IntroductionStand density management is essential for adaptive silviculture, thinning decisions, growth modeling, and yield prediction in forestry, particularly for plantations. Despite extensive research on self-thinning rules and the maximum size-density law, significant gaps remain in the biophysical understanding and validation of the relationships among key stand variables and parameters.MethodsThis study theoretically explored and validated the relationship between maximum size-density and two key metrics: average diameter at breast height (D) and tree height (H). We used time-series data from a 30-year clear-cut, fully stocked Chinese fir plantation, a fast-growing commercial species in China, for validation.ResultsA growth balance status for fully stocked stands was proposed, wherein prior to self-thinning, the growth rate of the stand basal area (G) aligns with that of the average tree height (H), expressed as G'/(G−b0)=H'/H and approaching a constant slope, b1. Generalized maximum size-density and stand density index (SDI) equations were developed: N1.0=A×D−2 and SDI=A⋅D−2 with A=4×(b0+b1H)/π, differing from traditional equations. Additionally, a generalized self-thinning equation, v=kHqN1.0−1 or w=c1HqN1.0−1, was introduced, indicating that in fully stocked stands, tree volume or biomass depends on both tree height and tree count.DiscussionThese findings advance understanding of the maximum size-density law and self-thinning boundary, providing refined tools for managing stand density in Chinese fir plantations.
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