Forecasting probability distributions of forest yield allowing for a Bayesian approach to management planning

Probability distributions of stand basal area were predicted and evaluated in young mixed stands of Scots pine (Pinus sylvestris L.), Norway spruce (Picea abies (L.) Karst.) and birch (Betula pendula Roth and Betula pubescens Ehrh.) in Sweden. Based on an extensive survey of young stands, individual tree basal area growth models were estimated using a mixed model approach to account for dependencies in data and derive the variance/covariance components needed. While most of the stands were reinventoried only once, a subset of the stands was revisited a second time. This subset was used to evaluate the accuracy of the predicted stand basal area distributions. Predicting distributions of forest yield, rather than point estimates, allows for a Bayesian approach to planning and decisions can be made with due regard to the quality of the information.

[1]  J. P. Kimmins.  Modelling the Sustainability of Forest Production and Yield for a Changing and Uncertain Future , 1990 .

[2]  D. Sengupta.  Linear models , 2003 .

[3]  Annika Kangas,et al.  On the prediction bias and variance in long-term growth projections , 1997 .

[4]  Annika Kangas,et al.  Optimization bias in forest management planning solutions due to errors in forest variables , 1999 .

[5]  H. Todd Mowrer.  Estimating components of propagated variance in growth simulation model projections , 1991 .

[6]  J. Lappi.  Mixed linear models for analyzing and predicting stem form variation of Scots pine , 1986 .

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

[8]  D. Harville.  Maximum Likelihood Approaches to Variance Component Estimation and to Related Problems , 1977 .

[9]  J. B. Pickens,et al.  Use of stochastic production coefficients in linear programming models: objective function distribution, feasibility, and dual activities , 1988 .

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

[11]  Hannu Hökkä,et al.  A method for using random parameters in analyzing permanent sample plots. , 1995 .

[12]  W. Hays.  Statistical theory. , 1968, Annual review of psychology.

[13]  Annika Kangas,et al.  Methods for assessing uncertainty of growth and yield predictions , 1999 .

[14]  R. Haight,et al.  Feedback Thinning Policies for Uneven-Aged Stand Management with Stochastic Prices , 1990, Forest Science.

[15]  W. Strawderman,et al.  A comparison of hierarchical Bayes and empirical Bayes methods with a forestry application , 1992 .

[16]  R. Mendelsohn,et al.  Timber Harvesting with Fluctuating Prices , 1988 .

[17]  Kurt H. Riitters,et al.  Dynamic programming for optimization of timber production and grazing in ponderosa pine , 1982 .

[18]  Juha Lappi,et al.  A Height Prediction Model with Random Stand and Tree Parameters: An Alternative to Traditional Site Index Methods , 1988 .

[19]  P. Lohmander,et al.  The economics of forest management under risk [adaptive optimization, forest economics, stochastic dynamic programming, stochastic growth, stochastic optimization, stochastic prices, stochastic processes, windthrow probability] , 1987 .

[20]  W. R. Wykoff,et al.  Calibrating a model of stochastic effects on diameter increment for individual-tree simulations of stand dynamics , 1993 .

[21]  Timo Pukkala,et al.  A method for stochastic multiobjective optimization of stand management , 1997 .

[22]  W. Strawderman,et al.  Predictive posterior distributions from a Bayesian version of a slash pine yield model , 1996 .

[23]  L. Valsta,et al.  A Scenario Approach to Stochastic Anticipatory Optimization in Stand Management , 1992, Forest Science.

[24]  George Z. Gertner.  Prediction bias and response surface curvature , 1991 .

[25]  Jerome K. Vanclay,et al.  Compatible Deterministic and Stochastic Predictions by Probabilistic Modeling of Individual Trees , 1991, Forest Science.

[26]  L. Bondesson,et al.  A method to determine optimal stand data acquisition policies , 1994 .

[27]  D. R. Betters,et al.  Optimization with expected values of random yield coefficients in renewable resource linear programs , 1988 .

[28]  A. Groot,et al.  An individual-tree basal area growth model for black spruce in second-growth peatland stands , 1999 .

[29]  R. H. Hamre,et al.  Spatial Accuracy Assessment in Natural Resources and Environmental Sciences , 1996 .

[30]  H. T. Mowrer,et al.  Variance propagation in growth and yield projections , 1986 .

[31]  T. Penttilä,et al.  Individual-tree basal area growth models for Scots pine, pubescent birch and Norway spruce on drained peatlands in Finland. , 1997 .

[32]  G. Staahl.  Optimizing the utility of forest inventory activities , 1994 .

[33]  Annika Kangas,et al.  On the bias and variance in tree volume predictions due to model and measurement errors , 1996 .

[34]  E. Green,et al.  Bayesian analysis of the linear model with heterogeneous variance , 1998 .

[35]  K. Nyström,et al.  Individual tree basal area growth models for young stands of Norway spruce in Sweden , 1997 .

[36]  H. Burkhart,et al.  A simulation study assessing the effect of sampling for predictor variable values on estimates of yield , 1984 .

[37]  J. Gove,et al.  Optimizing the management of uneven-aged forest stands : a stochastic approach , 1992 .

[38]  Shoufan Fang,et al.  A Bayesian approach for estimating the parameters of a forest process model based on long-term growth data , 1999 .

[39]  George Z. Gertner,et al.  Effects of measurement errors on an individual tree-based growth projection system , 1984 .