基于混合模型的落叶松微纤丝角模型

以黑龙江省七台河市林业局金沙林场9株人工落叶松2 790个样品数据为例,选择6个常用方程进行非线性回归分析,把拟合精度最高的修正Logistic模型作为微纤丝角基础模型y=b1/[1+ exp(b2x)]+b3,然后,利用S-PLUS软件中的NLME过程,拟合非线性微纤丝角模型.采用AIC、BIC、对数似然值和似然比检验等模型评价统计指标对不同模型的精度进行比较分析.结果表明:当对微纤丝角-年龄关系进行拟合时,b1,b2,b3同时作为混合参数时模型拟合效果最好.把相关性结构包括复合对称结构(CS)、一阶自回归结构AR(1)、一阶移动平均结构MA(1)及一阶自回归与移动平均结构[ARMA(1,1)]加入到微纤丝角最优混合模型中,一阶自回归与移动平均模型[ ARMA(1,1)]显著提高了微纤丝角混合模型的拟合精度.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.因此,混合模型在应用上不仅能反映总体微纤丝角预测,而且能通过方差协方差结构和误差相关性结构校正随机参数来反映个体微纤丝角差异.     

Modeling Branch Length and Branch Angle with Linear Mixed Effects for Dahurian Larch

In this study,the sample data was based on 2 190 branch length and angle samples of 30 trees from dahurian larch（Larix gmeiinii） plantations located in Wuying Forest Bureau in Heilongjiang Province.The stepwise regression techniques were used to develop branch length and branch angle models:BL= b₁ + b₂ DINC + b₃ DINC² + b₄ DBH·DINC²,BA = b₁ + b₂ DINC + b₃ DINC² + b₄ DBH·DINC.Then,the developed models were fitted using linear mixed-effects modeling approach based on LME procedure of S-PLUS software.Evaluation statistics,such as AIC,BIC, Log Likelihood and Likelihood ratio test were used for model comparisons.The results showed that the branch length and branch angle models with parameters b₁,b₂,b₃ as mixed effects showed the best performance.Exponential and power functions were incorporated into mixed branch length and branch angle model.The addition of the exponential and power functions significantly improved the mixed-effects model.The plots of standardized residuals indicated that the mixed-effect model with exponential and power functions showed more homogeneous residual variance than the mixed-effects model.Validation confirmed that the mixed model with calibration of random parameters could provide more accurate and precise prediction.Therefore,the application of mixed model not only showed the mean trends of branch length and branch angle,but also showed the individual difference based on variance-covariance structure.     

基于非线性混合模型的东北兴安落叶松树高和直径生长模拟

以黑龙江省带岭林业局大青川林场80株人工兴安落叶松解析木数据为例,采用Richards生长模型作为基础模型,利用S-PLUS软件中的NLME过程,分别拟合非线性树高和直径生长模型。采用AIC、BIC、对数似然值和似然比检验等模型评价统计指标对不同模型的精度进行比较分析。结果表明:当对树高-年龄关系进行拟合时,b1、b3同时作为混合参数时模型拟合最好;当对直径-年龄关系进行拟合时,b1、b3同时作为混合参数时模型拟合最好。把相关性结构包括一阶自回归结构AR(1)、一阶移动平均结构MA(1)及一阶自回归与移动平均结构[ARMA(1,1)]加入到树高和直径最优混合模型中,一阶自回归结构AR(1)显著提高了树高混合模型的拟合精度,一阶移动平均结构MA(1)显著提高了直径混合模型的拟合精度。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。因此,混合模型在应用上不但能反映树高和直径的平均预测趋势,还能用方差协方差结构和误差相关性结构校正随机参数来反映个体之间的差异。     

Analysis of Basal Area for Chinese Fir Plantation Using Two Kinds of Nonlinear Mixed Effects Model(Two Levels)

