scholarly journals Stem taper and bark functions for Norway spruce in Norway

Silva Fennica ◽  
2019 ◽  
Vol 53 (3) ◽  
Author(s):  
Timo Pukkala ◽  
Kjersti Hanssen ◽  
Kjell Andreassen
Keyword(s):  
Norway Spruce ◽  
Fixed Effects ◽  
Site Index ◽  
Mixed Effects ◽  
Mixed Effects Model ◽  
Bark Thickness ◽  
Random Parameters ◽  
Stem Taper ◽  
Large Trees ◽  
Age Dependent

Based on data from long-term experimental fields with Norway spruce ( (L.) H. Karst.), we developed new stem taper and bark functions for Norway. Data was collected from 477 trees in stands across Norway. Three candidate functions which have shown good performance in previous studies (Kozak 02, Kozak 97 and Bi) were fitted to the data as fixed-effects models. The function with the smallest Akaike Information Criterion (AIC) was then chosen for additional analyses, fitting 1) site index-dependent and 2) age-dependent versions of the model, and 3) fitting a mixed-effects model with tree-specific random parameters. Kozak 97 was found to be the function with the smallest AIC, but all three tested taper functions resulted in fairly similar predictions of stem taper. The site index-dependent function reduced AIC and residual standard error and showed that the effect of site index on stem taper is different in small and large trees. The predictions of the age-independent and age-dependent models were very close to each other. Adding tree-specific random parameters to the model clearly reduced AIC and residual variation. However, the results suggest that the mixed-effects model should be used only when it is possible to calibrate it for each tree, otherwise the fixed-effects Kozak 97 model should be used. A model for double bark thickness was also fitted as fixed-effects Kozak 97 model. The model behaved logically, predicting larger relative but smaller absolute bark thickness for small trees.Picea abies

scholarly journals Evaluation of Different Calibration Approaches for Merchantable Volume Predictions of Norway Spruce Using Nonlinear Mixed Effects Model

Forests ◽  
2019 ◽  
Vol 10 (12) ◽  
pp. 1104
Author(s):  
Zdeněk Adamec ◽  
Radim Adolt ◽  
Karel Drápela ◽  
Jiří Závodský
Keyword(s):  
Norway Spruce ◽  
Tree Height ◽  
Mixed Effects ◽  
Mixed Effects Model ◽  
Wood Volume ◽  
Nonlinear Mixed Effects Model ◽  
Breast Height ◽  
Stem Taper ◽  
Total Tree

Research Highlights: Determination of merchantable wood volume is one of the key preconditions for sustainable forest management. This study explores accuracy of calibrated predictions of merchantable wood volume of Norway spruce (Picea abies (L.) H. Karst.) using stem taper curves (STC) in a form of a mixed model. Background and Objectives: The study is devoted to the determination of merchantable wood volume (over bark) of individual standing stems based on the integration of an STC model calibrated using upper diameter measurements. Various options of upper diameter measurement were tested and their impact on the accuracy of merchantable wood volume prediction was evaluated. Materials and Methods: To model stem taper curves, a Kozak 02 function was applied in a form of a nonlinear, mixed effects model. Accuracies of calibrated merchantable wood volume predictions obtained through remote (optical) upper diameter measurements were compared to accuracies corresponding to contact measurements by a caliper. The performance of two alternative methods used in the Czech National Forest Inventory (NFI) and forestry practice, involving diameter at breast height and total tree height as the only predictors, were also tested. The contact measurements were performed at identical stem positions after felling the respective sample tree. The calibration was done in order to account for factors inherent in particular location, and, optionally, also in a particular sample stem (within the respective location). Input data was sourced as part of a dedicated survey involving the entire territory of the Czech Republic. In total, 716 individual spruce trees were measured, felled and analysed at 169 locations. Results: In general, the best merchantable volume predictions were obtained by integrating the STC fitted (and calibrated) by minimising errors of stem cross-sectional areas instead of diameters. In terms of calibrated predictions, using single-directional, caliper measurement of upper diameter at 7 m (after felling) led to the best accuracy. In this case, the observed mean bias of merchantable volume prediction was only 0.63%, indicating underestimation. The best optical calibration strategy involved upper diameter measurements at two heights (5 and 7 m) simultaneously. Bias of this volume prediction approach was estimated at 2.1%, indicating underestimation. Conclusions: Concerning the prediction of merchantable stem volume of standing Norway spruce trees, STC calibration using two optical upper diameter measurements (at 5 and 7 m) was found to be practically applicable, provided a bias up to 3.7% can be accepted. This method was found to be more accurate than the existing national alternatives using diameter at breast height and the total tree height as the only predictors.

scholarly journals Model of mixed effects of height dependence on tree diameters in pine stands

