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McArthur and McArthur’s (1961) foliage height diversity (FHD) is widely used for determining structural complexity, from LiDAR vertical height (𝐻) profiles (Lefsky et al. 2002, Vierling et al. 2008, Simonson et al. 2014). FHD has however largely failed to disentangle the relationships between the ecosystem structural diversity and biodiversity, with early reports such as those from Thomas Lovejoy (1972) in the Amazon not finding evidences in the light of FHD. It remains unclear whether FHD is the most suitable means to determine the structural complexity of ecosystems. The calculation of FHD involves layering the vertical profile, which is essentially unnatural to describe a continuous variable (𝑋) such as height, and involve subjective steps such as the determination of the size of these layers, from which the value of FHD obtained is ultimately dependent upon. This is because FHD is based on Shannon’s (1948) entropy index, which was not originally designed to describe continuous variables, but meant for abundance data for categorical variables. In Adnan et al.(2021) we provided a mathematical framework for determining maximum entropy in 3D remote sensing datasets based on Lorenz curves and Gini (1921) coefficients (𝐺𝐶) determined from theoretical continuous distributions, intended to replace FHD as entropy measure in vertical profiles of LiDAR heights. This framework was developed for 1-dimensional variables (1D; 𝑋) such as tree heights, and 2-dimensional variables (2D; 𝑍∝ 𝑋 2) such as basal areas, and hereby we extend it to 3-dimensional variables (3D, 𝑍∝ 𝑋3) such as volumes.

Structural complexity is an essential morphological …