Nonlinear mixed effects model（NLMEM） is based on the relationship between the fixed and random effects in the regression function.The NLMEM has a competitive advantage in analyzing repeated measures data,the longitudinal data and multilevel data.This paper chose two kinds of two-level nonlinear mixed model to analyze basal area growth for Chinese Fir（Cunninghamia lanceolata）. Model 1 is a general two-level NLMEM and Model 2 is based on Model 1 to further consider the fixed effects parameters changes with a specific factor. Firstly,through the analysis of these two models, this paper defined the basic model to build the two-level NLMEM.Secondly,665 kinds of models derived from Model 1 and 2 703 kinds of models derived from Model 2 were calculated and compared. The results showed that:for Model 1,there were 57 kinds of models converging,and when the formal parameter b₀ considered the block effects and plot effects,b₁ and b₄ only considered the block effects, the model fitted the best;and for Model 2,there were 24 kinds of model converging,and when the formal parameter bs considered the block effects and plot effects,b₁ only considered block effects and the fixed effects b₀ changed with any level of block level, Model 2 fitted the best.Finally,by comparing the traditional nonlinear regression model,Model 1 and Model 2,the results showed that Model 1 and Model 2 fitted better than the traditional nonlinear regression, and Model 2 was best fitting model.     

基于线性混合模型的落叶松枝条基径模型

以黑龙江省五营林业局丽林林场30株人工落叶松2 190个枝条基径数据为例,利用逐步回归技术建立了落叶松枝条基径模型:BD=b1+b2DINC+b3DINC2+b4DBH.DINC2。然后,利用S-PLUS软件中的LME过程,拟合线性枝基径模型。采用AIC、BIC、对数似然值和似然比检验等模型评价统计指标对不同模型的拟合效果进行比较分析。结果表明:当拟合枝条基径模型时,b1、b2、b3同时作为混合参数时模型拟合最好。为了矫正混合模型构建过程中产生的异方差现象,把幂函数和指数函数加入到枝条基径混合模型中。指数函数显著提高了枝条基径混合模型的拟合效果,并且消除了异方差现象。模型模拟表明:对于大小相同树木,枝条基径随着着枝深度(DINC)的增加而增大,对于大小不同的树木,枝条基径随着胸径(DBH)的增加而增大。林木的胸径变量很好地反映了不同大小树木的枝条基径的变化。在不知道详细林分信息的前提下,可以利用树木变量合理地预测兴安落叶松人工林的枝条基径的变化规律。     

Modelling primary branch growth based on a multilevel nonlinear mixed‑effects model: a Pinus koraiensis plantation case study in north‑east China

On the basis of a multilevel nonlinear mixed?effects model approach, branch diameter and length growth models were developed for a Pinus koraiensis plantation in north?east China. The models developed were able to better capture the residual variation successfully by partitioning the residual variance into plot?, tree? and branch? level variations via random parameter modeling at the three levels. In addition to random effects, various time series correlation structures were evaluated to account for residual autocorrelation, and the AR(1) and ARMA(1,1) structures were selected for the branch diameter and length growth models, respectively. Model validation results using an independent data set confirmed that multilevel mixed models with an appropriate correlation structure produced more accurate and precise branch?specified diameter and length predictions. Overall, the models were suitable in describing the trends and inherent variability of crown profile and good enough to be included in growth simulation systems for Pinus koraiensis plantations.     

Accounting for serial correlation and its impact on forecasting ability of a fixed- and mixed-effects basal area model: a case study

Successfully accounting for serial correlations has always been a vital part of growth and yield modeling when using repeated measurement data. In this case study, 16 alternative functions addressing the serial correlations of errors from a basal area model of black spruce (Picea mariana (Mill.) B.S.P.) were examined and compared. Results from this study showed that functions incorporated into the fixed and mixed models to account for the serial correlations improved model fit. The serial correlation of the residuals from the fixed model with directly modeled error structure was significantly lower than that from the fixed model without a modeled error structure. For the mixed model, modeling error structure resulted in only a moderate reduction in serial correlation of residuals. The comparison of the fixed and mixed models with and without directly modeling the error structure showed that for fixed model, a substantial improvement in forecasting ability was achieved when the error structure was directly modeled to account for serial correlation, and when the forecasts were adjusted based on the estimated correlation. But for the mixed model, further modeling of the error structure to account for more serial correlation resulted in worsened or comparative forecasting ability of the fitted model.     

