With the development of national-scale forest biomass monitoring work, accurate estimation of forest biomass on a large scale is becoming an important research topic in forestry. In this study, the stem wood, branches, stem bark, needles, roots and total biomass models for larch were developed at the regional level, using a general allometric equation, a dummy variable model, a mixed effects model, and a Bayesian hierarchical model, to select the most effective method for predicting large-scale forest biomass. Results showed total biomass of trees with the same diameter gradually decreased from southern to northern regions in China, except in the Hebei province. We found that the stem wood, branch, stem bark, needle, root, and total biomass model relationships were statistically significant (p-values < 0.01) for the general allometric equation, linear mixed model, dummy variable model, and Bayesian hierarchical model, but the linear mixed, dummy variable, and Bayesian hierarchical models showed better performance than the general allometric equation. An F-test also showed significant differences between the models. The R² average values of the linear mixed model, dummy variable model, and Bayesian hierarchical model were higher than those of the general allometric equation by 0.007, 0.018, 0.015, 0.004, 0.09, and 0.117 for the total tree, root, stem wood, stem bark, branch, and needle models respectively. However, there were no significant differences between the linear mixed model, dummy variable model, and Bayesian hierarchical model. When the number of categories was increased, the linear mixed model and Bayesian hierarchical model were more flexible and applicable than the dummy variable model for the construction of regional biomass models.

The effect of evolutionary history on wood density variation may play an important role in shaping variation in wood density, but this has largely not been tested. Using a comprehensive global dataset including 27,297 measurements of wood density from 2621 tree species worldwide, we test the hypothesis that the legacy of evolutionary history plays an important role in driving the variation of wood density among tree species. We assessed phylogenetic signal in different taxonomic (e.g., angiosperms and gymnosperms) and ecological (e.g., tropical, temperate, and boreal) groups of tree species, explored the biogeographical and phylogenetic patterns of wood density, and quantified the relative importance of current environmental factors (e.g., climatic and soil variables) and evolutionary history (i.e., phylogenetic relatedness among species and lineages) in driving global wood density variation. We found that wood density displayed a significant phylogenetic signal. Wood density differed among different biomes and climatic zones, with higher mean values of wood density in relatively drier regions (highest in subtropical desert). Our study revealed that at a global scale, for angiosperms and gymnosperms combined, phylogeny and species (representing the variance explained by taxonomy and not direct explained by long-term evolution process) explained 84.3% and 7.7% of total wood density variation, respectively, whereas current environment explained 2.7% of total wood density variation when phylogeny and species were taken into account. When angiosperms and gymnosperms were considered separately, the three proportions of explained variation are, respectively, 84.2%, 7.5% and 6.7% for angiosperms, and 45.7%, 21.3% and 18.6% for gymnosperms. Our study shows that evolutionary history outpaced current environmental factors in shaping global variation in wood density.

Variations in biomass-carbon of forest can substantially impact the prediction of global carbon dynamics. The allometric models currently used to estimate forest biomass face limitations, as model parameters can only be used for the specific species of confirmed sites. Here, we collected allometric models LnW = a + b*Ln(D) (n = 817) and LnW = a + b*Ln(D²H) (n = 612) worldwide and selected eight variables (e.g., mean annual temperature (MAT), mean annual precipitation (MAP), altitude, aspect, slope, soil organic carbon (SOC), clay, and soil type) to predict parameters a and b using Random Forest. LnW = a + b*Ln(D), drove mainly by climate factors, showed the parameter a range from − 5.16 to − 0.90 [VaR explained (model evaluation index): 66.21%], whereas parameter b ranges from 1.84 to 2.68 (VaR explained: 49.96%). Another model LnW = a + b*Ln(D²H), drove mainly by terrain factors, showed the parameter a range from − 5.45 to − 1.89 (VaR explained: 69.04%) and parameter b ranges from 0.43 to 1.93 (VaR explained: 69.53%). Furthermore, we captured actual biomass data of 249 sample trees at six sites for predicted parameters validation, showing the R² (0.87) for LnW = a + b*Ln(D); R² (0.93) for LnW = a + b*Ln(D²H), indicating a better result from LnW = a + b*Ln(D²H). Consequently, our results present four global maps of allometric model parameters distribution at 0.5° resolution and provides a framework for the assessment of forest biomass by validation.

Accurate biomass estimations are important for assessing and monitoring forest carbon storage. Bayesian theory has been widely applied to tree biomass models. Recently, a hierarchical Bayesian approach has received increasing attention for improving biomass models. In this study, tree biomass data were obtained by sampling 310 trees from 209 permanent sample plots from larch plantations in six regions across China. Non-hierarchical and hierarchical Bayesian approaches were used to model allometric biomass equations. We found that the total, root, stem wood, stem bark, branch and foliage biomass model relationships were statistically significant (p-values < 0.001) for both the non-hierarchical and hierarchical Bayesian approaches, but the hierarchical Bayesian approach increased the goodness-of-fit statistics over the non-hierarchical Bayesian approach. The R² values of the hierarchical approach were higher than those of the non-hierarchical approach by 0.008, 0.018, 0.020, 0.003, 0.088 and 0.116 for the total tree, root, stem wood, stem bark, branch and foliage models, respectively. The hierarchical Bayesian approach significantly improved the accuracy of the biomass model (except for the stem bark) and can reflect regional differences by using random parameters to improve the regional scale model accuracy.

Knowledge of which biological and functional traits have, or lack, phylogenetic signal in a particular group of organisms is important to understanding the formation and functioning of biological communities. Allometric biomass models reflecting tree growth characteristics are commonly used to predict forest biomass. However, few studies have examined whether model parameters are constrained by phylogeny. Here, we use a comprehensive database (including 276 tree species) compiled from 894 allometric biomass models published in 302 articles to examine whether parameters a and b of the model $\mathrm{W}=\mathrm{a}{\mathrm{D}}^{\mathrm{b}}$ (where W stands for aboveground biomass, D is diameter at breast height) exhibit phylogenetic signal for all tree species as a whole and for different groups of tree species. For either model parameter, we relate difference in model parameter between different tree species to phylogenetic distance and to environmental distance between pairwise sites. Our study shows that neither model parameter exhibits phylogenetic signals (Pagel's λ and Blomberg's K both approach zero). This is the case regardless of whether all tree species in our data set were analyzed as a whole or tree species in different taxonomic groups (gymnosperm and angiosperm), leaf duration groups (evergreen and deciduous), or ecological groups (tropical, temperate and boreal) were analyzed separately. Our study also shows that difference in each parameter of the allometric biomass model is not significantly related to phylogenetic and environmental distances between tree species in different sites.