A non-asymptotic sigmoid growth curve for top height growth in forest stands

Jean-Daniel Bontemps (1) , Pierre Duplat (2)

1 Equipe Ecologie Forestère
2 Département des Recherches Techniques, ONF

Since the height horizon remains undetected in the vast majority of height series sampled in forest stands, even of notable ages, the realism of the traditional asymptotic-size modelling assumption is questioned. The aim of the study was to present an original non-asymptotic growth model, and to test its accuracy against asymptotic-size equations. The equation proposed is a first-order 4-parameter autonomous differential equation. The related sigmoid size curve has a parabolic branch of time. It was tested on 349 old growth series of top height (1047 stem analyses) selected to explore the maximum observed ranges of age and site conditions, in 7 temperate tree species growing in pure and even-aged stands The fitting accuracy of this equation and three classical asymptotic-size growth equations (Richards, Hossfeld-IV, and Korf equations) were compared, with parameterisations of increasing flexibility. For the different parameterisations, the proposed growth equation showed higher performances than asymptotic growth equations, attributed to its non-asymptotic property and to the mathematical independence between parameters related to the inflection point and late growth. Top height growth was therefore accurately modelled by a sigmoid curve not based on the asymptotic-size assumption. This equation may be of general relevance to tree growth modelling.

Mots clés: tree height; ontogeny; late growth; top height; asymptotic size; growth equation; modelling; stem analysis; evergreen species; broadleaved species

Domaines: Sylviculture, foresterie; Systèmes dynamiques [math.DS]; Ecosystèmes; Biodiversité et Ecologie

Jean-Daniel Bontemps, Pierre Duplat. A non-asymptotic sigmoid growth curve for top height growth in forest stands. Forestry, 2012, 85 (3), pp.353-368. ⟨10.1093/forestry/cps034⟩. ⟨hal-00868938⟩