Annals of Forest Science

, Volume 67, Issue 3, pp 305–305 | Cite as

Mortality of silver fir and Norway Spruce in the Western Alps — a semi-parametric approach combining size-dependent and growth-dependent mortality

  • Ghislain Vieilledent
  • Benoît Courbaud
  • Georges Kunstler
  • Jean-François Dhôte
Original Article



Tree mortality can be modeled using two complementary covariates, tree size and tree growth. Tree growth is an integrative measure of tree vitality while tree diameter is a good index of sensitivity to disturbances and can be considered as a proxy for tree age which may indicate senescence. Few mortality models integrate both covariates because classical model calibration requires large permanent plot data-sets which are rare. How then can we calibrate a multivariate mortality model including size and growth when permanent plots data are not available?


To answer this question, we studied Abies alba and Picea abies mortality in the French Swiss and Italian Alps.


Our study proposes an alternative semi-parametric method which includes a random sample of living and dead trees with diameter and growth measurements.


We were able to calibrate a mortality model combining both size-dependent and growth-dependent mortality. We demonstrated that A. alba had a lower annual mortality rate (10%) than P. abies (18%) for low growth (< 0.2 mmyear−1). We also demonstrated that for higher diameters (DBH ≥ 70 cm), P. abies had a higher mortality rate (0.45%) than A. alba (0.32%).


Our results are consistent with the mechanisms of colonization-competition trade-off and of successional niche theory which may explain the coexistence of these two species in the Alps. The method we developed should be useful for forecasting tree mortality and can improve the efficiency of forest dynamics models.


Abies alba conditional probability non-parametric model Picea abies tree mortality 



Diameter at Breast Height (DBH = 1.30 m)

P. abies

Picea abies (L.) Karst. (Norway Spruce)

A. alba

Abies alba Mill. (Silver Fir)


National Forest Inventory

Mortalité du sapin pectiné et de l’épicea commmun dans les alpes occidentales — une approche semi-paramétrique combinant la mortalité dépendant de la taille et de la croissance



Il est possible de modéliser la mortalité des arbres en utilisant deux covariables complémentaires : la taille et la croissance de l’arbre. La croissance est une mesure synthétique de la vitalité alors que le diamètre est un bon indicateur de la sensibilité aux perturbations et est très fortement corrélé à l’âge de l’arbre, qui détermine la sénescence. Peu de modèles de mortalité intègrent les deux covariables, car cela nécessite, pour les approches classiques, une calibration à partir de données de placettes permanentes qui sont rares. Comment obtenir un modèle de mortalité multivarié, incluant la taille et la croissance, lorsque des données de placettes permanentes ne sont pas disponibles?

Localisation géographique

Pour répondre à cette question, nous avons étudié la mortalité du sapin pectiné (Abies alba) et de l’epicéa commmun (Picea abies) dans les Alpes suisses françaises et italiennes.


Notre étude propose une méthode semi-parametrique alternative s’appuyant sur un échantillon d’arbres morts et vivants avec des mesures de diamètre et de croissance.


Nous avons obtenu un modèle combinant la mortalité dépendant à la fois de la taille et de la croissance. Nous avons démontré qu’A. alba avait un taux de mortalité inférieur (10 %) à celui de P. abies (18 %) pour une faible croissance (< 0.2 mman−1). De plus, pour de larges diamètres (DBH >- 70 cm), P. abies a un taux de mortalité supérieur (0.45 %) à A. alba (0.32 %).


Nos résultats sont en accord avec les mécanismes de niche de succession et de compromis entre colonisation et compétition qui sont invoqués pour expliquer la coexistence des deux espéces dans les Alpes. Notre méthode devrait contribuer à améliorer la prédiction du taux de mortalité et la précision des modèles de dynamique forestière.


Abies alba probabilités conditionnelles modèles non-paramétriques Picea abies mortalité des arbres 


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Copyright information

© Springer S+B Media B.V. 2010

Authors and Affiliations

  • Ghislain Vieilledent
    • 1
    • 2
    • 3
  • Benoît Courbaud
    • 1
  • Georges Kunstler
    • 1
  • Jean-François Dhôte
    • 4
    • 5
  1. 1.Cemagref-Mountain Ecosystems Research UnitSaint-Martin-d’Hères CedexFrance
  2. 2.Laboratoire d’Étude des Ressources Forêt BoisAgroParisTech-UMR1092NancyFrance
  3. 3.Cirad-UPR Dynamique ForestièreMontpellier Cedex 5France
  4. 4.Laboratoire d’Étude des Ressources Forêt BoisINRA-UMR1092NancyFrance
  5. 5.ONF-Département RechercheBoulevard de ConstanceFontainebleauFrance

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