大兴安岭不同区域落叶松相容性材积方程及异方差研究

[目的]对不同区域立木相容性材积方程以及不同异方差校正方法进行详细对比分析,建立相容性材积方程预估大兴安岭不同区域落叶松的立木材积。[方法]以大兴安岭3个不同区域的落叶松为研究对象,采用误差变量联立方程组的方法构建不同区域立木相容性材积方程。采用非线性额外平方和的方法(F检验)进行区域性检验。使用多种权函数分别对3个区域存在异方差的材积方程进行加权回归。[结果]表明:任何2个区域的立木材积方程都有显著不同(P0.000 1),区域1和区域3的材积相差较大,区域2与区域1和区域3的材积相差较小。不同区域立木材积方程的错误应用会导致较大的预测误差。在参数稳定性和评价指标方面,加权估计会优于普通最小二乘估计。基于平均相对误差(MRE)和总相对误差(TRE),区域1(-0.11、0.97)、区域2(0.04、0.08)和区域3(1.04、0.93)的最优权函数分别为1/F(x)、1/D4.99、1/D3.38。[结论]立木材积方程是森林调查和林分生长与收获模型的主要组成部分,本文所构建3个区域的相容联立方程组模型预测误差均不超过±3%。建立相容性立木材积方程时应考虑其异方差的影响。最优权函数没有统一的形式。为尽可能得到稳定的参数估计,在加权回归估计过程中应选用多种权函数进行对比分析。     

Juvenile diameter distributions of loblolly pine characterized by the two-parameter Weibull function

Diameter distributions of juvenile loblolly pine (Pinus taeda L.) were characterized utilizing a two-parameter Weibull distribution to aid in forecasting and simulation of young stands. Juvenile diameter distributions were studied to gain insight into the effects of various stand-level factors. Results show that diameter distributions in juvenile loblolly pine stands can be successfully characterized with the two-parameter Weibull function. Repeated measures analysis detected significant planting density, age, and age by planting density interaction effects for the scale and shape parameter estimates from the two-parameter Weibull distribution. Using parameter recovery techniques, estimated diameter distributions were derived from easily attainable stand-level characteristics (i.e. basal area per hectare, planting density, age, and quadratic mean diameter). A thorough understanding of juvenile diameter distributions should prove especially useful for operational planning of stands on short rotations that require estimates of productivity at early ages.     

Localization of growth estimates using non-parametric imputation methods

The purpose of this study was to examine different non-parametric imputation methods to reduce regional biases in growth estimates. Growth estimates were obtained using non-parametric k-nearest neighbour imputation (k-NN) to predict future 5-year diameter increment over bark at breast height for Scots pine (Pinus sylvestris L.) and Norway spruce (Picea abies). The Mahalanobis distance function was chosen as the most suitable measure of similarity, and then it was modified using weights provided by linear regression analysis. The use of weights from linear regression facilitated the examination of the correlation structure of the variables and allowed for transformations of the independent variables. Localization of the non-parametric estimates was obtained through a variety of methods, in particular, by using spatial coordinates as independent variables, by restricting the selection of neighbours to a circular area around the target tree, and by restriction the selection of neighbours to a local database. The localized estimates using spatial measures were then compared with non-spatial imputation and also with estimates from a parametric growth model. Results were then compared by vegetation zones in Finland. The differences between the non-spatial k-NN estimates and the localized spatial estimates were negligible when summarized to the stand level, and localization did not reduce the regional biases relative to the non-spatial k-NN estimates. Regional biases in northern Finland and in south-western Finland were reduced substantially using the non-parametric estimates rather than the parametric growth models, however, and the mean biases in all of the regions were quite similar, while the mean biases of the growth estimates obtained with the parametric model varied notably between the regions.     

