Developing allometric equations to estimate forest biomass for tree species categories based on phylogenetic relationships

Mingxi Yng, Xiolu Zhou,＊, Chnghui Peng,b,＊＊, Tong Li, Kexin Chen, Zelin Liu,Peng Li, Cicheng Zhng, Jiyi Tng, Ziying Zou

a School of Geographic Sciences, Hunan Normal University, Changsha, 410081, China

b Institute of Environment Sciences,Department of Biology Sciences,University of Quebec at Montreal,Case Postale 8888,Succursale Centre-Ville,Montreal,Quebec,H3C 3P8, Canada

Keywords:

ABSTRACT The development of allometric biomass models is important process in biomass estimation because the reliability of forest biomass and carbon estimations largely depends on the accuracy and precision of such models.National Forest Inventories (NFI) are detailed assessments of forest resources at national and regional levels that provide valuable data for forest biomass estimation.However, the lack of biomass allometric equations for each tree species in the NFI currently hampers the estimation of national-scale forest biomass.The main objective of this study was to develop allometric biomass regression equations for each tree species in the NFI of China based on limited biomass observations.These equations optimally grouped NFI and biomass observation species according to their phylogenetic relationships.Significant phylogenetic signals demonstrated phylogenetic conservation of the crown-to-stem biomass ratio.Based on phylogenetic relationships,we grouped and matched NFI and biomass observation species into 22 categories.Allometric biomass regression models were developed for each of these 22 species categories, and the models performed successfully (R2 = 0.97, root mean square error (RMSE) = 12.9 t?ha–1,relative RMSE=11.5%).Furthermore,we found that phylogeny-based models performed more effectively than wood density-based models.The results suggest that grouping species based on their phylogenetic relationships is a reliable approach for the development and selection of accurate allometric equations.

1.Introduction

As the main component of natural carbon sequestration in terrestrial ecosystems, forest ecosystems have sequestered more than 80% of all terrestrial aboveground carbon(Richter et al.,1999;Jandl et al.,2007),in which woody plants accounting for approximately 70%of the carbon storage(Laiho and Laine,1997).Forest carbon is the amount calculated based on directly measurable sizes,such as diameter,height,and volume.Forest carbon estimations are predominantly carried out by converting measurable tree variables.These tree variables have been surveyed for more than a century to compile the National Forest Inventory (NFI) in Europe and North America(McRoberts et al., 2012; Gschwantner et al.,2022).In China, the systematic NFI started in 1973 and is repeated at approximately five-year intervals.There are now nine consecutive surveys available.The NFI system has undergone continuous improvements with respect to sampling design,survey methods,and technical standards(Lei et al.,2009;Zeng et al.,2015;Yin et al.,2022).These NFIs provide data on forest area and volume, which have been converted to forest carbon dynamics to estimate the carbon sequestration ability of forests in China during the past half century (Fang et al., 2001; Zeng, 2014).In addition to area and volume,many countries actively use information on diameter at breast height (DBH)and tree height (H) in their NFIs to estimate forest carbon storage and understand the dynamic development trend of forest growth (Joosten et al., 2004; Domke et al., 2020).Consequently,NFIs play a primary role in forest ecosystem management and policy design to achieve global carbon neutrality.

The conversion of forest volume to biomass using forest volume and area data provided by the NFI has attracted significant attention(Wang et al.,2001;Henry et al.,2015).The approach,commonly known as the volume-derived method, is a non-destructive and easy-to-implement approach when compared with harvesting methods.There are two primary methods of converting volume into stand biomass: allometric biomass equations and biomass expansion factors.Within the allometric biomass equation method, there are two main types of biomass equations.The first type uses stand volume as the predictor variable to directly calculate whole biomass(Muukkonen,2007),i.e.,aboveground biomass (AGB) and belowground biomass (BGB).The second type includes two steps: (1) multiplying stand volume by the wood density to obtain stem biomass;(2) expanding stem biomass to whole biomass via the allometric equation, with stem biomass as the predictor variable(Fang et al.,2002).Alternatively,a simpler conversion involves biomass expansion factors to represent the ratio of biomass to volume for specific forest types or species.The stand biomass can be estimated by multiplying the stand volume and expansion factor.In addition, if the NFI information includes DBH and H, stand biomass can be summed from individual tree biomass estimated by allometric equations using DBH or DBH and H as the predictor variable (Chave et al., 2005; Zianis et al.,2005;Forrester,2017; Luo et al.,2020;Loubota Panzou et al.,2021).