2021 ◽  
Author(s):  
Н.Н. Дубенок ◽  
В.В. Кузьмичев ◽  
А.В. Лебедев
Keyword(s):  
Fixed Effects ◽  
Mixed Effects ◽  
Mixed Effects Model ◽  
Fixed Effects Model ◽  
Permanent Sample Plots ◽  
Diameter At Breast Height ◽  
Breast Height ◽  
Russian State ◽  
Pine Stands ◽  
The Relationship

Основными исходными данными для определения запаса служат результаты обмеров диаметров и высот деревьев. Но обмеры диаметров деревьев на высоте груди выполнить намного проще, чем обмеры высот, поэтому ограничиваются замерами высот 15–25 деревьев. Цель исследования – по материалам измерения модельных деревьев в сосновых древостоях выбрать наиболее адекватную простую модель, которая передает зависимость между высотой деревьев и диаметром на высоте груди. Объектом исследования послужили сосновые древостои искусственного происхождения на постоянных пробных площадях в Лесной опытной даче Российского государственного агарного университета – МСХА имени К.А. Тимирязева. В работе используются данные обмеров деревьев на 17 постоянных пробных площадях с 1934 по 2005 гг. Возраст древостоев на момент проведения измерений от 50 до 125 лет. По итогам проведения 77 перечетов массив данных составил 1157 наблюдений. И модель фиксированных эффектов, и модель смешанных эффектов адекватно описали зависимость между высотами и диаметрами деревьев в культурах сосны. Но, как и ожидалось, первая модель имеет худшие значения метрик качества по сравнению со второй. Модель со смешанными эффектами более точно предсказывает значения высот по сравнению с моделью фиксированных эффектов. Недостающие значения высот большого количества деревьев на участке можно вычислить более точно с помощью модели смешанных эффектов, а не применения модели фиксированных эффектов или использования только фиксированной части (средний отклик) модели смешанных эффектов. Применение разработанной модели должно ограничиваться только в тех условиях, к которым относятся экспериментальные материалы The main data for the stock of research results is the diameter of measurements and heights of trees. But measurements of the diameter at breast height are much easier to perform than measurements of heights, therefore, they are limited to measuring the heights of 15–25 trees. The aim of the study is to select the most adequate simple model based on the measurements of model trees in pine antiquities, which conveys the relationship between the height of trees and the diameter at breast height. The object of the study was pine stands of artificial origin on permanent test plots in the Forest Experimental Station Russian State Agararian University – Moscow Timiriazev Agricultural Academy. The work uses data from tree measurements on 17 permanent sample plots from 1934 to 2005. The age of the stands at the time of measurements was from 50 to 125 years. As a result of 77 enumerations, the data array amounted to 1157 observations. Both the fixed effects model and the mixed effects model adequately describe the relationship between heights and diameters of trees in pine stumps. But, as expected, the first model has worse quality metrics than the second. The mixed effects model more accurately predicts heights from the fixed effects model. The missing heights of a large number of trees on a site can be calculated accurately using mixed effects models, rather than using fixed effects models or using only a fixed portion (mean response) of the mixed effects model. The application of the developed model should be limited only in those conditions to which the experimental materials are applied.

A note on Griffing's models for the diallel cross

1975 ◽  
Vol 85 (3) ◽  
pp. 575-576 ◽  
Author(s):  
B. K. Thompson
Keyword(s):  
Fixed Effects ◽  
Diallel Cross ◽  
Mixed Effects ◽  
Mixed Effects Model ◽  
Fixed Effects Model

SUMMARYSome misconceptions concerning the application of Griffing's fixed effects model I and mixed effects model B are discussed.

Modelling of wood density and fibre dimensions in mature Norway spruce

2007 ◽  
Vol 37 (8) ◽  
pp. 1373-1389 ◽  
Author(s):  
Dag Molteberg ◽  
Olav Høibø
Keyword(s):  
Norway Spruce ◽  
Fixed Effects ◽  
Fibre Length ◽  
Basic Density ◽  
Ring Width ◽  
Tree Height ◽  
Site Index ◽  
Residual Variance ◽  
Fibre Width ◽  
Width Measurements

Basic density (BD), fibre length (FL), fibre width (FW), and fibre wall thickness (FWT) were investigated in 46 Norway spruce ( Picea abies (L.) Karst.) trees from five different stands in eastern Norway. From each tree, wood samples were collected in different radial and longitudinal positions. Random coefficient mixed models were used to investigate variation within as well as among trees, both within and among stands. The R2 with random effects included, describing the best possible (individual) fit of the observed data to the models, were 0.90 for BD, 0.99 for FL, 0.88 for FW, and 0.91 for FWT. With only fixed effects, the best model explained 56% of the total variation for BD, 94.5% for FL, 61% for FW, and 63% for FWT. A common model for all trees, without tree and site information, predicted FL well but BD, FW, and FWT poorly. Adding site index, breast height diameter, and tree height to the models reduced the residual variance considerably for FW, FWT, and particularly BD, whereas only a minor improvement was gained for FL. The latter type of models might be easier to use for industrial purposes. Although information about ring width gave further improvements, ring width measurements are time consuming and difficult to perform in the forest and in industrial environments.

