Advertisement

Descriptive Models

  • Annikki MäkeläEmail author
  • Harry T. ValentineEmail author
Chapter
  • 32 Downloads

Abstract

The topics discussed in this chapter span two centuries of modelling effort. We begin with sections that deal with some mathematical details of descriptive growth models of whole trees, then move to saturating functions and numerical switches that will prove useful in later chapters. We end the chapter with a simple empirical model of crown dynamics and stand density that makes use of some of the earlier material.

Supplementary material

488748_1_En_2_MOESM1_ESM.zip (1 kb)
crise_mod_runs (ZIP 2kb)

References

  1. Affleck DLR (2006) Poisson mixture models for regression analysis of stand-level mortality. Can J For Res 36(11):2994–3006CrossRefGoogle Scholar
  2. Assmann E (1970) The principles of forest yield study. Pergamon Press, OxfordGoogle Scholar
  3. Beekhuis J (1965) Crown depth of radiata pine in relation to stand density and height. N Z J For 10:43–61Google Scholar
  4. Bertalanffy LV (1957) Quantitative laws of metabolism and growth. Q Rev Biol 32:217–231CrossRefGoogle Scholar
  5. Bontemps JD, Duplat P (2012) A non-asymptotic sigmoid growth curve for top height growth in forest stands. Forestry 85(3):353–368CrossRefGoogle Scholar
  6. Box GEP, Cox DR (1964) An analysis of transformations. J R Stat Soc B 26:1059–1072Google Scholar
  7. Brown GS (1962) The importance of stand density in pruning prescriptions. Emp For Rev 41(3):246–257Google Scholar
  8. Burkhart HE, Tomé M (2012) Modeling trees and stands. Springer, New YorkCrossRefGoogle Scholar
  9. Clutter JL, Jones EP Jr (1980) Prediction of growth after thinning in old-field slash pine plantations. USDA Forest Service Research Paper SE-217Google Scholar
  10. Dean TJ, Jerez M, Cao QV (2013) A simple stand growth model based on canopy dynamics and biomechanics. For Sci 59(3):335–344Google Scholar
  11. Diéguez-Aranda U, Castedo-Dorado F, Álvarez-González JG, Rodríguez-Soalleiro R (2005) Modelling mortality of Scots pine (Pinus sylvestris L.) plantations in the northwest of Spain. Eur J For Res 124(2):143–153CrossRefGoogle Scholar
  12. García O (1983) A stochastic differential equation model for the height growth of forest stands. Biometrics 39:1059–1072CrossRefGoogle Scholar
  13. García O (2005) Unifying sigmoid univariate growth equations. For Biom Modell Inform Sci 1: 63–68Google Scholar
  14. García O (2008) Visualization of a general family of growth functions and probability distributions – the growth-curve explorer. Environ Model Softw 23:1474–1475CrossRefGoogle Scholar
  15. García O (2009) A simple and effective forest stand mortality model. Math Comput For Nat Resour Sci (MCFNS) 1(1):1–9Google Scholar
  16. Gompertz B (1825) On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. Philos Trans R Soc Lond 115: 513–585Google Scholar
  17. Harmsen K (2000) A modified Mitscherlich equation for rainfed crop production in semi-arid areas: 1. theory. NJAS-Wagen J Life Sci 48(3):237–250CrossRefGoogle Scholar
  18. Jones O, Maillardet R, Robinson A (2009) Introduction to scientific programming and simulation using R. Chapman & Hall/CRC, Boca RatonCrossRefGoogle Scholar
  19. Mäkelä A, Valentine HT, Helmisaari H (2008b) Optimal co-allocation of carbon and nitrogen in a forest stand at steady state. New Phytol 180:114–123CrossRefGoogle Scholar
  20. McMurtrie R, Wolf L (1983) Above- and below-ground growth of forest stands: a carbon budget model. Ann Bot 52(4):437–448CrossRefGoogle Scholar
  21. Panik MJ (2013) Growth curve modeling: theory and applications. John Wiley & Sons, HobokenGoogle Scholar
  22. Pienaar LV, Turnbull KJ (1973) The Chapman-Richards generalization of von Bertalanffy’s growth model for basal area growth and yield in even-aged stands. For Sci 19:2–22Google Scholar
  23. Richards FJ (1959) A flexible growth function for empirical use. J Exp Bot 10:290–300CrossRefGoogle Scholar
  24. Ryan MG, Phillips N, Bond BJ (2006) The hydraulic limitation hypothesis revisited. Plant Cell Environ 29:367–381CrossRefGoogle Scholar
  25. Thompson DW (1992) On growth and form. Dover Publications, Inc., New YorkCrossRefGoogle Scholar
  26. Thornley JHM (1976) Mathematical models in plant physiology. Academic Press, LondonGoogle Scholar
  27. Thornley JHM, Johnson IR (1990) Plant and crop modelling. Clarendon Press, OxfordGoogle Scholar
  28. Valentine HT, Amateis RL, Gove JH, Mäkelä A (2013) Crown-rise and crown-length dynamics: application to loblolly pine. Forestry 86:371–375CrossRefGoogle Scholar
  29. Valentine HT, Ludlow AR, Furnival GM (1994b) Modeling crown rise in even-aged stands of Sitka spruce or loblolly pine. For Ecol Manage 69:189–197CrossRefGoogle Scholar
  30. Verhulst PF (1838) Notice sur la loi que la population poursuit dans son accroissement. Correspondance Mathématique et physique 10:113–121Google Scholar
  31. Winsor CP (1932) The Gompertz curve as a growth curve. Proc Natl Acad Sci U S A 18:1–8CrossRefGoogle Scholar
  32. Zeide B (1993) Analysis of growth equations. For Sci 39:594–616Google Scholar
  33. Zhao D, Borders B, Wang M, Kane M (2007) Modeling mortality of second-rotation loblolly pine plantations in the Piedmont/Upper Coastal Plain and Lower Coastal Plain of the southern United States. For Ecol Manage 252(1):132–143CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.University of HelsinkiHelsinkiFinland
  2. 2.USDA Forest ResearchDurhamUSA

Personalised recommendations