Previous studies have provided evidence that allometric relationships vary among different tree species(Xiang et al.,2016).However,the high level of accuracy achieved by specific species equations may restrict their applicability to other species.If an equation based on one species is applied to another species, a substantial bias may occur in the biomass estimation.The estimation of forest biomass based on the NFI information may be hindered by the lack of adequate equations for predicting biomass for every species.Such a limitation arises because conducting destructive harvests,which are labour-intensive,time-consuming,costly and sometimes impossible, pose challenges for obtaining the necessary data (Ishihara et al., 2015; Xiang et al., 2016).Consequently, the estimation of forest biomass based on the NFI remains an urgent need,which could facilitate the comprehensive analysis and classification of the species in NFI.

The NFI of China provides volume information for 57 individual tree species and five mixed forest types derived from the ninth National Forest Inventory of China.However,we found that only 20 specific species(or forest types)have sufficient field data comprising more than 10 samples for parameterizing their regression models.Although it is the largest public dataset of biomass measurements for China’s forest ecosystems(Luo et al.,2013),including 131 species measured over the past decades,many species have only one or a few measured samples.This means that many species in the NFI were not measured or there was a lack of sufficient samples.Parameterizing an allometric equation requires an adequate sample that is representative of each species, and this is a dilemma faced by modellers.This difficulty may also be an issue in estimating forest carbon in other countries.In a previous study in Europe(Zianis et al., 2005), among all the equations reporting sample sizes,more than 16%of the biomass equations were estimated from a number of samples varying from 3 to 10.This limited amount of data samples may result in considerable uncertainties in biomass estimation, highlighting the pressing need for more samples of specific species.However,owing to the substantial cost of conducting biomass measurements,it is impractical to record a large number of samples for each tree species in an NFI.

To date, for those NFI species that lacked sufficient measurement samples,several approaches have been generally applied for modelling:(1) collecting field data by empirically grouping species according to their traits,that is shade tolerance,evergreens,softwood,and hardwood,to construct the equations for these species (Jenkins et al., 2003; Weiskittel et al.,2015);(2)using the equations of specific species to directly estimate the biomass for other species that have similar traits, namely wood density,deciduous,or conifer(Fang et al.,2001;Guo et al.,2010;Zhou et al.,2019);and(3)using a general equation for the species(Chave et al., 2014).Overall, little attention has been paid to grouping tree species to estimate forest carbon based on NFI information.Therefore,further studies should be conducted to develop more suitable methods for accurate estimation of biomass.

The biomass of a species in an NFI can be computed using different biomass equations for different species groups (Akindele and LeMay,2006).However, this potentially increases the complexity of evaluating the amount of carbon stored in forest based on NFI.If the species cannot be closely matched, the equations cannot adequately explain the variation in biomass measurements (Ducey, 2012).Potential errors may be caused by directly applying the model coefficients of one species to another species(Jenkins et al.,2003).Alternatively,if general equations are applied across species, it would be useful to predict the global-scale forest biomass.Nevertheless, for a single country, NFI-based biomass estimation may need a more accurate approach.A general equation may result in large errors at some sites or species (Chave et al., 2014).Therefore, to use existing measurements and reduce inconsistencies between the model and predicted species, there is a need to explore a consistent method for estimating forest biomass at a relatively large scale.This raises the question of how to parameterize the regression model for the species in the NFI using available data from other species,that is, how to solve the tree species grouping problem (observed tree species vs.species counted in the NFI) to address the issue of the inconsistency between there being fewer measurements available and the necessary statistical criteria for estimating the biomass of each tree species (Jenkins et al., 2003; Weiskittel et al., 2015).Modelling by grouping based on similarities and differences between tree species is an urgent problem for an improved understanding of forest carbon sequestration at the national scale.

