Rethinking maximum stand basal area and maximum SDI from the aspect of stand dynamics

Abstract The maximum stand basal area (BA) and maximum stand density index (SDI) are often used to express stand carrying capacity in forestry. But their definitions are inconsistent in the literature. The maximum stand BA in most previous studies is associated with an upper boundary for a population of stands and is commonly derived from maximum size-density relationships (MSDRs). The maximum stand BA implied by MSDRs, under the assumption that stands attain maximum BA while attaining maximum SDI, is non-decreasing and divergent. We defined the maximum stand BA and maximum SDI for individual stands based on their BA and SDI development behaviors. Based on the mathematical relationships among stand BA, SDI, thinning, and quadratic mean diameter trajectories and their observed full trajectories in 551 unthinned plots selected from six long-term loblolly pine experimental studies, we theoretically and empirically proved that stands would achieve their maximum BA only after reaching their maximum SDI. The general mean maximum stand BA and maximum SDI for loblolly pine in the southern US were 46.2 m2 ha−1 and 1002 trees ha−1, respectively, and both showed significant variation (30.2–61.7 m2 ha−1 and 600–1410 trees ha−1, respectively). With the information of site quality, initial density and silvicultural treatments, our developed models could estimate the magnitude and timing of maximum stand BA for loblolly pine stands. Insights into individual stand BA and SDI trajectories provide more information for developing site specific silvicultural prescriptions.