University of Oulu

Pyy, J., Ahtikoski, A., Laitinen, E., Siipilehto, J. (2017) Introducing a Non-Stationary Matrix Model for Stand-Level Optimization, an Even-Aged Pine (Pinus Sylvestris L.) Stand in Finland. Forests, 8 (5), 163. doi:doi:10.3390/f8050163

Introducing a non-stationary matrix model for stand-level optimization, an even-aged pine (Pinus Sylvestris L.) stand in Finland

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Author: Pyy, Johanna1; Ahtikoski, Anssi2; Laitinen, Erkki1;
Organizations: 1Faculty of Sciences, University of Oulu, P.O. Box 8000, FI-90014 Oulu, Finland
2Natural Resources Institute Finland (Luke) Oulu, Paavo Havaksen tie 3, FI-90014 Oulu, Finland
3Natural Resources Institute Finland (Luke), Latokartanonkaari 9, FI-00790 Helsinki, Finland
Format: article
Version: published version
Access: open
Online Access: PDF Full Text (PDF, 0.3 MB)
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Language: English
Published: Multidisciplinary Digital Publishing Institute, 2017
Publish Date: 2019-01-29


In general, matrix models are commonly applied to predict tree growth for size-structured tree populations, whereas empirical–statistical models are designed to predict tree growth based on a vast amount of field observations. From the theoretical point of view, matrix models can be considered to be more generic since their dependency on ad hoc growth conditions is far less prevalent than that of empirical–statistical models. On the other hand, the main pitfall of matrix models is their inability to include variation among the individuals within a size class, occasionally resulting in less accurate predictions of tree growth compared to empirical–statistical models. Thus, the relevant question is whether a matrix model can capture essential tree-growth dynamics/characteristics so that the model produces accurate stand projections which can further be applied in practical decision-making. Such a dynamic characteristic in our model is the basal area of trees, which causes nonlinearity in time. Therefore, our matrix model is a nonlinear model. The empirical data for models was based on 20 sample plots representing 8360 tree records. Further, according to the model, stand projections were produced for three Scots pine (Pinus sylvestris L.) sapling stands (age of 25 years, stand density fluctuating from 850 to 1400 stems ha−1 ). Then, (even-aged) stand management was optimized by applying sequential quadratic programming (SQP) among those growth predictions. The objective function of the optimization task was to maximize the net present value (NPV) of the ongoing rotation. The stands were located in Northern Ostrobothnia, Finland, on nutrient-poor soil type. The results indicated that initial stand density had an effect on optimal solutions—optimal stand management varied with respect to thinnings (timing and intensity) as well as to optimal rotation. Further, an increasing discount rate shortened considerably the optimal rotation period, and relaxing the minimum thinning removal to 30 m3 ha−1 resulted in an increase both in number of thinnings and in the maximum net present value.

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Series: Forests
ISSN: 1999-4907
ISSN-E: 1999-4907
ISSN-L: 1999-4907
Volume: 8
Issue: 5
Article number: 163
DOI: 10.3390/f8050163
Type of Publication: A1 Journal article – refereed
Field of Science: 111 Mathematics
Funding: We want to acknowledge the Jenny and Antti Wihuri foundation for financial support.
Copyright information: © 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (