European Journal of Forest Research

, Volume 135, Issue 3, pp 581–592 | Cite as

Selecting the trees to be harvested based on the relative value growth of the remaining trees

  • Jari VauhkonenEmail author
  • Timo Pukkala
Original Paper


Developing forest management plans based on tree-level decision factors is motivated by an increasing availability of single-tree forest inventory data and the needs to compare various silvicultural systems. Tree-level decision making makes it unnecessary to make an explicit pre-thinning choice between even- or uneven-aged forest management regimes since the cutting type is a result of optimal tree-level decisions. In this study, the management decisions were based on the development of 5-year value growth rate simulated at the level of individual trees and under varying degrees of competition. The specific objective was to retain trees with relative value growth rate higher than a specified threshold and harvest the other trees. The probability of removal was modeled using tree diameter, species, and pre-thinning average tree size and density as predictors. The feasibility of the approach was evaluated both at tree and stand levels and under the given uncertainty of prices and growth. By retaining trees that had at least 3 or 5 % value growth, the trees to be removed were mainly large dominant trees. Smaller trees were proposed to be harvested in stands where high competition called for releasing growing space to improve the relative value growth of the remaining trees. When the degree of uncertainty in growth and timber prices increased, fewer trees were harvested from small and large diameter classes. The approach provides instructions to obtain the required value growth despite changes in the timber prices and growth. These instructions are also feasible from the silvicultural point of view. Options for developing similar instructions for different regions, different types of uncertainties, such as assortment-specific trends in timber prices, or complete tree-level inventory data for large areas are discussed.


