基于非线性混合模型的落叶松树干削度模型

以黑龙江省带岭林业局大青川林场84株人工落叶松解析木数据为例,采用Max和Burkhart分段削度模型作为基础模型,利用SAS软件中的似乎不相关回归过程得到该分段削度模型的4个参数和2个拐点参数同时估计。参数估计显著性检验(P<0.000 1)以及模型检验(F=31 392.30,P<0.000 1)都证明该分段模型能较好地描述落叶松树干干形变化。然后以该分段模型为基础模型,采用非线性混合模型的方法,建立落叶松人工林树干削度混合效应模型。结果表明:当考虑样地效应影响时,b1,b2同时作为混合参数时模型拟合最好;当考虑树木效应影响时,b2,b4同时作为混合参数时模型拟合最好。无论考虑样地效应影响还是考虑树木效应影响,混合模型的拟合精度都比基本模型的拟合精度高,并且考虑树木效应影响要比考虑样地效应影响的精度更高。模型检验结果表明:混合模型通过校正随机参数值能提高模型的预测精度。     

Stem taper equations for poplars growing on farmland in Sweden

We developed a simple polynomial taper equation for poplars growing on former farmland in Sweden and also evaluated the performance of some well-known taper equations. In Sweden there is an increasing interest in the use of poplar. Effective management of poplar plantations for high yield production would be facilitated by taper equations providing better predictions of stem volume than currently available equations. In the study a polynomial stem taper equation with five parameters was established for individual poplar trees growing on former farmland. The outputs of the polynomial taper equation were compared with five published equations. Data for fitting the equations were collected from 69 poplar trees growing at 37 stands in central and southern Sweden (lat. 55-60° N). The mean age of the stands was 21 years (range 14-43), the mean density 984 stems ha -1 (198 3,493), and the mean diameter at breast height (outside bark) 25 cm (range 12-40). To verify the tested equations, performance of accuracy and precision diameter predictions at seven points along the stem was closely analyzed. Statistics used for evaluation of the equations indicated that the variable exponent taper equation presented by Kozak (1988) performed best and can be recommended. The stem taper equation by Kozak (1988) recommended in the study is likely to be beneficial for optimising the efficiency and profitability of poplar plantation management. The constructed polynomial equation and the segmented equation presented by Max & Burkhart (1976) were second and third ranked. Due to the statistical complexity of Kozak’s equation, the constructed polynomial equation is alternatively recommended when a simple model is requested and larger bias is accepted.     

Modeling stem profile of Lebanon cedar,Brutian pine,and Cilicica fir in Southern Turkey using nonlinear mixed-effects models

The Max and Burkhart segmented taper model was fitted using nonlinear mixed-effects modeling techniques to account for within- and between-individual stem profile variation for Lebanon cedar (Cedrus libani A. Rich.), brutian pine (Pinus brutia Ten.), and cilicica fir (Abies cilicica Carr.) in Turkey. About 75% of the trees were randomly selected for model development, with the remainder used for model validation. Diameter measurements from various heights were evaluated for tree-specific calibrations by predicting random-effects parameters using an approximate Bayesian estimator. The procedure was tested with a validation dataset. Predictive accuracy of the model was improved by including random-effects parameters for a new tree based on upper stem diameter measurements. Prediction in stem diameter was less biased and more precise across the all sections of bole when compared to predictions based only on fixed-effects parameters. In the future, the proposed mixed models can be applied to region wide three species stands by fitting the model to a larger data set that more closely represents regional variation.     

