Optimizing the management of uneven-aged Pinus nigra stands between two stable positions

Abstract

This study proposes a discrete optimal control model to obtain harvest strategies that maximize the net present value (NPV) of the timber harvested from uneven-aged Pinus nigra stands located in the Spanish Iberian System, between two stable positions. The model was constructed using an objective function that integrates financial data on the harvesting operations with a matrix model describing the population dynamics. The initial and final states are given by the stable diameter distribution of the stand, and the planning horizon is 70 years. The scenario analysis corresponding to the optimal solutions revealed that the stand diameter distribution does not deviate substantially from the equilibrium position over time and that the NPV for the optimal harvesting schedule was always greater than the NPV for the "sustainable/stable" harvesting strategy. The NPV increase for the different scenarios is between 5.36% and 14.43%, showing a greater increase in higher site index scenarios and higher recruitments.

Demonstrating the Effect of Height Variation on Stand-Level Optimization with Diameter-Structured Matrix Model

“…Finally, it should bear in mind that this study excludes any consideration of sustainability (cf. [41]) or ecosystem services (cf. [10]), solely focusing on the financial performance of timber production.…”

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

“…Since the model rests on sustainability and stability criteria, it is important to investigate the sensitivity of the results to deviations from the equilibrium (stable diameter distribution); in particular, whether the strong linear relationship between the dimensionless numbers, ρNPV and ρPV, and s is sensitive to changes in the equilibrium position. In this regard, there have been two recent studies involving Pinus nigra stands in the study area (López et al 2013(López et al , 2016, both maximising the same NPV function, constrained by the same matrix model to describe the population dynamics, and with the same initial condition (the stable diameter distribution), as used in this study. Additionally, in the second one the final condition was assumed as the stable diameter distribution of the stand, and a wide variety of typical management scenarios in the study area, obtained by combining three rates of diameter growth (Qualities I-III), three levels of basal area (G = 22, 24 and 26 m 2 ha -1 ), and three levels of recruitment (R = 200, 520 and 840 stems ha -1 ), were considered.…”

“…These can be interpreted as economic performance indicators for forest management, inspired by the ROA accounting concept, showing how profitable the forest is, relative to its total value, with sustainability and stability criteria. Moreover, we demonstrated that there are strong linear correlations between those numbers and s; to that end, it will be used the matrix model applied to uneven-aged managed Pinus nigra stands by López et al ( , 2013López et al ( , 2016, which accurately describes the stand dynamics.…”

“…Considering that the main aim for the stands in the study area is the production of timber, the objective function is the NPV of all management operations over a planning horizon of T years, discounted to the beginning of the period, that is (eqn. 9): 9where vk(t) is the stumpage value that corresponds to class k at year t (€ stem -1 ) and i is the discount rate (López et al 2013(López et al , 2016. The first summation represents the income derived from the sale of timber, and the second is the final stocking value.…”

“…The stumpage value model applied in this study comes from López et al (2013López et al ( , 2016. In Tab.…”