indicates that allometries vary among both stands and species and contain subtle nonlinearities which are themselves variable by species. Using a planned contrasts analysis, we were able to attribute some of the observed among-stand heterogeneity to differences in stand age. However, variability in these results point to additional sources of stand-level heterogeneity, which if identified could improve the accuracy of more » live-tree biomass estimation. « less
; ;
Award ID(s):
Publication Date:
Journal Name:
Canadian Journal of Forest Research
Sponsoring Org:
National Science Foundation
More Like this
  1. Species distribution models (SDMs) are a commonly used tool, which when combined with earth system models (ESMs), can project changes in organismal occurrence, abundance, and phenology under climate change. An often untested assumption of SDMs is that relationships between organisms and the environment are stationary. To evaluate this assumption, we examined whether patterns of distribution among larvae of four small pelagic fishes (Pacific sardine Sardinops sagax , northern anchovy Engraulis mordax , jack mackerel Trachurus symmetricus , chub mackerel Scomber japonicus ) in the California Current remained steady across time periods defined by climate regimes, changes in secondary productivity, and breakpoints in time series of spawning stock biomass (SSB). Generalized additive models (GAMs) were constructed separately for each period using temperature, salinity, dissolved oxygen (DO), and mesozooplankton volume as predictors of larval occurrence. We assessed non-stationarity based on changes in six metrics: 1) variables included in SDMs; 2) whether a variable exhibited a linear or non-linear form; 3) rank order of deviance explained by variables; 4) response curve shape; 5) degree of responsiveness of fishes to a variable; 6) range of environmental variables associated with maximum larval occurrence. Across all species and time periods, non-stationarity was ubiquitous, affecting at leastmore »one of the six indicators. Rank order of environmental variables, response curve shape, and oceanic conditions associated with peak larval occurrence were the indicators most subject to change. Non-stationarity was most common among regimes defined by changes in fish SSB. The relationships between larvae and DO were somewhat more likely to change across periods, whereas the relationships between fishes and temperature were more stable. Respectively, S. sagax , T. symmetricus , S. japonicus , and E. mordax exhibited non-stationarity across 89%, 67%, 50%, and 50% of indicators. For all species except E. mordax , inter-model variability had a larger impact on projected habitat suitability for larval fishes than differences between two climate change scenarios (SSP1-2.6 and SSP5-8.5), implying that subtle differences in model formulation could have amplified future effects. These results suggest that the widespread non-stationarity in how fishes utilize their environment could hamper our ability to reliably project how species will respond to climatic change.« less
  2. Abstract Pinus edulis Engelm. is a short-stature, drought-tolerant tree species that is abundant in piñon-juniper woodlands throughout semiarid ecosystems of the American Southwest. P. edulis is a model species among ecophysiological disciplines, with considerable research focus given to hydraulic functioning and carbon partitioning relating to mechanisms of tree mortality. Many ecological studies require robust estimates of tree structural traits such as biomass, active sapwood area, and leaf area. We harvested twenty trees from Central New Mexico ranging in size from 1.3 to 22.7 cm root crown diameter (RCD) to derive allometric relationships from measurements of RCD, maximum height, canopy area (CA), aboveground biomass (AGB), sapwood area (AS), and leaf area (AL). Total foliar mass was measured from a subset of individuals and scaled to AL from estimates of leaf mass per area. We report a strong nonlinear relationship to AGB as a function of both RCD and height, whereas CA scaled linearly. Total AS expressed a power relationship with RCD. Both AS and CA exhibited strong linear relationships with AL (R2 = 0.99), whereas RCD increased nonlinearly with AL. We improve on current models by expanding the size range of sampled trees and supplement the existing literature for this species.more »Study Implications: Land managers need to better understand carbon and water dynamics in changing ecosystems to understand how those ecosystems can be sustainably used now and in the future. This study of two-needle pinon (Pinus edulis Engelm.) trees in New Mexico, USA, uses observations from unoccupied aerial vehicles, field measurements, and harvesting followed by laboratory analysis to develop allometric models for this widespread species. These models can be used to understand plant traits such biomass partitioning and sap flow, which in turn will help scientists and land managers better understand the ecosystem services provided by pinon pine across North America.« less
  3. Abstract
    Excessive phosphorus (P) applications to croplands can contribute to eutrophication of surface waters through surface runoff and subsurface (leaching) losses. We analyzed leaching losses of total dissolved P (TDP) from no-till corn, hybrid poplar (Populus nigra X P. maximowiczii), switchgrass (Panicum virgatum), miscanthus (Miscanthus giganteus), native grasses, and restored prairie, all planted in 2008 on former cropland in Michigan, USA. All crops except corn (13 kg P ha−1 year−1) were grown without P fertilization. Biomass was harvested at the end of each growing season except for poplar. Soil water at 1.2 m depth was sampled weekly to biweekly for TDP determination during March–November 2009–2016 using tension lysimeters. Soil test P (0–25 cm depth) was measured every autumn. Soil water TDP concentrations were usually below levels where eutrophication of surface waters is frequently observed (> 0.02 mg L−1) but often higher than in deep groundwater or nearby streams and lakes. Rates of P leaching, estimated from measured concentrations and modeled drainage, did not differ statistically among cropping systems across years; 7-year cropping system means ranged from 0.035 to 0.072 kg P ha−1 year−1 with large interannual variation. Leached P was positively related to STP, which decreased over the 7 years in all systems. These results indicate that both P-fertilized and unfertilized cropping systems mayMore>>
  4. Despite its importance for forest regeneration, food webs, and human economies, changes in tree fecundity with tree size and age remain largely unknown. The allometric increase with tree diameter assumed in ecological models would substantially overestimate seed contributions from large trees if fecundity eventually declines with size. Current estimates are dominated by overrepresentation of small trees in regression models. We combined global fecundity data, including a substantial representation of large trees. We compared size–fecundity relationships against traditional allometric scaling with diameter and two models based on crown architecture. All allometric models fail to describe the declining rate of increase in fecundity with diameter found for 80% of 597 species in our analysis. The strong evidence of declining fecundity, beyond what can be explained by crown architectural change, is consistent with physiological decline. A downward revision of projected fecundity of large trees can improve the next generation of forest dynamic models.