理论造材:削度方程和出材率表的编制

本文提出了计算机理论造材仅根据削度方程和单株带,去皮胸径的转换关系式两个模型,可不必由削度方程推导材长方程和材积比方程。比相关指数,均方程为指标,结合残差图分析,选择了杉木、落叶松的削度方程;结合标准树高曲线,是可仅根据优势高为任一具体林分编制（一元）单株出材率表（特称之为自动调整出材率表）。     

Segmented taper equations with crown ratio and stand density for Dahurian Larch (<Emphasis Type="Italic">Larix gmelinii</Emphasis>) in Northeastern China

Segmented taper equation was selected to model stem profile of Dahurian larch (Larix gmelinii Rupr.). The data were based on stem analysis of 74 trees from Dailing Forest Bureau in Heilongjiang Province, Northeastern China. Two taper equations with crown ratio and stand basal area were derived from the Max and Burkhart’s (1976) taper equation. Three taper equations were evaluated: (1) the original equation, (2) the original equation with crown ratio, and (3) the original equation with basal area. SAS NLIN a...     

Correction to: Agroforestry can enhance foraging and nesting resources for pollinators with focus on solitary bees at the landscape scale

Agroforestry Systems - A correction to this paper has been published: https://doi.org/10.1007/s10457-021-00641-7     

Operationalizing a Framework for Assessing the Enabling Environment for Community Forest Enterprises: A Case Study from Nepal

Small-scale Forestry - We demonstrate how Baynes et al.’s (Glob Environ Change 35:226–238, 2015. https://doi.org/10.1016/j.gloenvcha.2015.09.011) framework can be operationalized as a...     

Correction to: RNAi,what is its position in crop protection?

Journal of Pest Science - A correction to this paper has been published: https://doi.org/10.1007/s10340-021-01393-0     

Correction to: The olfactive responses of Tetranychus urticae natural enemies in citrus depend on plant genotype,prey presence,and their diet specialization

Journal of Pest Science - A correction to this paper has been published: https://doi.org/10.1007/s10340-021-01364-5     

Correction to: Assessment of cable tensile forces in active winch-assist harvesting using an anchor machine configuration

European Journal of Forest Research - A correction to this paper has been published: https://doi.org/10.1007/s10342-021-01385-w     

Correction to: When is it biological control? A framework of definitions,mechanisms, and classifications

Journal of Pest Science - A correction to this paper has been published: https://doi.org/10.1007/s10340-021-01386-z     

Correction to: Orius laevigatus strengthens its role as a biological control agent by inducing plant defenses

Journal of Pest Science - A correction to this paper has been published: https://doi.org/10.1007/s10340-021-01357-4     

A merchantable volume system for Pinus sylvestris L. in the major mountain ranges of Spain

? Accurate estimation of stem volume makes it possible to estimate the monetary value of one of the many commodities and services that forests provide to society, i.e. timber.

? In the present study a compatible volume system for Scots pine in the major mountain ranges of Spain (the Pyrenees, Southern Iberian Range, Northern Iberian Range, Soria and Burgos Mountains, Central Range and Galician Mountains) was developed with data from 2 682 destructively sampled trees. Several well-known taper functions were evaluated. A second-order continuous-time autoregressive error structure was used to correct the inherent autocorrelation in the hierarchical data, allowing the model to be applied to irregularly spaced and unbalanced data.

? The compatible segmented model of Fang et al. (2000) best described the experimental data. It is therefore recommended for estimating diameter at a specific height, height to a specific diameter, merchantable volume, and total volume for the six mountain ranges analyzed.

? The non-linear extra sum of squares method indicated differences in mountain range-specific taper functions. A different taper function should therefore be used for each mountain range in Spain.

     

Ecosystem services from coffee agroforestry in Central America: estimation using the CAF2021 model

The goal of sustainable coffee production requires multiple functions from agroforestry systems. Many are difficult to quantify and data are lacking, hampering the choice of shade tree species and agronomic management. Process-based modelling may help quantify ecosystem services and disservices. We introduce and apply coffee agroforestry model CAF2021 (https://doi.org/10.5281/zenodo.5862195). The model allows for complex systems with up to three shade tree species. It simulates coffee yield, timber and fruit production by shade trees, soil loss in erosion, C-sequestration, N-fixation, -emission and -leaching. To calibrate the model, we used multivariate data from 32 different treatments applied in two long-term coffee agroforestry experiments in Costa Rica and Nicaragua. Without any further calibration, the model was then applied to agroforestry systems on 89 farms in Costa Rica and 79 in Guatemala where yields had been reported previously in farmer interviews. Despite wide variation in environmental and agronomic conditions, the model explained 36% of yield variation in Costa Rica but only 15% in Guatemala. Model analysis quantified trade-offs between yield and other ecosystem services as a function of fertilisation and shading.