杨树微纤丝角的变异及其与木材性质的相关关系

微纤丝角为细胞次生壁S2层微纤丝排列方向与细胞主轴所形成的夹角,与木材的物理性质、力学性质和化学性质都有着直接的关系。应用x射线衍射法测定了7个杨树无性系(14株样木)胸径处各年轮的微纤丝角,并对应分析和测定了各年轮的木材基本密度、纤维长度、纤维宽度和纤维素含量。研究结果表明,杨树微纤丝角在年轮间存在显著差异,其径向变异规律为从髓心向外以微纤丝角逐渐降低,年轮间的平均微纤丝角在7.8旱?8褐洌荒静幕久芏取⑾宋ざ取⑾宋矶群拖宋睾吭谀曷旨湟泊嬖谙灾钜臁O喙胤治霰砻鳎⑾怂拷怯肽静幕久芏取⑾宋ざ取⑾宋矶群拖宋睾看嬖谙灾母合喙毓叵??0.01),相关系数分别为-0.450、-0.586、-0.516和-0.660。回归分析结果表明,多项式方程可较好地描述杨树微纤丝角与所测定的木材性质的关系,相关系数均在-0.45以上(n=125)。本文的研究结果认为,在今后针对杨树材性改良的育种计划中,微纤丝角是一个重要的选育和改良指标。图3表3参34。     

Interpretation of X-ray diffractograms of wood for assessments of microfibril angles in fibre cell walls

Summary Graphical models have been developed to represent X-ray diffraction patterns for microfibril arrangements in each of the characteristic secondary wall layers of fibres in normal earlywood, latewood, compression wood, and tension wood. Models for usual combinations of typical layers S₁, S₂, and S₃, and for complex tissues including more than one S₂ layer class indicate a basis for a new analytical technique for diffractograms.Diffractograms of tissues from earlywood or latewood zones may involve effects of three to four S₂ layer variations, possibly including tension wood or compression wood. The new technique enables assessment of the microfibril angle for each. Corresponding probable experimental errors are considered. Thus it is demonstrated that, even without direct calibration by other methods for measuring microfibril angle, realistic comparative values may be obtained for all S₂ layer classes substantially represented. Such data constitute significantly more reliable indices of actual values than those provided by other techniques. Also, the data give qualitative information on other aspects of the variability of fibre types within each specimen.     

利用非线性混合模型模拟杉木林优势木平均高

介绍国内外利用非线性混合效应模型方法模拟林分优势木平均高的研究进展情况。以江西省大岗山实验局不同初植密度的人工杉木为研究对象,考虑初植密度的随机效应,选择常用的Richards和Logistic形式,通过变换混合效应参数个数来构造优势木平均高和林龄关系的非线性混合效应模型。采用确定系数、均方误差和平均绝对残差等模型评价指标对不同模型的精度进行比较分析。结果表明:无论是Richards形式还是Logistic形式的优势木平均高与林龄关系的非线性混合效应模型,其估计精度比传统的回归模型估计精度明显提高;但是增加随机效应参数个数并不一定绝对提高模型的估计精度,相反估计精度有可能下降。以(4)式为基础的Logistic方程中,3个参数都作为混合模型的模拟精度最高。     

美洲黑杨×青杨F2代基本材性性状遗传变异研究

利用美洲黑杨×青杨杂交三代谱系探索了木材密度、纤维长、纤维宽、纤维长宽比和微纤丝角等性状的遗传变异规律.结果表明基本密度与纤维长受主基因的控制,表现为"质量- 数量性状",其杂种优势明显且在F     

Effect of growing site on the fundamental wood properties of natural hybrid clones of <Emphasis Type="Italic">Acacia</Emphasis> in Vietnam

We investigated clonal and site variations in wood fiber length, microfibril angle, and specific gravity of seven natural hybrid clones of Acacia (Acacia mangium × Acacia auriculiformis) grown in northern and southern Vietnam. Fiber length did not differ between clones or between sites. The microfibril angle of the S₂ layer did not significantly differ between clones but significantly differed between sites. Clone and site significantly affected specific gravity. The significant effects of genetic × environmental interactions on wood properties indicated the difference in the response of clones to different growing conditions. The trends of changes in fiber length, microfibril angle, and specific gravity from the vicinity of the pith to near the bark were similar for all clones at each site; however, variations in fiber length, microfibril angle, and specific gravity were more visible in northern Vietnam than in southern Vietnam, with a significant effect of genetic factors. This difference may be attributable to winter, which is experienced in northern Vietnam but not in southern Vietnam. For clone selection for plantation in the northern region, combining growth rate with wood properties was recommended. On the other hand, for plantation in the southern region, clone selection depends mainly on the growth rate, taking into consideration the specific gravity.     

