Dimensionless numbers for the sustainable harvesting of a monospecific uneven-aged forest

Abstract

This study proposes a simple and direct method based on dimensionless numbers to provide reliable approximations of the population growth rate, the “sustainable/stable” harvest rate, the proportion of trees that has to remain unharvested to retain the stable diameter distribution, and the stable diameter distribution of a forest stand. Those numbers, obtained under conditions of stable equilibrium from a matrix model, could also serve to estimate boundaries between sustainable and unsustainable harvesting. To exemplify and test the results, the model uses data from uneven-aged managed Pinus nigra Arnold stands, considering three levels of tree diameter growth, six levels of basal area, and 33 levels of recruitment, creating a total of 594 planning scenarios. The best approximation of all the variables observed occurred in any case for the scenarios with the lowest level of diameter growth, the lowest level of basal area, and the highest recruitment level. Furthermore, the study reveals the existence of a strong positive linear correlation between those variables and their respective approximations, as well as a small distance between the stable diameter distribution of the stand and its approximation. Finally, we incorporate natural disturbances into the dimensionless numbers and criteria.

Dimensionless numbers for the net present value and the perpetual value of sustainable timber harvests from a monospecific uneven-aged forest

“…Note that ρNPV and ρPV are dimensionless numbers. Furthermore, given that there is a strong positive linear correlation between s and s‚ (López & Fullana 2015), it is expected that, for previously defined values of i and T, there must be a strong positive linear correlation between these variables ρNPV and ρPV, and s, as we demonstrate below.…”

“…The corresponding problems simulated a wide variety of typical management cases in the study area; and (c) the number n and width w of the diameter classes. As shown in López & Fullana (2015), these scaling factors n and w could have a limited influence on s and therefore on the NPV, PV, ρNPV and ρPV values.…”

“…By applying conditions of stable equilibrium from a matrix model, a recent study (López & Fullana 2015) found dimensionless numbers λ0, s‚ and s′ to provide reliable approximations of, respectively, the population growth rate, λ0, the "sustainable/stable" harvest rate, s, where (eqn. 1):…”