Individual-tree diameter growth models for black spruce and jack pine plantations in northern Ontario

Individual-tree distance independent diameter growth models were developed for black spruce and jack pine plantations. Data used in this study came via stem analysis on 1170 black spruce (Picea mariana [Mill.] B.S.P.) and 800 jack pine (Pinus banksiana Lamb.) trees sampled from 75 stands of 25 even-aged monospecific plantations for each species in the Canadian boreal forest region of northern Ontario. Of the 75 stands, 50 were randomly selected for each species and all trees from these stands were used for model development. Trees from the remaining stands were used for model evaluation.A nonlinear mixed-effects approach was applied in fitting the diameter growth models. The predictive accuracy of the models was improved by including random effects coefficients. Four selection criteria - random, dominant or codominant, tree size close to quadratic mean diameter, and small sized - were evaluated for accuracy in predicting random effects for a new stand using the developed models. Random effects predicted based on trees selected using the random selection criterion provided more accurate diameter predictions than those using trees obtained via other selection criteria for both species. The models developed here are very important to forest managers as the diameters predicted by these models or, their stand-level summaries (i.e., basal area, average diameter), are used as inputs in any forest growth and yield models. In addition, individual-tree diameter growth models can be used to directly forecast changes in diameter distribution of stands.     

Adapting a growth equation to model tree regeneration in mountain forests

Management and risk analysis of protection forests depend on a reliable estimation of regeneration processes and tree growth under different site conditions. While the growth of forest stands and thus the average growth of larger trees is well studied and published in yield tables as well as embodied in numerous simulation models, there is still a lack of information about the crucial initial stages of tree growth. Thus, we evaluated juvenile tree growth for different site conditions in the Swiss Alps and developed an approach to model both the early and later stages of growth based on the Bertalanffy equation. This equation is physiologically well founded and requires only two parameter estimates: a maximum tree height and a growth parameter. Data for the parameter estimation were available from studies of tree regeneration at a range of sites in Switzerland: growth patterns of larch (Larix decidua) were available from a high-elevation afforestation experiment. For spruce (Picea abies), data were obtained from a blowdown area in the Alps. The growth equation was fitted to the observed data and we found a good correlation of the fitted curves with the observed data. The parameter estimates were validated with independent data sets. The extrapolated growth curves, calculated with the estimated growth rates, correspond well to the validation data. Thus, it is possible to use the Bertalanffy equation to model both the early and later stages of growth. With this approach, we provide a basis for modelling the growth of juvenile and mature trees of different tree species in mountain forests of the European Alps.     

Comparison of treewise and standwise forest simulators by means of quantile regression

Predicting forest development under varying treatment schedules forms the basis of forest management planning. The actual growth predictions are made with a forest simulator which includes growth equations and additional models for predicting a number of varying tree, forest and site properties. Forest growth simulators typically include either tree-level or stand-level growth models, but these two approaches have not been thoroughly compared. We set out here to compare these two approaches with the SIMO simulator framework in a small data set from southern Finland based on 60 sample plots in 30 stands, the development of which was known for 20 years. The stands chosen were very dense, so that the simulators could be tested under extreme conditions. The results show that the stand-level model is more accurate in almost all cases and its computational burden is much lower. It could therefore be advisable to use tree-level models for short-term predictions, which would ensure detailed information on forest structure for planning the near-future operations. Stand-level models would be more advisable in longer term predictions, especially when accurate volume estimates are considered more important than the forest structure. The errors observed in these simulators were analysed further by quantile regression, which allows empirical estimates of confidence intervals to be obtained for the simulator.     

Influence of canopy structure on the survival and growth of underplanted seedlings

This study explores the indirect relationship between forest structural measures and initial seedling survival and growth along a structural gradient between 64% to 92% canopy closure. The gradient was created by applying various levels of midstory removal to fifty 0.05 ha areas located within a mixed-hardwood riparian forest corridor. Twelve yellow-poplar (Liriodendron tulipifera L.) and cherrybark oak (Quercus pagoda Raf.) containerized seedling pairs were underplanted within each area. Canopy closure was estimated using hemispherical photography; height-to-canopy and basal area were recorded at each seedling pair. Survival, basal diameter, and height were monitored through two growing seasons. Species-specific mortality and height growth models were developed for one and two growing seasons following underplanting. The interaction of height-to-canopy and basal area along with canopy closure were found to be the most strongly related to mortality. Height to the forest canopy and initial seedling size explained the most variance in height increment. Although the height increment models possess limited predictive power (R² range from 0.22 to 0.36), both mortality and growth analyses emphasize the importance of quantifying vertical canopy structure, along with the more commonly considered horizontal measures of forest structure (basal area and stem density), when evaluating seedling development beneath a forest canopy.     