In evolutionary biology, a phylogenetic relationship is considered a surrogate for analyzing variations in species traits,under the assumption that closely related species, that is, tree species close to each other in a phylogenetic tree,are more similar than distant ones(Burns and Strauss,2011; Anacker and Strauss, 2016).Phylogeny has been identified as a robust factor controlling biomass allocation patterns across a wide range of plant sizes, particularly at the family level within higher taxonomic levels(McCarthy and Enquist,2007).We hypothesized that tree species with closer phylogenetic relationships would exhibit similar allometric relationships.Following this,the set of biomass equations constructed by grouping tree species according to the phylogenetic relationship and matching with species in NFIs may serve to mitigate the level of uncertainty associated with estimating forest biomass.In this study,we tested the effect of phylogenetic relationships on the traits of crown and stem biomass,grouped the species according to phylogenetic relationship,and then constructed allometric equations based on each species group.We also compared the goodness-of-fit of the models for different species groups,such as wood density-based groupings.Our objectives were(1)to group species according to their phylogenetic relatedness and investigate the relationship between phylogenetic relatedness and biomass allometry;(2)to develop stand biomass allometric models using stem biomass as the predictor variable for each of the phylogeny-based species groups,by taking advantage of the availability of the NFI data.

2.Materials and methods

2.1.Overview and framework

The study encompassed two distinct datasets: field biomass measurements and NFI information.To effectively group the species,a novel approach based on phylogenetic relationship was adopted.The phylogenetic approach facilitated the grouping of species according to evolutionary similarities among the species.Subsequently, the two datasets were carefully divided into the same categories and matched, which finally yielded 22 categories.After grouping, allometric models were developed through nonlinear regression analysis.In the models,the stem biomass served as the predictor variable, while the whole biomass was considered the dependent variable.To determine the stem biomass,the stem volume was multiplied by the corresponding wood density.Overall,by integrating phylogenetic relationships, proper categorization, and accurate estimation, the framework helps to reduce biomass estimation errors and provides a more robust understanding of biomass patterns and allocation strategies(Fig.1).

Fig.1.Flow chart for modelling China’s forest biomass at the national scale.Bs,stem biomass; Bw, whole biomass; AGB, above-ground biomass; BGB, belowground biomass.

2.2.Data source

The data included two parts: (1) The field forest measurements of volume per hectare (m3?ha–1) and dry weight of biomass per hectare(t?ha–1)of each tree organ,that is,foliage,flowers,fruit,branches,stems,coarse roots, and fine roots for 128 species at 994 sites in forest ecosystems of China(Luo et al.,2013,Figs.1 and 2;Table S1).These data were collected from harvested sample plots and used to develop allometric models to describe the relationship between stem and whole biomass(Bw) and analyse the phylogenetic relationships of biomass allocation.Among the data,measurements without any main organ biomass that is,stem biomass, crown biomass, aboveground biomass (AGB), and belowground biomass (BGB) were excluded from the final dataset that included whole biomass.(2) The latest (ninth) NFI for China’s forests from 2014 to 2018,which compiles information on forest area and volume of five age groups,comprising young,middle,near-mature,mature,and over-mature dominant tree species and forest types totalling 62 species types in 31 provinces of the country (Table S2).Among the 62 species types,the specific tree species name was known for 40 species.A total of 16 species were identified and categorized at the genus level,and six forest types were classified as mixed forests.As a compilation of national resource statistics,the NFIs have undergone a systematic sampling design and rigorous statistical tests to provide reliable information at the national scale(Fang et al.,2001;Lei et al.,2009;Zhang and Wang,2021),although errors may still exist.The information released from these NFIs has been used to publish reports on forest biomass and carbon storage(Food and Agriculture Organization,2020).According to these data,we assigned the species in data (1) and (2) as Measured-species and NFI-species, respectively.The two datasets include some established species categories for mixed stands and multi-species, such as “mixed broadleaf–conifer forests”,“mixed broadleaf forest”,and“mixed conifer forests”.However, the categories were not included in the tree species grouping process due to the availability of sufficient measurements for parameterization(refer to Table S4 in Supporting Information).