Optimal thinning Risk Uncertainty Forest structure Adaptive optimization 


  1. Bettinger P, Boston K, Siry JP, Grebner DL (2008) Forest management and planning. Academic Press, New YorkGoogle Scholar
  2. Chappelle DE, Nelson TC (1964) Estimation of optimal stocking levels and rotation ages of loblolly pine. For Sci 10:471–502Google Scholar
  3. Duerr WA, Fedkiw J, Guttenberg S (1956) Financial maturity: a guide to profitable timber growing. Technical bulletin No 1146, United States Department of Agriculture, Washington, pp 1–74Google Scholar
  4. Eerikäinen K, Miina J, Valkonen S (2007) Models for the regeneration establishment and the development of established seedlings in uneven-aged, Norway spruce dominated stands of southern Finland. For Ecol Manag 242:444–461CrossRefGoogle Scholar
  5. Eriksson LO (1994) Two methods for solving stand management problems based on a single tree model. For Sci 40:732–758Google Scholar
  6. Eyvindson K, Kangas A (2016) Evaluating the required scenario set size for stochastic programming in forest management planning: incorporating inventory and growth model uncertainty. Can J For Res 46:340–347CrossRefGoogle Scholar
  7. Haight RG, Monserud RA (1990) Optimizing any-aged management of mixed-species stands. I: performance of a coordinate-search process. Can J For Res 20:15–25CrossRefGoogle Scholar
  8. Heinonen T, Pukkala T (2007) The use of cellular automaton approach in forest planning. Can J For Res 37:2188–2200CrossRefGoogle Scholar
  9. Knoke T (2012) The economics of continuous cover forestry. In: Pukkala T, von Gadow K (eds) Continuous cover forestry. Managing forest ecosystems, vol 23. Springer, Dordrecht, pp 167–193CrossRefGoogle Scholar
  10. Laasasenaho J (1982) Taper curve and volume equations for pine spruce and birch. Commun Inst For Fenn 108:1–74Google Scholar
  11. Leskinen P, Kangas J (1998) Modelling and simulation of timber prices for forest planning calculations. Scand J For Res 13:469–476CrossRefGoogle Scholar
  12. Lohmander P (2007) Adaptive optimization of forest management in a stochastic world. In: Weintraub A, Romero C, Bjørndal T, Epstein R, Miranda J (eds) Handbook of operations research in natural resources. International series in operations research and management science, vol 99. Springer, New York, pp 525–543Google Scholar
  13. Maltamo M, Næsset E, Vauhkonen J (eds) (2014) Forestry applications of airborne laser scanning: concepts and case studies. Managing forest ecosystems, vol 27. Springer, DordrechtGoogle Scholar
  14. Mehtätalo L, Peltola H, Kilpeläinen A, Ikonen VP (2014) The response of basal area growth of scots pine to thinning: a longitudinal analysis of tree-specific series using a nonlinear mixed-effects model. For Sci 60:636–644Google Scholar
  15. Packalén P, Vauhkonen J, Kallio E, Peuhkurinen J, Pitkänen J, Pippuri I, Strunk J, Maltamo M (2013) Predicting the spatial pattern of trees with airborne laser scanning. Int J Remote Sens 34:5154–5165CrossRefGoogle Scholar
  16. Pinheiro J, Bates D, DebRoy S, Sarkar D, R Core Team (2016) nlme: linear and nonlinear mixed effects models. R package version 3.1–124.
  17. Pretzsch H, Biber P, Ďurský J (2002) The single tree-based stand simulator SILVA: construction, application and evaluation. For Ecol Manag 162:3–21CrossRefGoogle Scholar
  18. Pukkala T (2015) Optimizing continuous cover management of boreal forest when timber prices and tree growth are stochastic. For Ecosyst 2:6. doi: 10.1186/s40663-015-0028-5 CrossRefGoogle Scholar
  19. Pukkala T, Kellomäki S (2012) Anticipatory vs adaptive optimization of stand management when tree growth and timber prices are stochastic. Forestry 85:463–472CrossRefGoogle Scholar
  20. Pukkala T, Miina J (1998) Tree-selection algorithms for optimizing thinning using a distance-dependent growth model. Can J For Res 28:693–702CrossRefGoogle Scholar
  21. Pukkala T, Lähde E, Laiho O (2009) Growth and yield models for uneven-sized forest stands in Finland. For Ecol Manag 258:207–216CrossRefGoogle Scholar
  22. Pukkala T, Lähde E, Laiho O (2014) Optimizing any-aged management of mixed boreal forest under residual basal area constraints. J For Res 23:627–636CrossRefGoogle Scholar
  23. Pukkala T, Lähde E, Laiho O (2015) Which trees should be removed in thinning treatments? For Ecosyst 2:32. doi: 10.1186/s40663-015-0056-1 CrossRefGoogle Scholar
  24. R Core Team (2013) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria.
  25. Rasinmäki J, Mäkinen A, Kalliovirta J (2009) SIMO: an adaptable simulation framework for multiscale forest resource data. Comput Electron Agric 66:76–84CrossRefGoogle Scholar
  26. Rummukainen A, Alanne H, Mikkonen E (1995) Wood procurement in the pressure of change: resource evaluation model till year 2010. Acta For Fenn 248:1–98Google Scholar
  27. Tapio (2006) Hyvän metsänhoidon suositukset (in Finnish for “forestry management practice recommendations”). Forestry Development Centre Tapio, Helsinki, Finland. ISBN 10-952-5118-91-6Google Scholar
  28. Valbuena R, Vauhkonen J, Packalen P, Pitkänen J, Maltamo M (2014) Comparison of airborne laser scanning methods for estimating forest structure indicators based on Lorenz curves. ISPRS J Photogramm Remote Sens 95:23–33CrossRefGoogle Scholar
  29. Valbuena R, Eerikäinen K, Packalen P, Maltamo M (2016) Gini coefficient predictions from airborne lidar remote sensing display the effect of management intensity on forest structure. Ecol Indic 60:574–585CrossRefGoogle Scholar
  30. Valsta L (1992) A scenario approach to stochastic anticipatory optimization in stand management. For Sci 38:430–447Google Scholar
  31. Vauhkonen J, Mehtätalo L (2015) Matching remotely sensed and field measured tree size distributions. Can J For Res 45:353–363CrossRefGoogle Scholar
  32. Vauhkonen J, Packalen P, Malinen J, Pitkänen J, Maltamo M (2014) Airborne laser scanning based decision support for wood procurement planning. Scand J For Res 29(Suppl 1):132–143CrossRefGoogle Scholar
  33. Wikström P (2001) Effect of decision variable definition and data aggregation on a search process applied to a single-tree simulator. Can J For Res 31:1057–1066CrossRefGoogle Scholar
  34. Wikström P, Edenius L, Elfving B, Eriksson LO, Lämås T, Sonesson J, Öhman K, Wallerman J, Waller C, Klintebäck F (2011) The Heureka forestry decision support system: an overview. Math Comput For Nat Resour Sci 3:87–94Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.School of Forest SciencesUniversity of Eastern FinlandJoensuuFinland

Personalised recommendations