Modelling mortality of Scots pine (Pinus sylvestris L.) plantations in the northwest of Spain

Mortality is an important element of growth and yield models, especially if only low intensity silvicultural treatments are carried out. The objective of the present study was to develop a model for predicting tree number decline in planted even-aged stands of Scots pine (Pinus sylvestris L.) in Galicia (northwestern Spain). The model was constructed using data from two inventories of a trial network involving 68 permanent plots located in unthinned stands, or stands thinned lightly from below. Two alternatives were tested. In one alternative, a two-step modelling strategy was applied. First, a binary response function predicting the survival probability of all the trees in the stand was constructed, and an equation for reduction in tree number was developed, using only data where death had occurred over the period analyzed. Three different approaches were then used to compare the application of the above-mentioned functions together. In the other alternative, a mortality function for directly predicting the reduction in tree number was fitted, including all plots (with and without occurrence of mortality). Both alternatives provided similar results, showed logical behavior, and performed satisfactorily in evaluation tests. However, in choosing the best strategy for inclusion in a stand-level simulator, the use of the second alternative is recommended because it possesses the path invariance property required in a mortality model.     

Stand-level diameter distribution yield model for black spruce plantations

The objectives of this study were to develop and demonstrate a stand-level diameter distribution yield model and associated algorithm for black spruce (Picea mariana (Mill.) B.S.P) plantations. Employing a parameter prediction approach within the context of a stand density management diagram (SDMD), model development consisted of four sequential steps: (1) obtaining maximum likelihood estimates for the location, scale and shape parameters of the Weibull probability density function (PDF) for 296 empirical diameter frequency distributions; (2) developing and evaluating parameter prediction equations in which the parameter estimates of the Weibull PDF were expressed as functions of stand-level variables employing stepwise regression and seemingly unrelated regression techniques; (3) explicitly incorporating the parameter prediction equations into the SDMD modelling framework; and (4) developing an associated PC-based algorithm and demonstrating its utility in density management decision-making. The results indicated that the parameter prediction equations described 74.4, 87.1 and 66.8% of the variation in location, scale and shape parameter estimates, respectively. Incorporating the parameter prediction equations into the structure of the SDMD enabled the prediction of the temporal dynamics of the diameter frequency distribution by density management regime, site quality and region. An algorithmic version of the model is provided as a decision-support aid in which forest managers are able to simultaneously contrast multiple density management regimes in terms productivity, product value and optimal site occupancy.     

Site quality of pedunculate oak (<Emphasis Type="Italic">Quercus robur</Emphasis> L.) stands in Galicia (northwest Spain)

Accurate estimates of forest productivity are required for sustainable forest management. Height of dominant and codominant trees at a reference age is often used as a measure of site productivity. Eight algebraic difference equations based on the models proposed by Sloboda, Bertalanffy-Richards, Korf, Hossfeld, and McDill-Amateis were tested on the transformed, longitudinal data structure that considers all possible growth intervals. Autocorrelation was modelled by expanding the error term as an autoregressive process according to this data structure. Generalized nonlinear least squares methods were used for model fitting. Several numerical and graphic analyses were used to compare the different candidate models. The relative error in dominant height prediction was used to select 60 years as the best reference age. An algebraic difference equation based on the model proposed by Korf provided the best compromise between biological and statistical aspects and produced the most adequate site index curves. This model is therefore recommended for height growth prediction and site classification of pedunculate oak stands in Galicia. The model is polymorphic and base-age invariant, having only one asymptote. Predictions of height for age intervals between t₁ and t₂ of more than 15 years should be considered with caution because of the associated critical error.     

