University of Oulu

Pyy, J.; Laitinen, E.; Ahtikoski, A. Demonstrating the Effect of Height Variation on Stand-Level Optimization with Diameter-Structured Matrix Model. Forests 2020, 11, 226.

Demonstrating the effect of height variation on stand-level optimization with diameter-structured matrix model

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Author: Pyy, Johanna1; Laitinen, Erkki1; Ahtikoski, Anssi2
Organizations: 1Faculty of Sciences, University of Oulu, FI-90014 Oulu, Finland
2Natural Resource Institute Finland (Luke), FI-90014 Oulu, Finland
Format: article
Version: published version
Access: open
Online Access: PDF Full Text (PDF, 0.8 MB)
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Language: English
Published: Multidisciplinary Digital Publishing Institute, 2020
Publish Date: 2020-12-01


The weakness of the population matrix models is that they do not take into account the variation inside the class. In this study, we introduce an approach to add height variation of the trees to the diameter-structured matrix models. In this approach, a new sub-model that describes the height growth of the trees is included in the diameter-structured model. We used this height- and diameter-structured matrix model to maximize the net present value (NPV) for the remaining part of the ongoing rotation for Scots pine (Pinus sylvestris L.) stand and studied how the height variation affects to the results obtained through stand-level optimization. In the optimization, the height variation was taken into account by setting the lower saw-log price for the short trees. The results show that including the height variation into the optimization reduced the financial outcome by 16–18% and considerably changed the structure of optimal management (e.g., timings for thinnings, rotation period and intensity of thinnings). We introduced an approach that can be applied to include not only height variation but also variation of other tree properties (such as branchiness or the amount of heartwood and sapwood) into the matrix models.

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Series: Forests
ISSN: 1999-4907
ISSN-E: 1999-4907
ISSN-L: 1999-4907
Volume: 11
Issue: 2
Article number: 226
DOI: 10.3390/f11020226
Type of Publication: A1 Journal article – refereed
Field of Science: 111 Mathematics
Copyright information: © 2020 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 (