2.3.Examination of the effect of phylogenetic relationship

Fig.2.Field sites for measuring tree biomass and stem volume in China,with a total of 994 sites and 128 tree species.The green colour represents the forest cover,and the blue circles represents the forest plots.(For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

To test whether phylogeny influenced tree morphology, we calculated the crown-to-stem biomass ratio(crown biomass:stem biomass)to represent the relative size of different tree organs.We screened for tree species with at least four biomass observations,resulting in a total of 50 species (Table S3).To assess the mean crown-to-stem biomass ratios at the species level, phylogenetic trees of all the species selected were acquired from the largest mega-tree of vascular plants using the V.Phylo-Maker R package (Jin and Qian, 2019).Furthermore, the phylogenetic signal can capture the tendency of closely related species to exhibit similar trait values due to shared evolutionary history.It quantifies the degrees of trait (e.g., crown-to-stem biomass ratio) conservation or divergence along the branches of a phylogenetic tree,providing insights into the role of phylogenetic relationships in shaping trait variation.When there is a high phylogenetic signal,it suggests that closely related species are more similar in their traits, indicating a strong degree of phylogenetic conservatism.Conversely, a low phylogenetic signal implies that traits are influenced more by other factors such as environmental conditions rather than shared ancestry.To determine the phylogenetic signal of the crown-to-stem biomass ratio, we computed Pagel’s λ value, a widely used indicator for quantifying phylogenetic signals.Pagel’s λ is a number between 0 and 1,where λ=1 indicates that the trait variation depends entirely on phylogeny, and λ = 0 indicates that there is no phylogenetic dependence (Pagel, 1999).The statistical measure assumes of a Brownian model of trait evolution and is evaluated using the phylosig function from the phytools package in R(Revell,2012).We obtained a p-value to assess whether λ was significantly different from 0,that is,the validity of a phylogenetic signal.

2.4.Species grouping

The two species data sets, Measured-species and NFI-species, were classified into an equal number of groups (22 groups) based on their phylogenetic relationship, number of measured biomass samples (primarily for Measured-species), and wood density (primary for NFIspecies).Subsequently, the species groups of the two species datasets were paired according to the phylogenetic relationship (Fig.1).The average trait values of closely related phylogenetic groups are closer than those of distantly related groups (Losos, 2008; Crisp et al., 2009).Nevertheless, some species could be exceptions.A few NFI-species that do not belong to any genus or family of Measure-species could not be grouped based on phylogenetic relationship.The level of phylogenetic closeness among the hardwood species in Group#9(Model 9)exhibits a wide range of variation.They could first be classified by class of seed plants into gymnosperm and angiosperm and then grouped based on similar wood density.

Another modelling requirement is to ensure that there are sufficient measurements for each group.For developing a biomass allometric model, it is necessary to have a wide range of data that encompasses small to large trees.We grouped tree species with a suitable number of biomass samples measured, which allowed for reliable model parameterization.Although the plant classification system is still under development,there is a universal consensus on the genus-level classification of dominant tree species in national forests.If the tree species in NFIs do not have sufficient observed biomass data for common species,observations from the same genus can be used to determine the parameters of the biomass equation by regression fitting.Using the V.PhyloMaker package,we generated two phylogenetic trees for the 128 Measured-species and 59 NFI-species in the ninth NFI of China (Fig.1).The NFI-species and Measured-species were matched according to two phylogenetic trees and the number of biomass samples observed for each species.

