No abstract

No abstract

This contribution presents an approach to model individual tree height-diameter relationships for Scots pine (Pinus sylvestris) in multi-size and mixedspecies stands in Estonia using the Estonian Permanent Forest Research Plot Network. The dataset includes 22,347 trees. The main focus of the study was to use an approach that is spatially explicit allowing for high accuracy prediction from a minimum set of predictor variables that can be easily derived. Consequently, the height-diameter relationship is modeled as a function of only the stand quadratic mean diameter (dg) and the plot geographical coordinates. A specific generalized additive model gam is employed that allows for the integration of a varying coefficient term and 2-dimensional surface estimators representing a spatial trend and a spatially varying coefficient term. The high flexibility of the model is needed due to the very few predictor variables that subsume a variety of potential influential factors. Subsequently, a linear mixed model is used that quantifies the random variation between plots and between measurement occasions within plots, respectively. Hence, our model is based on the theory of structured additive regression models (Fahrmeir et al. 2007) and separates a structured (correlated) spatial effect from an unstructured (uncorrelated) spatial effect. Additionally, the linear mixed model allows for calibration of the model using height measurements as pre-information.Model bias is small, despite the somewhat irregular distribution of experimental areas within the country. The overall model shows some similarity with earlier applications in Finland. However, there are important differences involving the model form, the predictors and the method of parameter estimation.

We used six models, ranging from simple parameter-sparse models to complex process-based 7 models: 3PG, 4C, ANAFORE, BASFOR, BRIDGING and FORMIND. For each model, the initial 8 degree of uncertainty about parameter values was expressed in a prior probability distribution. 9Inventory data for Scots pine on tree height and diameter, with estimates of measurement 10 uncertainty, were assembled for twelve sites, from four countries: Austria, Belgium, Estonia and 11Finland. From each country, we used data from two sites of the National Forest Inventories (NFI), 12 and one Permanent Sample Plot (PSP). The models were calibrated using the NFI-data and tested 13 against the PSP-data. Calibration was done both per country and for all countries simultaneously, 14 thus yielding country-specific and generic parameter distributions. We assessed model 15 performance by sampling from prior and posterior distributions and comparing the growth 16 predictions of these samples to the observations at the PSP"s. 17We found that BC reduced uncertainties strongly in all but the most complex model. 18 Surprisingly, country-specific BC did not lead to clearly better within-country predictions than 19 generic BC. BMC identified the BRIDGING model, which is of intermediate complexity, as the 20 most plausible model before calibration, with 4C taking its place after calibration. In this BMC, 21 model plausibility was quantified as the relative probability of a model being correct given the 22 information in the PSP-data. We discuss how the method of model initialisation affects model 23 performance. Finally, we show how BMA affords a robust way of predicting forest growth that 24 accounts for both parametric and model structural uncertainty. 25 26 27

No abstract

Aim of study: The present study evaluates a set of competition indices including spatially explicit indices combined with different competitor selection approaches and non-spatially explicit competition indices. The aim was to quantify and describe the neighbouring effects on the tree diameter growth of silver birch trees.Area of study: Region throughout Estonia. Material and methods:Data from the Estonian Network of Forest Research Plots was used. After quantifying the selected indices, the best non-spatial indices and spatial indices (combined with neighbour selection methods) were separately devised into a growth model as a predictor variable to assess the ability of the diameter growth model before and after adding competition measures. To test the species-specific effect on the competition level, the superior indices were recalculated using Ellenberg's light indicators and incorporated into the diameter growth model.Main results: Statistical analyses showed that the diameter growth is a function of neighbourhood interactions and spatial indices were better growth predictors than non-spatial indices. In addition, the best selections of competitive neighbours were acquired based on the influence zone and the competition elimination angle concepts, and using Ellenberg's light values had no significant improvement in quantifying the competition effects.Research highlights: Although the best ranking spatial competition measures were superior to the best non-spatial indices, the differences were negligible.

No abstract

This paper describes a new SAS/STAT ® procedure for fitting models to non-normal or normal data with correlations or nonconstant variability. The GLIMMIX procedure is an add-on for the SAS/STAT product in SAS ® 9.1 on the Windows platform. PROC GLIMMIX extends the SAS mixed model tools in a number of ways. For example, it• models data from non-Gaussian distributions• implements low-rank smoothing based on mixed models • provides new features for LS-means comparisons and display• enables you to use SAS programming statements to compute model effects, or to define link and variance functions• fits models to multivariate data in which observations do not all have the same distribution or linkApplications of the GLIMMIX procedure include estimating trends in disease rates, modeling counts or proportions over time in a clinical trial, predicting probability of occurrence in time series and spatial data, and joint modeling of correlated binary and continuous data.This paper describes generalized linear mixed models and how to use the GLIMMIX procedure for estimation, inference, and prediction.