Skip to main content
  • Original Article
  • Published:

Predicting individual tree mortality in northern hardwood stands under uneven-aged management in southern Québec, Canada

Prévision de la mortalité des tiges individuelles dans les peuplements de feuillus nobles sous aménagement inéquienne dans le sud du Québec, Canada

Abstract

This study proposes a generalized linear mixed model to predict individual tree mortality in northern hardwood stands under uneven-aged management. The model is based on a complementary log-log (CLL) link function, and was calibrated using permanent-plot data. Tree vigor, stem product, diameter at breast height and stand basal area were tested as explanatory variables. A plot and an interval random effect were specified to account for spatial correlations. When compared with the traditional logit link function, the CLL facilitates the inclusion of the time factor. In this case study, there was an important variability of mortality predictions between the plots and the intervals for a given plot. The interval random effect is thought to be associated with catastrophic mortality. Since both tree vigor and stem product proved to be significant mortality predictors, we recommend that these variables be evaluated to increase the accuracy of mortality models.

Résumé

Cette étude présente un modèle linéaire mixte généralisé pour la prévision de la mortalité dans les peuplements de feuillus nobles sous aménagement. Le modèle utilise une fonction de lien log-log complémentaire (LLC) et a été étalonné à l’aide de données de placettes permanentes. La vigueur de l’arbre, le produit, le diamètre à hauteur de poitrine et la surface terrière ont été testés comme variables explicatives. Des effets aléatoires de placette et d’intervalle ont été spécifiés dans le modèle afin de tenir compte des corrélations spatiales. Comparée au traditionnel logit, la fonction de lien LLC facilite l’inclusion du facteur temps. Dans ce cas d’étude, il existait une importante variabilité des prévisions entre les placettes et les intervalles de temps d’une même placette. On présume que l’effet aléatoire d’intervalle représente la mortalité catastrophique. Puisque la vigueur et le produit des tiges se sont avérés être des variables significatives, il est recommandé de les évaluer afin d’améliorer la précision des modèles de mortalité.

References

  1. Álvarez González J.G., Castedo Dorado F., Ruiz González A.D., López Sánchez C.A., von Gadow K., A two-step mortality model for even-aged stands of Pinus radiata D. Don in Galicia (Northwestern Spain), Ann. For. Sci. 61 (2004) 439–448.

    Article  Google Scholar 

  2. Bakuzis E.V., Hansen H.L., Balsam fir, A monographic review, Univ. of. Minnesota Press, Minneapolis, 1965.

    Google Scholar 

  3. Bédard S., Brassard F., Les effets réels des coupes de jardinage dans les forêts publiques du Québec en 1995 et 1996, Ministère des Ressources naturelles du Québec, Direction de la recherche forestière, Rapport, 2002.

  4. Bédard S., Majcen Z., Meunier S., Coupe de jardinage dans les forêts feuillues du Québec — Mise à jour des résultats de recherche, InfoForêt 81 (2004) 3–6.

    Google Scholar 

  5. Blum B.M., Red spruce, in: Burns R.M., Honkala B.H. (Eds.), Silvics of North America, Vol. 1, USDA Agriculture Handbook No. 654, 1990, pp. 250–259.

  6. Breslow N.E., Lin X., Bias correction in generalised linear mixed models with single component of dispersion, Biometrika 82 (1995) 81–91.

    Article  Google Scholar 

  7. Browne W.J., Draper D., A comparison of Bayesian and likelihood-based methods for fitting multilevel models, Bayesian Analysis 1 (2006) 473–514.

    Article  Google Scholar 

  8. Caspersen J.P., Elevated mortality of residual trees following single-tree felling in northern hardwood forests, Can. J. For. Res. 36 (2006) 1255–1265.

    Article  Google Scholar 

  9. Cox D.R., Oakes D., Analysis of survival data, Chapman and Hall Ed., New York, 1984.

    Google Scholar 

  10. Duchesne L., Ouimet R., Morneau C., Assessment of sugar maple health based on basal area growth pattern, Can. J. For. Res. 33 (2003) 2074–2080.

    Article  Google Scholar 

  11. Erdmann G.G., Oberg R.R., Fifteen-year results from six cutting methods in second-growth northern hardwoods, USDA For. Serv. Res. Pap. NC-100, 1973.

  12. Fang Z., Bailey R.L., Nonlinear mixed effects modeling for slash pine dominant height growth following intensive silvicultural treatments, For. Sci. 47 (2001) 287–300.

    Google Scholar 

  13. Fang Z., Bailey R.L., Shiver B.D., A multivariate simultaneous prediction system for stand growth and yield with fixed and random effects, For. Sci. 47 (2001) 550–562.

    Google Scholar 

  14. Frank R.M., Balsam fir, in: Burns R.M., Honkala B.H. (Eds.), Silvics of North America, Vol. 1, USDA Agriculture Handbook No. 654, 1990, pp. 26–35.