2.5.Modelling

We used a conventional allometric equation (power-law function;Huxley, 1924) to model the allometric relationship between stem biomass and whole biomass.Stem biomass was calculated by multiplying the volume with wood density,which can be represented by the slope of the linear regression equation for the dependent variable stem biomass and the independent variable wood volume (V) (Liu et al., 2019; Zhou et al.,2019).Therefore,the biomass equation used at the national scale was constructed as follows:

where y is the whole biomass (Bw= AGB + BGB) per hectare, x is the stem biomass per hectare(Bs),ρ is the wood density,V is the stem volume per hectare, α and β are two undetermined parameters, and β is the allometric scaling coefficient.This biomass equation was used to estimate the whole biomass per unit area.Given that the information released in China’s NFI only included the forest volume and area data for dominant tree species and age groups corresponding to each province,Eqs.1 and 2 were parameterized based on the grouped species and field measurements at the plot level(Fig.1).The wood density ρ of a species can be estimated based on wood industry standards, literature, public wood density databases, and field measurements of stem biomass and volume (Chinese Academy of Forestry Sciences, Research Institute of Wood Industry,1982;Zanne et al.,2009;National National Forestry and Grassland Administration, 2017).For reference, we listed the wood density values for each NFI-species(Fig.4).

2.6.Modelling comparison

In the Measured-species dataset consisting of 128 species and 994 measurements, 63 species had a small number of measurements, only 165 in total.The number of these species accounted for a large proportion of Measured-species, reaching 49.2%.We compared these species using different grouping methods parameterized in Eq.1 by grouping the species based on phylogenetic relationship (Grouping I) and different wood densities (Grouping II).Grouping II included two different classifications of wood density values using different initial values to avoid coincidences in the results.The two groups were compared according to residual error,root mean square error(RMSE),relative RMSE(%RMSE),percentage error (error), and coefficient of determination (R2) for the species rarely measured.We calculated the RMSE and %RMSE for the whole biomass for plot i,as follows:

where N denotes the number of plots of measured biomass in each equation, and yobs_iand ypred_iare the measured whole biomass and estimated whole biomass of plot i in each equation, respectively.RMSE and%RMSE were used to assess the prediction errors and performance of models.A lower RMSE value signifies higher predictive accuracy,while a lower %RMSE value indicates increased stability in the model’s performance across different data subsets.In addition, the R2value, which ranges from 0 to 1, provides information on the goodness-of-fit of the model.

Furthermore, the model test was designed using training and test datasets.We selected four categories,namely Models 12,13,17,and 22,each having a large sample size(greater than 50).The data were divided into training and test datasets in a 7:3 ratio.We compared the model performance on training and test datasets separately using two distinct grouping methods based on phylogeny and wood density.

3.Results

3.1.Biomass allocation phylogeny and grouped species

Fig.3.Phylogenetic trees of selected species and the ratio of crown biomass to stem biomass (CB/SB).Purple denotes gymnosperms, and dark blue denotes angiosperms.Available data from 50 species were sifted through measurements for the analysis.The phylogenetic tree was constructed using R package V.PhyloMaker.Pagel’s λ is a phylogenetic signal with a value between 0 and 1.The significant level is＊p<0.05.(For interpretation of the references to colour in this figure legend,the reader is referred to the Web version of this article.)

Tree crown-to-stem biomass ratio is a phylogenetically conserved characteristic.We detected a significant phylogenetic signal(Pagel’s λ=0.359, p < 0.05; Fig.3), indicating that the close tree species tended to have similar morphology.Based on the phylogenetic relationship and number of measured data, the NFI-species were grouped into 22 categories (Fig.4).There were 10 categories of angiosperms and 12 categories of gymnosperms.A total of 22 species-specific allometric models were developed, and each model corresponded to a category of NFI-species.Twelve models corresponded to a single species, and 10 models corresponded to species groups, which included a total of 59 species.Corresponding to these 22 categories of NFI-species, each Measured-species was also merged into 22 categories.This ensured that the model could be parameterized based on the samples measured ranging from 9 to 266.The number of species measured included in the models ranged from 1 to 24,with a median of 4.