scholarly journals Generalized Nonlinear Mixed-Effects Individual Tree Crown Ratio Models for Norway Spruce and European Beech

Forests ◽  
2018 ◽  
Vol 9 (9) ◽  
pp. 555 ◽  
Author(s):  
Ram Sharma ◽  
Zdeněk Vacek ◽  
Stanislav Vacek
Keyword(s):  
Norway Spruce ◽  
Model Fitting ◽  
Basal Area ◽  
European Beech ◽  
Logistic Function ◽  
Mixed Effects ◽  
Mixed Effects Model ◽  
Individual Tree ◽  
Mixed Effects Modeling ◽  
Species Mixture

Tree crowns are commonly measured to understand tree growth and stand dynamics. Crown ratio (CR—crown depth-to-total height ratio) is significantly affected by a number of tree- and stand-level characteristics and other factors as well. Generalized mixed-effects CR models were developed using a large dataset (measurements from 14,669 trees of Norway spruce (Picea abies (L.) Karst.) and European beech (Fagus sylvatica (L.)) acquired from permanent research plots in various parts of the Czech Republic. Among several tree- and stand-level variables evaluated, diameter at breast height, height to crown base, dominant height, basal area of trees larger in diameter than a focal tree, relative spacing index, and variables describing the effects of species mixture and canopy height differentiation significantly contributed to CR variation. We included sample-plot-level variations caused by randomness in the data and other stochastic factors into the CR models using the mixed-effects modeling approach. The logistic function, which predicts the values between 0 and 1, was chosen to develop the generalized CR mixed-effects model. A large proportion of the CR variation (R2adj ≈ 0.63 (Norway spruce); 0.72 (European beech)) was described by generalized mixed-effects model without significant residual trends. Testing the CR model against a part of the model fitting dataset confirmed its high prediction precision. Our CR model can be useful for growth simulation using inventory databases that lack crown measures. Other potential implications of our CR models in forest management are mentioned in the article.

Repeated Measurement Designs

1983 ◽  
Vol 32 (3-4) ◽  
pp. 153-168 ◽  
Author(s):  
A, C. Mukhopadhyay ◽  
Rita Saha
Keyword(s):  
Fixed Effects ◽  
Mixed Effects ◽  
Repeated Measurement ◽  
Mixed Effects Model ◽  
Fixed Effects Model

In the present paper Repeated Measurement Designs (RMD's) have been studied under mixed effects model, assuming unit effects to be random and most of the optimality results of RMD's proved under fixed effects model by Hedayat et. al (1978), Magda (1980) and Cheng et. al (1980) have been reestablished in the context of mixed effects model.

scholarly journals Comparison of Fixed- and Mixed-effects Approaches to Taper Modeling for Scots Pine in West Poland

Forests ◽  
2019 ◽  
Vol 10 (11) ◽  
pp. 975 ◽  
Author(s):  
Karol Bronisz ◽  
Michał Zasada
Keyword(s):  
Random Effects ◽  
Scots Pine ◽  
Fixed Effects ◽  
Mixed Effects ◽  
Mixed Effects Model ◽  
Fixed Effects Model ◽  
Validation Data ◽  
Data Set ◽  
Taper Model ◽  
Model Approach

Diameter measurements along the stem, which are the basis for taper models, usually have a hierarchical structure. Mixed-effects models, where fixed and random effects are distinguished, are a possible solution for this type of data. However, in order to fully absorb the potential of this method, random effects prediction, which requires additional measurements (diameter along stem), is recommended. This article presents a comparison of various fitting methods (mixed- and fixed-effects model approaches) of the variable-exponent taper model created by Kozak for determining the outside bark diameter along the stem and predicting the tree volume of Scots pine trees in west Poland. During the analysis, it was assumed that no additional measured data were available for practical use; therefore, for the mixed-effects model approach, fixed effects prediction without random effects was applied. Both fitting strategies were compared based on modeling and an independent validation data set. The comparison of mixed- and fixed-effects fitting strategies for the diameter along the stem indicated that the taper model fitted using the mixed-effects model approach better fit the data. Moreover, the error rate for the total tree volume prediction for the independent data set was lower for the mixed-effects model solution than for the fixed-effects one.