杉木人工林林分断面积生长模型的贝叶斯法估计

以江西杉木人工林为例,以Korf型、Richards型和Hossfeld型3种模型为基础,通过广义代数差分法(GADA)分别建立杉木林分断面积生长模型。结果表明:以Richards型为基础的杉木林分断面积预测精度最高,以Richards型模型为最优模型,分别基于贝叶斯法和传统法(非线性最小二乘法)估计杉木林分断面积生长模型。研究发现,利用贝叶斯法估计杉木林分断面积生长模型,预测精度相当且预测值的可靠性比传统法好。     

A review of stand basal area growth models

Growth and yield modeling has a long history in forestry. The methods of measuring the growth of stand basal area have evolved from those developed in the U.S.A. and Germany during the last century. Stand basal area modeling has progressed rapidly since the first widely used model was published by the U.S. Forest Service. Over the years, a variety of models have been developed for predicting the growth and yield of uneven/even-aged stands using stand-level approaches. The modeling methodology has not only moved from an empirical approach to a more ecological process-based approach but also accommodated a variety of techniques such as: 1) simultaneous equation methods, 2) difference models, 3) artificial neural network techniques, 4) linear/nonlinear regres-sion models, and 5) matrix models. Empirical models using statistical methods were developed to reproduce accurately and precisely field observations. In contrast, process models have a shorter history, developed originally as research and education tools with the aim of increasing the understanding of cause and effect relationships. Empirical and process models can be married into hybrid mod-els in which the shortcomings of both component approaches can, to some extent, be overcome. Algebraic difference forms of stand basal area models which consist of stand age, stand density and site quality can fully describe stand growth dynamics. This paper reviews the current literature regarding stand basal area models, discusses the basic types of models and their merits and outlines recent progress in modeling growth and dynamics of stand basal area. Future trends involving algebraic difference forms, good fitting variables and model types into stand basal area modeling strategies are discussed.     

兴安落叶松材积模型中的异方差研究

为进一步提高兴安落叶松材积模型估计精度,文章选择V=aDbHc为材积模型形式,对模型的异方差性进行了研究。文章分别使用了图示法及戈德菲尔特-夸检验方法证实模型中存在较强的异方差性,并分别以因变量,自变量及模型本身构造权函数,以加权回归估计和普通非线性回归估计方法结果进行对比分析。研究结果表明:加权回归估计优于普通非线性回归估计;在构造的众多权函数中,以权函数1/D2H为最优;并进一步证实不同的模型有不同的最优权函数形式。     

Detecting trends in diameter growth of Norway spruce on long-term forest research plots using linear mixed-effects models

The objective of the study was to introduce a simultaneous approach to extracting growth trends from diameter increment series by combining tree- and stand-level information in the framework of mixed-effects modeling. The model results are compared with those of the sequential modeling approach according to Yue et al. Can J For Res 41:1577–1589, (2011). Comprehensive data from periodically repeated tree and stand measurements on 113 Norway spruce long-term forest research stands distributed throughout southwestern Germany as well as annually resolved diameter growth data from stem analysis of 581 sample trees are used for model parameterization. Results provide clear evidence for distinct temporal variation due to environment-related effects after accounting for tree- and stand-level effects on diameter growth of Norway spruce over the past 136 years, with especially high growth levels during the last four decades. Most remarkable is the considerable increase in diameter growth rates following the 1947–1952 growth depression. From the early 1960s onwards, growth rates fluctuated on an elevated level until most recent years. Model comparison reveals that results of the sequential and simultaneous modeling approaches are similar with respect to the course of the time-specific environmental effects on growth. We conclude that the proposed simultaneous modeling approach has the advantages of extracting growth trends at a higher level of precision and being the more parsimonious modeling option.     

面向虚拟森林经营管理的树木交互式参数建模方法

从树木构筑概念出发,将传统的几何建模技术与树木形态结构结合,提出了一种交互式参数建模的方法.采用主干、枝条、叶片三类参数来描述和定义树木,约定了一系列的建模规则和参数化调节方法,并构建了一个树类.林业管理者通过输入熟悉的参数平台交互式地构建各种具有不同几何特征的树木,并且能够建立不同生长阶段的三维几何树模型,其模型简单且形态逼真,能够充分地表现树木的空间结构.     