  5. Abstract Background and Aims

    An individual plant consists of different-sized shoots, each of which consists of different-sized leaves. To predict plant-level physiological responses from the responses of individual leaves, modelling this within-shoot leaf size variation is necessary. Within-plant leaf trait variation has been well investigated in canopy photosynthesis models but less so in plant allometry. Therefore, integration of these two different approaches is needed.


    We focused on an established leaf-level relationship that the area of an individual leaf lamina is proportional to the product of its length and width. The geometric interpretation of this equation is that different-sized leaf laminas from a single species share the same basic form. Based on this shared basic form, we synthesized a new length-times-width equation predicting total shoot leaf area from the collective dimensions of leaves that comprise a shoot. Furthermore, we showed that several previously established empirical relationships, including the allometric relationships between total shoot leaf area, maximum individual leaf length within the shoot and total leaf number of the shoot, can be unified under the same geometric argument. We tested the model predictions using five species, all of which have simple leaves, selected from diverse taxa (Magnoliids, monocots and eudicots) and from differentmore »growth forms (trees, erect herbs and rosette herbs).

    Key Results

    For all five species, the length-times-width equation explained within-species variation of total leaf area of a shoot with high accuracy (R2 > 0.994). These strong relationships existed despite leaf dimensions scaling very differently between species. We also found good support for all derived predictions from the model (R2 > 0.85).


    Our model can be incorporated to improve previous models of allometry that do not consider within-shoot size variation of individual leaves, providing a cross-scale linkage between individual leaf-size variation and shoot-size variation.

    « less