  15. Garber S.M., Maguire D.A., Modeling stem taper of three central Oregon species using nonlinear mixed effects models and autoregressive error structures, For. Ecol. Manage. 179 (2003) 507–522.

    Article  Google Scholar 

  16. Godman R.M., Yawney H.W., Tubbs C.H., Sugar maple, in: Burns R.M., Honkala, B.H., (Eds.), Silvics of North America, Vol. 2, USDA Agriculture Handbook No. 654, 1990, pp. 78–91.

  17. Gregoire T.G., Generalized error structure for forestry yield models, For. Sci. 33 (1987) 423–444.

    Google Scholar 

  18. Gregoire T.G., Schabenberger O., Barrett J.P., Linear modelling of irregularly spaced, unbalanced, longitudinal data from permanent-plot measurements, Can. J. For. Res. 25 (1995) 137–156.

    Article  Google Scholar 

  19. Grondin P., Ansseau C., Bélanger L., Bergeron J.-F., Bergeron Y., Bouchard A., Brisson J., De Grandpré L., Gagnon G., Lavoie C., Lessard G., Payette S., Richard P.J.H., Saucier J.-P., Sirois L., Vasseur L., Écologie forestière, in: Bérard J.A., Côté M. (Eds.), Manuel de foresterie, Les Presses de l’Université Laval, Sainte-Foy, Québec, 1996, pp. 133–279.

    Google Scholar 

  20. Hall D.B., Bailey R.L., Modeling and prediction of forest growth variables based on multilevel nonlinear mixed models, For. Sci. 47 (2001) 311–321.

    Google Scholar 

  21. Hamilton D.A. Jr., A logistic model of mortality in thinned and unthinned mixed conifer stands of northern Idaho, For. Sci. 32 (1986) 989–1000.

    Google Scholar 

  22. Hatcher R.J., Mortality and regeneration following partial cutting of spruce-balsam fir-hardwood stands at Lake Edward, P.Q., Government of Canada, Department of Northern Affairs and National Resources, Forestry Branch, Forest Research Division, Project Q-44, 1959.

  23. Hosmer D.W. Jr., Lemeshow S., Applied logistic regression, 2nd ed., John Wiley & Sons, New York, 2000.

    Book  Google Scholar 

  24. Jack S.B., Long J.N., Linkage between silviculture and ecology: an analysis of density management diagrams, For. Ecol. Manage 86 (1996) 205–220.

    Article  Google Scholar 

  25. Jutras S., Hökkä H., Alenius V., Salminen H., Modeling mortality of individual trees in drained peatland sites in Finland, Silva Fenn. 37 (2003) 235–251.

    Google Scholar 

  26. Leites L.P., Robinson A.P., Improving taper equations of loblolly pine with crown dimensions in a mixed-effects modeling frame-work, For. Sci. 50 (2004) 204–212.

    Google Scholar 

  27. LeMay V.M., MSLS: a linear least squares technique for fitting a simultaneous system of equations with a generalized error structure, Can. J. For. Res. 20 (1990) 1830–1839.

    Article  Google Scholar 

  28. Lin X., Breslow N.E., Bias correction in generalized linear mixed models with multiple components of dispersion, J. Am. Stat. Assoc. 91 (1996) 1007–1016.

    Article  Google Scholar 

  29. Littell R.C., Milliken G.A., Stroup W.W., Wolfinger R.D., SAS System for Mixed Models, SAS Institute Inc., Cary, NC, 1996.

    Google Scholar 

  30. Lorimer C.G., Tests of age-independent competition indices for individual trees in natural hardwood stands, For. Ecol. Manage. 6 (1983) 343–360.

    Article  Google Scholar 

  31. Majcen Z., Richard, Y., Ménard, M., Grenier, Y., Choix des tiges à marquer pour le jardinage d’érablières inéquiennes, Guide technique, Ministère de l’Énergie et des Ressources du Québec, Direction de la recherche forestière, Mémoire No. 96, 1990.

  32. Majcen Z., Bédard S., Meunier S., Accroissement et mortalité quinze ans après la coupe de jardinage dans quatorze érablières du Québec méridional, Ministère des Ressources naturelles et de la Faune du Québec, Direction de la recherche forestière, Mémoire de recherche, No. 148, 2005.

  33. Martel J., Bergeron C., Demers G., Fortin Y, Hénaire F., Méthode d’échantillonnage pour les suivis des interventions forestières, Exercice 2001–2002, Ministère des Ressources naturelles du Québec, Direction de l’assistance technique, 2001.

  34. McCullagh P., Neider J.A., Generalized linear models, 2nd ed., Chapman & Hall/CRC, Monographs on Statistics and Applied Probability 37, New York, 1989.

    Google Scholar 

  35. McCulloch C.E., Searle S.R., Generalized, linear, and mixed models, John Wiley & Sons, New York, 2001.

    Google Scholar 

  36. McLintock T.F., Factors affecting wind damage in selectively cut stands of spruce and fir in Maine and northern New Hampshire, USDA For. Serv. Northeastern Forest Exp. Stn., Sta. Pap. No. 70, 1954.

