Using Limit Value Constraint Theory to Better Understand the Self-Thinning Rule of Forest

Abstract

Stand density management is important for decision-making regarding adaptive silviculture and thinning, growth modelling, and yield prediction in forests, especially plantations. Although substantial research related to the self-thinning rule and maximum size-density law has been conducted, there are still critical gaps that exist in the biophysical explanation and validation of the relationships among stand variables and relevant parameters. In this study, time series observations from six plots of fully stocked Chinese fir plantations with different densities of planted trees were used to characterise the growth of stand basal area (G), average height (H), and diameter at breast height (D). The growth trends in the stand parameters and the relationships among them were analysed. As indicated by previous studies, in the fully stocked stands, there was a significant linear relationship between G and H. This study also resulted in the following new findings: (1) At the beginning, the growth rate of stand basal area (PG) was greater than the growth rate of average height (PH), but PG decreased quickly as the stands approached canopy closure and then became stable. Meanwhile, as the stands neared canopy closure, the rate of increase in the G/H ratio decelerated, ultimately resulting in a stable G/H value that approached the first limit value. This led to a stand growth balance status that continued until self-thinning took place. (2) Artificial thinning broke the growth balance status, but the stands returned to balance status if they were still young enough. Self-thinning also broke the growth balance status and lead to fluctuating growth rates of both G and H, but the fluctuations were very slight, which showed a trend in similar growth rates of G and H. (3) The findings implied that the stand G and H growths were allometric at the beginning but became isogonic as canopy closure and self-thinning were approached. On the other hand, the H growth rate was generally greater than that of D, but both growth rates showed a trend in similar values after the stands matured. Subsequently, the H/D ratio is anticipated to stabilize and gradually converge towards the second limit value once the stands reach maturity. The results implied that the stand growth balance status and two limit values can be used to identify and select fully stocked stands that are needed for the development of maximum size-density equations and self-thinning rules.