3.2.Allometric relationship between stem biomass and whole biomass

Using existing data on destructive stem biomass and whole biomass across forest ecosystems in China, we were able to fit 22 allometric models for all species (59) in the ninth NFI of China.The relationships between stem biomass and whole biomass were effectively explained by the allometric models(Fig.5).All of these models,with R2values ranging from 0.901 to 0.997, demonstrate a high level of performance, with an average variance explained of 97.0% (Table 1).The parameters of the biomass models for the 22 models are listed in Table 1.All the models were highly significant(p<0.01)for both parameters α and β.The value of the RMSE ranged from 7.0 to 24.1 t?ha–1, with an average of 12.9 t?ha–1.The mean%RMSE for the whole biomass of the allometric models was 11.5%(ranging from 6.1%to 22.5%).The scaling coefficient(β)was higher for angiosperm species,with an average of 0.90,and significantly lower for gymnosperm species,with an average of 0.84(p <0.01).

3.3.Comparison of different species groupings

To compare the fitting accuracy of the allometric models between different species groups,we selected eight models(with＊in Table 1)to test the fitting ability of Groupings I and II,including 63 species and 165 field measurements.Depending on the wood density (WD) measured,these species were classified into four groups (Table 2).Their wood densities were distributed at 0.40,0.50,0.60(WD Classification 1;t?m–3)and 0.35, 0.45 and 0.55 (WD Classification 2; t?m–3).These models (in Table 2) can be substituted for the models with asterisks(＊) in Table 1.The model number,sample size(N),parameters α and β,and values of R2,RMSE,and%RMSE are listed in Table 2.The error analysis indicated that the residual range for Grouping I (-48% to 48%) was less than that of Grouping II(-95%to 53%for WD Classification 1;-99%to 53%for WD Classification 2;see Fig.6).The slope for Grouping I was 0.01,while for Grouping II, the slopes were -0.07 and -0.13 corresponding to WD Classification 1 and 2, respectively.The significant difference in RMSE and %RMSE between the two groups indicated that the model performance of Grouping I was more effective than that of Grouping II.On average,the grouping based on the phylogenetic relationship presented a higher goodness-of-fit than the models grouped based on wood density.

The robustness test results showed that both the phylogeny and wood density-based models demonstrated consistent performance between the training and test datasets(Figs.S1 and S2).The model evaluation on the test set suggested that the phylogeny-based model(R2=0.964;RMSE=12.4 t?ha–1; %RMSE = 12.1%) outperforms the wood density-based model(R2=0.964;RMSE= 13.4 t?ha–1;%RMSE=13.0%;Fig.S3).

Fig.4.Grouping and classification of NFI-species and Measured-species based on the phylogenetic relationships and the number of measured biomass samples recorded.The left(orange)and right(light green)phylogenetic trees are the measured tree species,with angiosperms on the left and gymnosperms on the right.The number in parentheses after the tree species names indicates the number of records measured for that species.The NFI-species at the top are listed in order of phylogenetic relationships.The symbol“√”corresponds to the NFI-species above for grouping to construct biomass models.There were 22 groups in total,that is 22 models could be developed.(For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

4.Discussion

Our results have demonstrated a relatively strong fit for the allometric relationship between stem biomass and whole biomass.The whole biomass (Bw) estimated using the phylogeny model effectively fit the measured values, compared with that estimated by the wood density model (Figs.5 and 6).This suggested that the classification of existing tree species according to the phylogenetic relationship can be used to construct suitable biomass equations.The biological meaning of this approach lies in the fact that the allometric relationships of tree species with close phylogenetic relationships have similar characteristics(Reich et al., 2014; Sun et al., 2020).This result confirms our hypothesis.In addition to analyzing the allometric relationship between the stem and whole-tree biomass, we tested the phylogenetic signal.A significant signal was observed for the crown-to-stem biomass ratio (Fig.3).Phylogenetic analysis suggested that the allometric relationship between stem and crown biomass was generally related to the phylogenetic relationship of the species, showing phylogenetic conservatism in the geometric structural characteristics of trees (Reich et al., 2014; Poorter et al.,2015).Although we only focused on the relationship between the crown and stem biomass in the present study, previous works have reported that phylogeny influences the scaling exponent of allometric relationships of root biomass with DBH(Sun et al.,2020).Consequently,considering phylogeny can facilitate the classification of species into appropriate categories based on their shared evolutionary histories.Biomass allometric equations and estimations of forest carbon can be used for improving the model by considering species classification.Overall, developing biomass models by grouping tree species according to phylogenetic relationships can achieve a high degree of fitting accuracy.

