Integrated whole-tree biomass and volume equations are in great demand due to the simultaneous need to improve estimation of forest carbon stocks and to quantify the distribution of wood volume within trees for estimating whole-tree utilization potential. While the volume of the dominant stem in a tree has been extensively studied, the relative mass and volume of branches has received much less attention. It is particularly challenging to quantify the branch volume and branch mass in trees with a deliquescent branching architecture (i.e., hardwoods) and it is even difficult to model the dominant stem for such trees because the lack of apical dominance makes definition of the dominant stem more obscure.New profile models allow for volume and mass estimation of the dominant stem and whole tree from ground to the top of the tree. Cumulative branch volume and mass can be estimated at different relative heights from the whole-tree and dominant stem profiles by simple subtraction. The models were developed from intensive, destructive sampling of 32 trees from a temperate hardwood forest in Michigan, USA. The species in the sample were primarily American beech (Fagus grandifolia Ehrh.) and sugar maple (Acer saccharum Marsh.). A mixed-effects modeling framework was used throughout model development of volume, density, and mass profiles. Non-linear mixed-effects composite models were used for cumulative volume profiles to account for among tree variation and the ability to correlate multiple measurements within an individual tree. Species-specific linear mixed-effects models were developed for basic density profiles. Species-specific non-linear mixed-effects models were also developed for cumulative mass profiles compared to density-integral and constant density models.
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