S M Nazmuz Sakib Forest Spectral Diversity Index

Forest structural diversity underpins ecosystem function, resilience, and biodiversity, yet existing metrics often summarize only coarse stand-level attributes such as height distributions , basal area, or spatial point patterns. Recent advances in terrestrial laser scanning (TLS) and quantitative structure models (QSMs) now provide branch-resolved tree architecture at scale, while spectral graph theory and similarity-sensitive diversity measures offer principled tools for comparing complex structures. This article introduces the S M Nazmuz Sakib Forest Spectral Diversity Index (abbre-viated Sakib-Index, denoted Sakib-Index q (F)), a mathematically grounded measure of forest structural diversity that couples graph Laplacian spectra with the Leinster-Cobbold similarity-sensitive diversity framework. A forest stand is modeled as a graph of graphs: each tree is represented by a branch-level graph derived from TLS/QSM data, and tree-tree interactions are encoded by a stand-level adjacency graph. The Laplacian of the resulting forest graph yields eigenmodes whose energy distribution over each tree defines a spectral fingerprint. Kernel similarities between these fingerprints form a similarity matrix Z, which, together with a vector of tree abundances p, is passed into the Leinster-Cobbold diversity formula to obtain Sakib-Index q (F) as an effective number of structurally distinct trees. We formalize this construction, state the S M Nazmuz Sakib Forest Spectral Diversity Principle, and propose the S M Nazmuz Sakib Structural Risk Hypothesis connecting low values of Sakib-Index q (F) to joint mechanical and growth-related risks. Using representative data synthesized and rescaled from published TLS-based structural studies, we illustrate the behavior of the Sakib-Index across contrasting forest stands and demonstrate its relationships with canopy height variation, LiDAR-derived Lorenz-entropy metrics, species diversity, and aboveground biomass. A category-theoretic viewpoint is sketched, viewing forest stands as objects of a category and the Sakib-Index as a composition of functors 1 through similarity systems. The framework appears to be a novel integration of existing theories and a promising candidate for remote-sensing-based indicators of forest structural complexity and resilience.