两水平非线性混合模型对杉木林优势高生长量研究

利用两水平非线性混合模型对杉木(Cunninghamia lanceolata)优势高进行分析。概述了两水平非线性混合模型并简单介绍了该模型的参数估计方法;选用了5种常见的Richards和Logistic 形式模型作为构建混合模型的基础模型,利用建模数据分别对这些基础模型各自衍生出的19种混合模型进行计算及比较,结果表明:这5种基础模型对应的最佳混合模型分别为模型(3-1) 模型(3-5);最后把这些最佳混合模型及传统的回归模型两两进行比较,结果表明:二水平非线性混合模型拟合效果比传统的回归模型拟合效果要好,并且基础模型4对应的二水平混合模型(式3-4)拟合效果最好。     

On the origin of growth stresses in trees

Summary A mechanism for growth stress generation is studied which involves a contractive strain in the microfibril direction and swelling strain in the transverse direction in the developing wall of wood cells. A cylindrically anisotropic elastic model is used to calculate the accumulation of residual stresses in the S₂ wall as it is formed. An explicit relation between the shrinkage/swelling strains in the growth increment of the cell wall and the resulting axial and circumferential stresses induced in the cell is derived. For gymnosperm cells the transition from tensile stress in normal wood cells to compressive stress in compression wood cells is found with increasing microfibril angle.     

Anatomy and lignin distribution of reaction wood in two Magnolia species

Summary Anatomical features of reaction wood formed in two Magnolia species, M. obovata Thunb. and M. kobus DC. which are considered to be among the primitive angiosperms, were observed. In addition, the distribution of guaiacyl and syringyl units of lignins in the cell walls of normal and reaction wood was examined using ultraviolet (UV)- and visible light (VL)- microspectrophotometry coupled with the Wiesner and M?ule reactions. The two Magnolia species formed a tension-like reaction wood without possessing the typical gelatinous layer (G-layer) on the upper side of the inclined stem or branch, in which a radial growth promotion occurred. Compared with the normal wood, the reaction wood had the following anatomical features: (1) the secondary walls of fiber tracheids lacked the S₃ layer, (2) the innermost layer of fiber-tracheid walls showed a small microfibril angle, a fact being similar to the orientation of the microfibril angle of the G-layer in tension wood, and (3) the amounts of lignin decreased in the cell walls of fiber tracheids, especially with great decrease in proportion of guaiacyl units in lignins. In addition, VL-microspectrophotometry coupled with the Wiesner and M?ule reactions adopted in the present study showed potential to estimate the lignin contents in the cell walls and the proportion of guaiacyl and syringyl units in lignins. Received: 15 July 1998     

Variation in wood properties of six natural acacia hybrid clones in northern Vietnam

Wood properties of six 8-year-old natural acacia hybrid clones between Acacia mangium and Acacia auriculiformis, planted in Bavi, Vietnam, were studied. The hybrid clones possessed obvious heterosis in growth and in some wood properties. The characteristics of growth, air-dry specific gravity, lengths of fibers and vessel elements, S₂ microfibril angle, green moisture content, and shrinkage were examined to clarify the variation among clones. From the results, the differences among the clones in growth and in some wood properties were significant. The pattern of distribution of specific gravity showed that there were low and high specific gravity zones in the stem. Specific gravity at stump height or at 3.0 m was useful for prediction of specific gravity in the whole tree stem. Moreover, clones with high specific gravity can be predicted at a young age. There was no significant correlation between diameter growth and specific gravity. Of the six clones studied, clone BV5 was selected as the best based on its growth ability and specific gravity. Part of this report was presented at the 57th Annual Meeting of the Japan Wood Research Society, Hiroshima, August 2007     

黄土高原半干旱区油松人工林枯落物截留雨量模拟研究

为建立合适的枯落物截留雨量预估模型,利用2008-2011年定位观测数据,采用回归分析方法对黄土高原半干旱区油松人工林枯落物对降雨的截留与林外降雨量(P)、林内穿透雨量(TF)之间的关系进行建模研究;运用Bootstrap方法,对模型进行参数特征分析.结果表明:枯落物截留与林内外降雨量均可用非线性模型Ic=aPb进行回归模拟,回归方程分别为Ic=0.499P0.627和Ic=0.717TF0.513.该模型不仅具有较高的拟合精度,且拟合方程参数稳定性良好,经检验方程均达到显著性要求,可用于预估该区域油松人工林的枯落物截留量.     

