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

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.RésuméCette 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.

[1]  William J. Browne,et al.  Bayesian and likelihood-based methods in multilevel modeling 1 A comparison of Bayesian and likelihood-based methods for fitting multilevel models , 2006 .

[2]  P. McCullagh,et al.  Generalized Linear Models , 1972, Predictive Analytics.

[3]  William R. Wykoff,et al.  A Basal Area Increment Model for Individual Conifers in the Northern Rocky Mountains , 1990, Forest Science.

[4]  Timothy G. Gregoire,et al.  Linear modelling of irregularly spaced, unbalanced, longitudinal data from permanent-plot measurements , 1995 .

[5]  N. Breslow,et al.  Bias Correction in Generalized Linear Mixed Models with Multiple Components of Dispersion , 1996 .

[6]  Timo Pukkala,et al.  Predicting stand damage and tree survival in burned forests in Catalonia (North-East Spain) , 2007, Annals of Forest Science.

[7]  Timothy G. Gregorie,et al.  Generalized Error Structure for Forestry Yield Models , 1987, Forest Science.

[8]  D. Bates,et al.  Mixed-Effects Models in S and S-PLUS , 2001 .

[9]  J. Caspersen.  Elevated mortality of residual trees following single-tree felling in northern hardwood forests , 2006 .

[10]  Craig G. Lorimer,et al.  Tests of age-independent competition indices for individual trees in natural hardwood stands , 1983 .

[11]  James N. Long,et al.  Linkages between silviculture and ecology: an analysis of density management diagrams , 1996 .

[12]  Robert L. Bailey,et al.  Modeling and Prediction of Forest Growth Variables Based on Multilevel Nonlinear Mixed Models , 2001 .

[13]  D. Cox,et al.  Analysis of Survival Data. , 1986 .

[14]  David A. Hamilton,et al.  A Logistic Model of Mortality in Thinned and Unthinned Mixed Conifer Stands of Northern Idaho , 1986, Forest Science.

[15]  Valerie LeMay,et al.  MSLS: a linear least squares technique for fitting a simultaneous system of equations with a generalized error structure , 1990 .

[16]  S. R. Searle,et al.  Generalized, Linear, and Mixed Models , 2005 .

[17]  R. Littell.  SAS System for Mixed Models , 1996 .

[18]  D. Pothier,et al.  Stand-level prediction of balsam fir mortality in relation to spruce budworm defoliation , 2006 .

[19]  David W. Hosmer,et al.  Applied Logistic Regression , 1991 .

[20]  Robert L. Bailey,et al.  Nonlinear Mixed Effects Modeling for Slash Pine Dominant Height Growth Following Intensive Silvicultural Treatments , 2001 .

[21]  Jerome K. Vanclay,et al.  Modelling Forest Growth and Yield: Applications to Mixed Tropical Forests , 1994 .

[22]  Michael L. Clutter,et al.  A Multilevel Approach to Individual Tree Survival Prediction , 2006 .

[23]  K. Gadow,et al.  A two-step mortality model for even-aged stands of Pinus radiata D. Don in Galicia (Northwestern Spain) , 2004 .

[24]  D. E. Johnson,et al.  Analysis of Messy Data Volume I: Designed Experiments , 1985 .

[25]  R. Ouimet,et al.  Assessment of sugar maple health based on basal area growth pattern , 2003 .

[26]  E. V. Bakuzis,et al.  Balsam Fir: A Monographic Review , 1965 .

[27]  R. Monserud,et al.  Modeling individual tree mortality for Austrian forest species , 1999 .

[28]  P. McCullagh,et al.  Generalized Linear Models, 2nd Edn. , 1990 .

[29]  Hannu Hökkä,et al.  Modeling Mortality of Individual Trees in Drained Peatland Sites in Finland , 2003 .

[30]  A. Robinson,et al.  Improving Taper Equations of Loblolly Pine with Crown Dimensions in a Mixed-Effects Modeling Framework , 2004, Forest Science.

[31]  S. Titus,et al.  A generalized logistic model of individual tree mortality for aspen, white spruce, and lodgepole pine in Alberta mixedwood forests , 2001 .

[32]  Ressources et industries forestières,et al.  Ressources et industries forestières, portrait statistique ... [ressource électronique] / Ministère des ressources naturelles, de la faune et des parcs, Direction du développement de l'industrie des produits forestiers , 1983 .

[33]  John A. Nelder,et al.  Generalized linear models. 2nd ed. , 1993 .

[34]  Richard M. Teck,et al.  Individual-tree probability of survival model for the Northeastern United States , 1990 .

[35]  Dallas E. Johnson,et al.  Analysis of messy data , 1992 .

[36]  N. Breslow,et al.  Bias correction in generalised linear mixed models with a single component of dispersion , 1995 .

[37]  Eric R. Ziegel,et al.  Generalized Linear Models , 2002, Technometrics.

[38]  Ralph D. Nyland,et al.  Silviculture: Concepts and Applications , 1996 .

[39]  R. Bailey,et al.  A Multivariate Simultaneous Prediction System for Stand Growth and Yield with Fixed and Random Effects , 2001 .

[40]  Robert R. Oberg,et al.  Fifteen-year results from six cutting methods in second-growth northern hardwoods. , 1973 .

[41]  R. Wolfinger,et al.  Generalized linear mixed models a pseudo-likelihood approach , 1993 .

[42]  Douglas A. Maguire,et al.  Modeling stem taper of three central Oregon species using nonlinear mixed effects models and autoregressive error structures , 2003 .