     

Developing a taper model for the Pinus elliottii × P. caribaea var. hondurensis hybrid in South Africa

A relatively new hybrid, Pinus elliottii × P. caribaea var. hondurensis (Pexc), for which a taper model does not exist, is being planted commercially in South Africa. This study primarily focused on developing a taper model for Pexc in South Africa. Taper data were collected from a total of 363 trees, in the Mpumalanga and Limpopo provinces, using a random sampling method. A subsample was selected to determine if altitude, rainfall, temperature or soil have a significant influence on the taper of Pexc. Only rainfall significantly influenced the overall taper. The Max and Burkhart segmented polynomial taper model, as well as the Kozak88, Kozak01 and Kozak02 variable exponent taper models, were fitted, compared and tested using the statistical analysis system (SAS). The predictive ability of the models was evaluated based on the results from the mean bias, standard deviation, the standard error of prediction and the average percentage deviation. The Kozak02 model had the best fit overall followed by the Max and Burkhart model (MB76). The MB76 model, however, predicted the volumes more accurately than the Kozak02 model.     

Mixed-effect non-linear modelling for diameter estimation along the stem of Tectona grandis in mid-western Brazil

This study evaluated the efficiency of taper functions and the application of mixed-effect modelling for diameter estimation along the stems of Tectona grandis. We sampled 266 trees of Tectona grandis, measuring the diameter at relative heights for volume determination, grouping the data according to three form-factor classes. Six taper functions were fitted, selecting the function with better fit performance. Six taper functions were fitted, selecting the function with better fit performance. The selected function was fitted in its basic formulation, and with the mixed non-linear modelling technique in different scenarios, and for the stem stratified in three portions of the total height. The precision and selection of the adjusted models were evaluated regarding the coefficient of determination, standard error of estimate, the Akaike information criterion, bias, quadratic error and absolute bias. According to the statistical criteria used, the model of Kozak was selected for the adjustments. For diameter estimation, the scenario with two coefficients as random effects provided an accuracy increase of 11.91%, and the mixed non-linear modelling better estimated the stem diameter for the stratified stems. In conclusion, the model of Kozak can be used to describe the stem shape of Tectona grandis, and the mixed-effect non-linear model approach was the best technique to estimate diameter along the stem of Tectona grandis.     

A simple stem taper model with mixed effects for boreal black spruce

We simplified Kozak’s taper model by setting the inflection point at 1.3 m (dbh) without losing accuracy and precision. The simplification was required to facilitate the estimation of the covariance parameters when using a mixed-effects method. This method was necessary to take into account the correlation among multiple diameter measurements on an individual stem. The simple stem taper model was fitted to an extended data set collected across the province of Quebec, Canada. Comparison of the predicted stem taper and the derived stem volume with those obtained using existing models showed a comparable predictive power for the simple model. Including a prediction of the tree random effects based on supplementary diameter measurements of the bole improves the predictive ability of the model around the extra diameter observation. This model offers welcome simplicity as a means of predicting tree taper at coarse resolution for planning tree harvesting.     