日本落叶松无性系微纤丝角遗传变异的研究

对10个10年生日本落叶松无性系的早材和晚材微纤丝角进行了测定,结果表明:早、晚材微纤丝角无性系间差异极显著,同一年轮内早材微纤丝角大于晚材.日本落叶松微纤丝角的径向变异规律为:在髓心处最大,以后逐渐减小.早、晚材微纤丝角与树木年轮间的变异模式(径向变异)以对数和乘幂式方程拟合效果较好,R2(R为相关系数)均在0.8以上.早、晚材微纤丝角同树高、形率、树皮厚度、主枝粗、枝干比、主枝夹角、主枝长的相关关系不显著,早、晚材微纤丝角同胸径、冠幅的相关关系达到显著水平;早材与晚材的微纤丝角也相关显著.早材和晚材的微纤丝角受中到强度遗传控制,广义遗传力分别为0.767 4、0.804 3.按照20%的选择率,早材和晚材的微纤丝角的遗传增益分别为21.82%和29.75%.     

Relationship between fibre morphology and shrinkage of wood

Summary This is a study on the shrinkage of wood representing the wide range of morphology variation in leaning trees. It involved 13 trees of Eucalyptus regnans, one of Eucalyptus sieberi and four of Pinus radiata, and specimens taken at close intervals around the circumference of each. Data indicated a systematic modulation, between extremes at upper and lower sides of each stem, in longitudinal growth strains, relative proportions of thin, medium and thick-walled fibres, microfibril angle in the S₂ layer of these, and both Klason and acid-soluble lignin content. Analyses indicated that the microfibril angle in S₂ was a prime factor in influencing both longitudinal and volumetric shrinkage reactions; proportion of thick-walled fibres in the tissue, thickness of S₂ relative to S₁, and variations in lignification also were involved. Unusually thick-walled fibres were associated with visco-elastic strain recovery effects, which could form a substantial part of dimensional changes apparently attributable to shrinkage.Relevant to 10 of the E. regnans trees in this study, appreciation is expressed to three colleagues for providing access to the detailed data on strain, cell wall thickness, and volumetric shrinkage involved in their published study [Nicholson, J. E., Hillis, W. E., and Ditchburne, N. 1975]. By prior arrangement to minimize duplication of effort, their data were derived from specimens from those trees that were involved in this study.     

Genetic correlations among juvenile wood quality and growth traits and implications for selection strategy in Pinus radiata D. Don

? Juvenile wood quality in Pinus radiata is affected by factors such as low density, stiffness, and high microfibril angle, spiral grain, and shrinkage. Adverse genetic correlations between growth and wood quality traits remain as one of the main constraints in radiata pine advanced generation selection breeding program.

? Juvenile wood property data for this study were available from two progeny tests aged 7 and 6 y. We estimated the genetic correlations between stiffness, density, microfibril angle, spiral grain, shrinkage in the juvenile core and DBH growth in radiata pine, and) to evaluated various selection scenarios to deal with multiple objective traits.

? Negative genetic correlations were found for modulus of elasticity (MoE) and density with microfibril angle, spiral grain, shrinkage, and DBH. We observed low to moderate unfavourable genetic correlations between all wood quality traits and DBH growth.

? These low to moderate genetic correlations suggest that there may be some genotypes which have high DBH growth performance while also having high wood stiffness and density, and that the adverse correlation between DBH and MoE may not entirely prohibit the improvement of both traits. Results indicate that, in the short term, the optimal strategy is index selection using economic weights for breeding objective traits (MAI and stiffness) in radiata pine.

? In the long-term, simultaneously purging of the adverse genetic correlation and optimizing index selection may be the best selection strategy in multiple-trait selection breeding programs with adverse genetic correlations.