  37. Milliken G.A., Johnson D.E., Analysis of messy data, Vol. 1, Designed experiments, Van Nostrand Reinhold Company, New York, 1984.

    Google Scholar 

  38. Monserud R.A., Sterba H., Modeling individual tree mortality for Austrian forest species, For. Ecol. Manage. 113 (1999) 109–123.

    Article  Google Scholar 

  39. MRNFP. Manuel d’aménagement forestier, 4e éd., Ministère des Ressources naturelles, de la Faune et des Parcs du Québec, Direction des programmes forestiers, 2003.

  40. Nienstaedt H., Zasada J.C., White spruce, in: Burns R.M., Honkala B.H. (Eds.), Silvics of North America, Vol. 1, USDA Agriculture Handbook No. 654, 1990, pp. 204–226.

  41. Nyland R.D., Silviculture: concepts and applications, 2nd ed., McGraw-Hill Ed, Toronto, 2002.

    Google Scholar 

  42. Parent B., Fortin C., Ressources et industries forestières, Portrait statistique édition 1999, Ministère des Ressources naturelles et de la Faune du Québec, Direction du développement de l’industrie des produits forestiers, 1999.

  43. Parent B., Fortin C., Ressources et industries forestières, Portrait statistique édition 2001, Ministère des Ressources naturelles du Québec, Direction du développement de l’industrie des produits forestiers, 2001.

  44. Parent B., Fortin C., Ressources et industries forestières, Portrait statistique édition 2005, Ministère des Ressources naturelles et de la Faune du Québec, Direction du développement de l’industrie des produits forestiers, 2005.

  45. Pinheiro J.C., Bates D.M., Mixed-effects models in S and S-PLUS, Springer/Verlag Ed., New York, 2000.

    Book  Google Scholar 

  46. Pothier D., Mailly D., Stand-level prediction of balsam fir mortality in relation to spruce budworm defoliation, Can. J. For. Res. 36 (2006) 1631–1640.

    Article  Google Scholar 

  47. González J.R., Trasobares A., Palahí M., Pukkala T., Predicting stand damage and tree survival in burned forests in Catalonia (North-East Spain), Ann. For. Sci. 64 (2007) 733–742.

    Article  Google Scholar 

  48. Robitaille A., Saucier J.-P., Paysages régionaux du Québec méridional, Ministère des Ressources naturelles du Québec, 1998.

  49. Rose C.E. Jr., Hall D.B., Shiver D.B., Clutter M.L., Border B., A multilevel approach to individual tree survival prediction, For. Sci. 52 (2006) 31–43.

    Google Scholar 

  50. Safford L.O., Bjorkbom J.C., Zasada J.C., Paper birch, in: Burns R.M., Honkala B.H. (Eds.), Silvics of North America, Vol. 2, USDA Agriculture Handbook No. 654, 1990, pp. 158–171.

  51. SAS Institute, The GLIMMIX Procedure, Nov. 2005, (On line), SAS Institute, Cary, NC, 2005, Available at http://support.sas.com/rnd/app/papers/glimmix.pdf[reviewed May 24th, 2006].

    Google Scholar 

  52. Smith D.M., Larson B.C., Kelty M.J., Ashton P.M.S., The practice of silviculture: Applied forest ecology (9th Ed.), John Wiley & Sons, New York, 1997.

    Google Scholar 

  53. Teck R.M., Hilt D.E., Individual-tree probability of survival model for the Northeastern United States, USDA For. Serv. Res. Pap. NE-642, 1990.

  54. Tubbs C.H., Houston D.R., American beech, in: Burns, R.M., Honkala, B.H., (Eds.), Silvics of North America, Vol. 2, USDA Agriculture Handbook No. 654, 1990, pp. 325–332.

  55. Vanclay J.K., Modelling forest growth and yield, applications to mixed tropical forests, CAB International, Wallingford, UK, 1994.

    Google Scholar 

  56. Wolfinger R., O’Connell M., Generalized linear models: a pseudo-likelihood approach, J. Statist. Comput. Simul. 48 (1993) 233–243.

    Article  Google Scholar 

  57. Wykoff W.R., A basal area increment model for individual conifers in the northern Rocky Mountains, For. Sci. 36 (1990) 1077–1104.

    Google Scholar 

  58. Yao X., Titus S.J., MacDonald S.E., A generalized logistic model of individual tree mortality for aspen, white spruce, and lodgepole pine in Alberta mixedwood forests, Can. J. For. Res. 31 (2001) 283–291.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Mathieu Fortin.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fortin, M., Bédard, S., DeBlois, J. et al. Predicting individual tree mortality in northern hardwood stands under uneven-aged management in southern Québec, Canada. Ann. For. Sci. 65, 205 (2008). https://0-doi-org.brum.beds.ac.uk/10.1051/forest:2007088

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://0-doi-org.brum.beds.ac.uk/10.1051/forest:2007088