Fig.5.Power equations(y=αxβ)of the allometric relationship between stem biomass and whole biomass.The equations were developed by grouping 22 tree species in the NFI by phylogenetic relationships.In the regressions,y and x denote whole biomass(t?ha–1)and stem biomass(t?ha–1),respectively;stem biomass is the product of wood density(ρ)and volume(V);α and β represent model regression coefficients.All data were measured in the field by destructive sampling for 128 species.The numbers in parentheses denote the 22 species grouped in the NFI (see Fig.4).R2 means coefficient of determination.

Table 1 Allometric models for estimation of whole biomass in NFI-species.The model numbers correspond to the ones in Figs.4 and 5.

Table 2 Allometric models parameterized based on the species wood density.

Fig.6.Comparison of model fitting between two parameterizations.(a)Grouping I, species were categorized according to their phylogenetic relationships, corresponding to the tree species in the equations with asterisks (＊) in Table 1.The biomass of these species was rarely measured or had few data samples.(b) Grouping II, species were classified according to wood density,corresponding to the models and WDs in Table 2.The tree species are the same as Group 1.(c)The values of RMSE and%RMSE are averages of all groups.WD,wood density; RMSE, root mean square error; %RMSE, relative RMSE.

In some cases, wood density can also be a reference factor for grouping species and modelling allometric relationships (Manuri et al.,2014).From the perspective of stem biomass,this is appropriate because species with the same wood density should have a similar relationship with volume-to-Bs.However, their metabolic patterns and nutrient use efficiency are not necessarily the same.This may result in differences in the ratios of crown-to-stem biomass and the allometric relationships between crown and stem biomass.This implies that the parameters of the biomass equation (Eq.1) would be different.A comparison of grouping approaches confirmed that mixing the measurements of the species that have different allometric relationships may lower the goodness-of-fit.The averages of the evaluation indicators (R2, RMSE, and %RMSE) for the goodness-of-fit indicated clear differences between Grouping I and Grouping II(the last line in Table 2).Fig.6 illustrated that Grouping I had lower residual errors, higher accuracy(RMSE),and higher precision(%RMSE) than Grouping II.Given that the different initial values were designed for Grouping II,the potential similarities in the results could be substantially reduced, which improved the robustness of the analysis.These findings partly confirm our hypotheses.In general,grouping species based on phylogenetic relationships may be a more effective solution.Species and wood density are the most essential dimensions for grouping species and constructing biomass equations.Conducting a comparison between these two dimensions could be beneficial for an improved understanding of the effects of species composition on modelling forest biomass at the national scale.We expect that biomass datasets will be continually updated in the future.These rich field data will ensure accurate model parameterizations.However, we were not able to test the effects of grouping in more dimensions, such as climatic zone,ecoregion,soil texture,or life habit,which may also influence the allometric relationship(Reich et al.,2014;Loubota Panzou et al.,2021).

The method presented in this study has broad application prospect.It addresses the issue of lack of measurements to obtain a biomass equation for a species and how the field data for other species are used to construct the biomass equation for this species.Constructing equations by grouping species without an agreed generalizable solution may become an issue because of the large biological differences between tree species.Biologically,allometric relationships reflect the metabolic efficiency of a plant as a whole.Metabolic efficiency is affected not only by climate or site conditions(Lines et al.,2012;Dusenge et al.,2019)but also by plant traits (Mcgill et al., 2006).This is also attributed to species evolution based on the taxonomy(Vasseur et al.,2012;Weng,2014).This implies that the appropriateness of tree species must be stressed equally in the analysis of the allometric relationships of different tree organs.Biomass may differ largely between the forests of the two species (Scheller and Mladenoff, 2005).A pronounced difference in carbon sequestration has been indicated for forest communities with different biodiversity (Wardle et al., 2012).In terms of practical applications, our method has demonstrated a trade-off between measuring costs and large field samples of demand for parameterizing the biomass of a specific species.In some cases,some tree species in the NFIs do not have sufficient biomass observations.Therefore,biomass equations based on fewer samples may have large uncertainties (van Breugel et al., 2011).Our method has provided an alternative option for collecting and grouping the data measured from tree species with similar traits.