A flexible stem taper and volume prediction method based on mixed-effects B-spline regression

Modelling stem taper and volume is crucial in many forest management and planning systems. Taper models are used for diameter prediction at any location along the stem of a sample tree. Furthermore, taper models are flexible means to provide information on the stem volume and assortment structure of a forest stand or other management units. Usually, taper functions are mean functions of multiple linear or nonlinear regression models with diameter at breast height and tree height as predictor variables. In large-scale inventories, an upper diameter is often considered as an additional predictor variable to improve the reliability of taper and volume predictions. Most studies on stem taper focus on accurately modelling the mean function; the error structure of the regression model is neglected or treated as secondary. We present a semi-parametric linear mixed model where the population mean diameter at an arbitrary stem location is a smooth function of relative height. Observed tree-individual diameter deviations from the population mean are assumed to be realizations of a smooth Gaussian process with the covariance depending on the sampled diameter locations. In addition to the smooth random deviation from the population average, we consider independent zero mean residual errors in order to describe the deviations of the observed diameter measurements from the tree-individual smooth stem taper. The smooth model components are approximated by cubic spline functions with a B-spline basis and a small number of knots. The B-spline coefficients of the population mean function are treated as fixed effects, whereas coefficients of the smooth tree-individual deviation are modelled as random effects with zero mean and a symmetric positive definite covariance matrix. The taper of a tree is predicted using an arbitrary number of diameter and corresponding height measurements at arbitrary positions along the stem to calibrate the tree-individual random deviation from the population mean estimated by the fixed effects. This allows a flexible application of the method in practice. Volume predictions are calculated as the integral over cross-sectional areas estimated from the calibrated taper curve. Approximate estimators for the mean squared errors of volume estimates are provided. If the tree height is estimated or measured with error, we use the “law of total expectation and variance” to derive approximate diameter and volume predictions with associated confidence and prediction intervals. All methods presented in this study are implemented in the R-package TapeR.     

Comparison of model forms for estimating stem taper and volume in the primary conifer species of the North American Acadian Region

? The performance of ten commonly used taper equations for predicting both stem form and volume in balsam fir [Abies balsamea (L.) Mill], red spruce[Picea rubens (Sarg.)], and white pine[Pinus strobus (L.)] in the Acadian Region of North America was investigated.

? Results show that the Kozak (2004) and Bi (2000) equations were superior to the other equations in predicting diameter inside bark for red spruce and white pine, while the Valentine and Gregoire (2001) equation performed slightly better for balsam fir.

? For stem volume, the Clark et al. (1991) equation provided the best predictions across all species when upper stem diameter measurements were available, while the Kozak (2004) and compatible taper equation of Fang et al. (2000) performed well when those measurements were unavailable.

? The incorporation of crown variables substantially improved stem volume predictions (mean absolute bias reduction of 7–15%; root mean square error reduction of 10–15%) for all three species, but had little impact on stem form predictions.

? The best taper equation reduced the predicted root mean square error by 16, 39, and 45% compared to estimates from the widely used Honer (1965) regional stem volume equations for balsam fir, red spruce, and white pine, respectively.

? When multiple taper equations exist for a certain species, the use of the geometric mean of all predictions is an attractive alternative to selecting the “best” equation.

     

A stem taper equation compatible to volume equation for <Emphasis Type="Italic">Paraserianthes falcataria </Emphasis>in Pare,East Java,Indonesia: its implications for the plantation management

A stem taper equation compatible to the volume equation was derived from the data of 172 trees sampled in the three plantations of Paraserianthes falcataria in Pare, East Java. The stem taper equation in this study was based on a conventional logarithmic volume equation, with the addition of one free parameter that minimized the standard errors of estimate to the observed diameter of stems at 1.0-m intervals. The derived equation was able to predict the stem taper of P. falcataria reasonably well, while it was not flexible enough to describe delicate changes of the taper in the upper portion of stem. The equation was able to predict bole length and the volume up to the top diameter 20 cm, the diameter size merchantable for sawn timber in Indonesia, with reasonable accuracy. An appropriate rotation age for sawn-timber production was found to be 8–9 years old, at which the mean annual increment of sawn timber would be maximized.