Generalized biomass and leaf area allometric equations for European tree species incorporating stand structure, tree age and climate

Highlights

• A database containing nearly 1000 European biomass equations was developed.

• Biomass and leaf area allometry were influenced by stand structure.

• Species traits were correlated with interspecific differences in responses to stand structure.

Abstract

Biomass and leaf area equations are often required to assess or model forest productivity, carbon stocks and other ecosystem services. These factors are influenced by climate, age and stand structural attributes including stand density and tree species diversity or species composition. However, such covariates are rarely included in biomass and leaf area equations. We reviewed the literature and built a database of biomass and leaf area equations for 24 European tree species and 3 introduced species. The final dataset contained 973 equations. Most of the equations were site-specific and therefore restricted to the edaphic, climatic and stand structural conditions of the given site. To overcome this limitation, the database was used to develop regional species-specific equations that can be used in a wide range of stands and to quantify the effects of climate, age and stand structure on biomass or leaf area. The analysis showed considerable inter- and intra-specific variability in biomass relationships. The intra-specific variability was related to climate, age or stand characteristics, while the inter-specific variability was correlated with traits such as wood density, specific leaf area and shade tolerance. The analysis also showed that foliage mass is more variable than stem or total aboveground biomass, both within and between species, and these biomass components have contrasting responses to age and changes in stand structure. Despite the large number of published equations, many species are still not well represented. Therefore, generic equations were developed that include species-specific wood density instead of species identity. Further improvements may be possible if future studies quantify the stand structure of individual tree neighbourhoods instead of using the stand means for all trees sampled with the given stand.

Introduction

Allometric relationships are critical for quantifying many aspects of ecology and forestry including the prediction of tree and stand variables to assess productivity, carbon stocks and other ecosystem services at the tree, stand, landscape or regional levels (Henry et al., 2013, Chave et al., 2014, Paul et al., 2016). They are also required when quantifying or modelling forest functioning, such as how light, water, nutrient and carbon pools and fluxes respond to changes in climate or management.

Allometric relationships are often expressed in the form of Eq. (1), implying a 1% change in variable X will result in a b% change in variable Y.

$$Y={\mathit{aX}}^{b_{y\text{,}x}}$$

The value of the exponent b has been hotly debated (Sileshi, 2014) and hypothesised to relate to mechanical constraints that prevent trees from buckling (Greenhill, 1881, McMahon, 1973), hydraulic constraints (Ryan et al., 2006) and biophysical constraints. Contributions regarding the biophysical constraints include geometric scaling (Yoda et al., 1963, Gorham, 1979, Pretzsch et al., 2012), which suggests proportionality between different linear dimensions; linear tree dimensions (e.g., diameter) are related to quadratic or area-related dimensions (e.g., leaf area) as linear ∝ quadratic^1/2 and to cubic variables (e.g., biomass) as linear ∝ cubic^1/3 or quadratic ∝ cubic^2/3. In contrast, the metabolic scaling theory describes resource distribution along hierarchical branching networks (West et al., 1999, West et al., 2009) and predicts that b_{biomass, diameter} = 8/3, b_{leaf area, diameter} = 4/3 (Pretzsch et al., 2012). However, b is usually not invariant for these relationships and the frequency distribution of b is not necessarily centred on the value of b predicted by the geometric or metabolic scaling theories (Coomes, 2006, Pretzsch, 2006, Ducey, 2012, Lines et al., 2012, Pretzsch and Dieler, 2012, Pretzsch et al., 2012, Pretzsch et al., 2013, Sileshi, 2014). Therefore, while the general allometric exponents may be useful for rough scaling they are less useful for modelling stand growth dynamics or for developing biomass and leaf area equations to upscale from tree measurements.

The variability in the exponent b is related to the fact that allometric relationships reflect current and past environmental conditions and provide information about within-tree carbon partitioning, which affects a trees’ ability to acquire and compete for resources. Therefore, allometric relationships between diameter and biomass (foliage, stems or roots) or leaf area can vary with age (Wirth et al., 2004, Genet et al., 2011, Shaiek et al., 2011), stand density (Monserud and Marshall, 1999), species mixing (Laclau et al., 2008) and site characteristics (Wirth et al., 2004, Russell et al., 2015). As a result, equations developed using trees sampled from a single stand may be unbiased and precise for that situation but they are unlikely to be suitable for other ages or stands that differ in structure, climate or site characteristics (Muukkonen, 2007). Despite this, variables describing age, site and stand structural characteristics such as density, species composition or diversity are rarely included in biomass equations (Zianis et al., 2005) because this would require a larger sample of trees from a range of ages and site conditions.

In a recent review, only about 24% of equations were found to contain more than one independent variable, usually diameter (Henry et al., 2011). Nevertheless, for some species there are already many published biomass equations (Zianis et al., 2005) and the suitability of each equation for use in different stands can be determined, for example, by sampling some trees and comparing the measured biomass with the biomass predicted by the published site-specific equations (Freese, 1960, Pérez-Cruzado et al., 2015). However, this requires destructive biomass sampling in each target stand. It also requires that there is a published equation suitable for that stand, for which the likelihood declines as the number of published equations declines. An alternative approach is to use all of the published site-specific equations to develop new “regional” allometric equations that include independent variables such as climate, age, stand density and any other important site characteristics.

Several studies have developed regional species-specific or even generic (species independent) biomass equations (Pastor et al., 1984, Wirth et al., 2004, Lambert et al., 2005, Case and Hall, 2008, Seidl et al., 2010, Shaiek et al., 2011, Chave et al., 2014, de-Miguel et al., 2014, Paul et al., 2016). These often combine raw data from many different studies, but such data do not exist for many species or regions, or biomass data that was used to develop site-specific equations has been lost or is unavailable. Therefore, some studies have used pseudo-observations calculated from published equations, such as predicted biomass values for each 1-cm or 5-cm diameter class (Jenkins et al., 2003, Muukkonen, 2007, Chojnacky et al., 2014) or a given number of pseudo-observations between the range of diameters sampled to produce the given site-specific equation (Pastor et al., 1984). Regardless of the approach used, most of the resulting regional or generic equations (i.e. generalized equations) have included only tree-level variables (e.g., diameter, height) and/or species-level variables (e.g., wood density) and therefore average out or group the variability in tree biomass that might otherwise be explained by age, climate, soils, stand density or species mixing (Wirth et al., 2004, Chojnacky et al., 2014, Weiskittel et al., 2015). Such variables could facilitate the development of biomass equations that are applicable to a wider range of sites and stands, and can be used to examine the effects of these factors on stand growth and biomass stocks.

Despite the large number of published equations, many European species are still not well represented. Therefore, the first objective of this study was to develop a database containing biomass and leaf area equations for 24 European tree species and 3 introduced species (Pseudotsuga menziesii, Robinia pseudoacacia and Prunus serotina) that are currently considered important by European foresters. The review of the literature resulted in a total of 973 equations, including raw data sets obtained from tables in publications or from our previous work. These data were used to test the hypotheses that: (1) foliage or branch mass are more variable than stem, coarse root or total aboveground biomass; (2) age, trees per hectare, basal area and climate all influence the relationships between tree diameter and biomass or leaf area; (3) these variables have contrasting effects on different biomass components; (4) there are significant differences between species in terms of their response to age, trees per hectare, basal area and climate, and these differences vary in relation to traits such as specific leaf area, wood density and shade tolerance. Our second objective was to develop generalized regional equations for each species, or species group, and each biomass component or leaf area, which include the independent variables age, trees per hectare, basal area, mean annual precipitation or mean annual temperature and can therefore be used in a wider range of forest types.