Nevertheless, uncertainty and issues remain.In grouping based on phylogenetic relationship,we found two main issues.One is that species may differ in traits,including if they are phylogenetically close.There are differences in the ratio of crown-to-stem biomass(e.g.,Pinus sylvestris vs.Pinus densiflora) and wood density(e.g., Pinus yunnanensis vs.Pinus dendata;Fig.3).Assigning them into the same group may reduce the model’s goodness-of-fit.In this case,we tend to group the species by wood density, but this may be a challenge if the wood density data are also unsuitable.Second,the phylogenetic trees would be over-pruned because of insufficient data or tree species samples.The clipped phylogenetic tree only contained a relatively small number of tree species,which may have led to two species with different characteristics appearing relatively close in the phylogenetic relationship.This may lead to misclassification of species,the direct effect of which may significantly reduce the fit of the model.During parameterization, for outliers in these species, we considered it necessary to carefully confirm their phylogenetic paths and consider whether grouping based on wood density is appropriate.In addition, some tree species are very different from each other.For example, it is taxonomically controversial whether Ginkgo biloba is a gymnosperm or an angiosperm.The species is difficult to group based on phylogenetic relationship.We tentatively classified this species as Cupressaceae, a group with a long evolutionary history.In addition to phylogeny, temperature, precipitation, soil moisture, and nutrient availability also significantly influence biomass allometric relationships(Chave et al., 2014).If tree species are grouped without considering environmental factors, there may be uncertainty in the modelling.The main reason for these uncertainties is the lack of data,which is difficult to resolve within the short term by expanding biomass datasets using harvesting methods.Our study aimed to maximize the use of measured data and explore improved methods for NFI-based forest biomass modelling.Other uncertainties, such as measurement errors in biomass and wood density, have been discussed in depth in many previous studies (Chave et al.,2009;Henry et al.,2010;Holdaway et al.,2014;Temesgen et al.,2015)and are beyond the scope of this study.

5.Conclusions

This study has provided an improved and reliable method for grouping species to establish an allometric biomass model with limited observational data.This grouping was based on the phylogenetic relationship and number of observed biomass records.We matched these observations with those of China’s ninth NFI,and established 22 biomass allometric models.The phylogeny-based biomass models showed a higher model efficiency and lower prediction error(R2=0.97,RMSE=12.9 t?ha–1, %RMSE = 11.5%) than the traditional wood density-based models, demonstrating higher accuracy biomass models for tree species grouping based on phylogenetic relationship.We applied the tree species grouping method to reduce uncertainty in the estimation of forest biomass.The approach presented in this study represents an effective framework for species grouping to develop biomass models that facilitate increasingly accurate national-scale extrapolations and could help reduce the uncertainty in forest carbon budget estimation.We hope that the theoretical approach to tree species grouping presented in this study will contribute to a more quantitative understanding of global forest biomass.

Funding

This work was supported by the Science and Technology Innovation Program of Hunan Province (2022RC4027) and the Joint Fund for Regional Innovation and Development of the National Natural Science Foundation of China(U22A20570).

Ethics approval and consent to participate

Not applicable.

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Not applicable.

Statement of authorship

Conceptualization:MY,XZ;Methodology:MY,XZ,TL;Investigation:MY, XZ; Visualization: MY; Funding acquisition: CP; Writing original draft: MY,XZ,TL,KC,CP,ZL, PL,CZ,JT, YZ.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

We thank Profs.Jing Wang and Jiaxiang Li for their constructive suggestions and valuable comments.

Appendix A.Supplementary data

Supplementary data to this article can be found online at https://doi.i.org/10.1016/j.fecs.2023.100130.