scholarly journals Idelalisib addition has neutral to beneficial effects on quality of life in bendamustine/rituximab-treated patients: results of a phase 3, randomized, controlled trial

2019 ◽  
Vol 17 (1) ◽  
Author(s):  
Marco Montillo ◽  
Árpád Illés ◽  
Tadeusz Robak ◽  
Alexander S. Pristupa ◽  
Malgorzata Wach ◽  
...  
Keyword(s):  
Quality Of Life ◽  
Fixed Effects ◽  
Controlled Trial ◽  
Statistical Significance ◽  
Mixed Effects ◽  
Mixed Effects Model ◽  
Symptom Improvement ◽  
Phase 3 ◽  
Kaplan Meier

Abstract Background In a phase 3 randomized, double-blind, placebo-controlled trial, treatment with idelalisib, a phosphoinositol-3 kinase δ inhibitor, + bendamustine/rituximab improved progression-free survival (PFS) and overall survival (OS) in adult patients with relapsed/refractory chronic lymphocytic leukemia (R/R CLL). Here we report the results of health-related quality of life (HRQL) analyses from this study. Methods From June 15, 2012 to August 21, 2014, 416 patients with R/R CLL were enrolled; 207 patients were randomized to the idelalisib arm and 209 to the placebo arm. In the 416 patients randomized to receive bendamustine/rituximab and either oral idelalisib 150 mg twice-daily or placebo, HRQL was assessed at baseline and throughout the blinded part of the study using the Functional Assessment of Cancer Therapy–Leukemia (FACT-Leu) and EuroQoL Five-Dimension (EQ-5D) visual analogue scale (VAS) questionnaires. The assessments were performed at scheduled patient visits; every 4 weeks for the first 6 months from the initiation of treatment, then every 8 weeks for the next 6 months, and every 12 weeks thereafter until end of study. Least-squares mean changes from baseline were estimated using a mixed-effects model by including treatment, time, and treatment-by-time interaction, and stratification factors as fixed effects. Time to first symptom improvement was assessed by Kaplan-Meier analysis. Results In mixed-effects model analysis, idelalisib + bendamustine/rituximab treatment led to clinically meaningful improvements from baseline in leukemia-associated symptoms. Moreover, per Kaplan-Meier analysis, the proportion of patients with symptom improvement was higher and time to improvement was shorter among patients in the idelalisib-containing arm compared with those who did not receive idelalisib. The physical and social/family FACT-Leu subscale scores, along with the self-rated health assessed by EQ-VAS, showed improvement with idelalisib over placebo, but the difference did not reach statistical significance. The functional and emotional FACT-Leu subscale scores remained similar to placebo. Conclusions Addition of idelalisib to bendamustine/rituximab, apart from improving PFS and OS, had a neutral to beneficial impact on HRQL in patients with R/R CLL, particularly by reducing leukemia-specific disease symptoms. Trial registration Clinicaltrials.gov NCT01569295. Registered April 3, 2012.

Modelling and prediction of dominant height and site index of Eucalyptus globulus plantations using a nonlinear mixed-effects model approach

2007 ◽  
Vol 37 (8) ◽  
pp. 1390-1403 ◽  
Author(s):  
Yue Wang ◽  
Valerie M. LeMay ◽  
Thomas G. Baker
Keyword(s):  
Site Index ◽  
Mixed Effects ◽  
Mixed Effects Model ◽  
Annual Rainfall ◽  
Maximum Temperature ◽  
Daily Maximum Temperature ◽  
Daily Maximum ◽  
Nonlinear Mixed Effects ◽  
Nonlinear Mixed Effects Model ◽  
Dominant Height

A nonlinear mixed-effects model approach was used to model dominant height and site index for Eucalyptus globulus Labill. plantations in southeastern Australia. Mixed effects were considered initially for all three parameters of a modified Chapman–Richards model. Inclusion of random effects improved fitting and accounted for the within-plot heteroscedasticity. To correct for within-plot autocorrelation, a power autocorrelation model allowing for irregular intervals for remeasurements was found to be most appropriate. Additional fertilizer application at age 1 year and a number of environmental variables were related to the fixed-effects parameters, but these were not statistically significant, whereas mean annual rainfall and average daily maximum temperature in July (winter) greatly reduced the residual variability among plots. The resulting nonlinear mixed-effects model combines dominant height and site index prediction into a single model and predicts polymorphic height growth rates on different sites. The model can be used to predict population-mean dominant heights and site indices for different growing conditions of E. globulus plantations using existing information of annual rainfall and daily maximum temperature. When prior measures of dominant heights at several ages are available for a plot, specific random effects can be estimated and localized predictions of dominant height or site index can be obtained.

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