Models for predicting tree and stand development on larch plantations in Hallormsstaður,Iceland

The aim was to model the growth of Siberian larch (Larix sibirica Ledeb.) and Russian larch (Larix sukaczewii Dyl., syn. L. sibirica var. sukaczewii) plantations in Hallormsstaeur, Iceland. The field inventory was carried out in eastern Iceland in June 2006. Models were constructed for predicting dominant height, total tree height and 5-year diameter increment. Several linear and non-linear forms of models were tested in preliminary analyses to find the equations that fitted the modelled characteristics best. Due to the spatially hierarchical correlation structure of the data (stands, plots and trees), the assumption of non-correlated error terms did not hold. Therefore, a random parameter modelling approach was adopted using mixed models when the estimates obtained for the random effects were statistically significant. The variance estimates for the random effects can be further used to calibrate the models. The models generated here performed well with independent test data and were consistent with the forest growth theory. They can be used to evaluate site quality and to estimate the growth and yield of larch stands in eastern Iceland in connection with forest planning.     

基于国家森林资源清查数据的不同生物量和碳储量估计方法的对比分析

[目的]通过对不同生物量和碳储量的估计方法进行对比分析,为确定在国家森林资源清查中生物量和碳储量的具体估计方法提供依据。[方法]以广东省2012年森林资源清查的100个杉木林和80个马尾松林的实测样地资料为基础,利用近年来我国建立的主要树种立木生物量模型,对改进IPCC法、生物量模型法和转换因子连续函数法(即方精云法)3种方法按一元和二元模型共6种方案进行了对比;同时,基于改进IPCC法一元和二元模型的生物量估计值,用平均含碳系数法、组分含碳系数法和固定含碳系数(0.5或0.47)法分别对碳储量进行估计。[结果]用二元生物量模型法得到的杉木林和马尾松林样地的总生物量分别为320 Mg和331 Mg,一元生物量模型法的结果分别相差0.9%和6.2%;改进IPCC法的估计结果,采用二元和一元模型时杉木林分别相差-3.6%和-11.9%,马尾松林分别相差-8.5%和-19.6%;而方精云法的估计结果,采用二元和一元模型时杉木林分别相差6.65倍和6.60倍,马尾松林分别相差-14.3%和-18.0%。平均含碳系数法和组分含碳系数法的碳储量估计结果,杉木林仅相差0.2%,马尾松林相差约0.4%;固定含碳系数法的估计结果因树种而异,对杉木林要低估0.6%5.4%,对马尾松林要低估3.3%9.1%。[结论]对生物量的估计,采用生物量模型法准确性最高,而林木水平的生物量模型其预估精度要高于林分水平的模型;IPCC法是基于材积源的通用方法,将其中的缺省参数改进为可变参数模型,可大大提高方法的适应性;方精云法只是基于IPCC法所建立的林分水平模型在大尺度上的一种具体应用方法,其精度要低于林木水平的生物量模型法,不适于中小尺度应用。对碳储量的估计,采用平均含碳系数法与组分含碳系数法差异很小,但采用固定含碳系数法则误差较大。     

匈牙利刺槐（（Robinia pseudoacacia L.）林的经营研究

匈牙利刺槐（（Robinia pseudoacacia L.)是在17世纪初从北美引入到欧洲的第个森林树种。在匈牙利，刺槐是非常重要的速生树种，为经济和生态目的，可以成功营造刺槐人工林。结合该树种的生长特点选择营林措施，可以最大限度的提高刺槐人工林的成活率和生产力。本文根据林分结构和森林产量长期实验林的研究成果，提出了刺槐林的抚育作业次序。制定好的营林计划和模式将会培育出效益刺槐林，并能使土地经营者更好地接受该树种。同时，刺槐也是一个非常有用的能源生产树种，本文展示了对这方面的研究成果。图2表1参8。     

Growth and nutrient concentration of two native forage legumes inoculated with Rhizobium and Mycorrhiza in Missouri, USA

The Center for Agroforestry at the University of Missouri has tested numerous native legumes for potential use in agroforestry and selected Illinois bundleflower (Desmanthus illinoensis (Michaux) MacMillan ex Robinson and Fern.) and panicled tick clover (Desmodium paniculatum (L.) DC.) for further testing. Our objective was to document the effect of arbuscular mycorrhizae (AM) (Glomus spp.) and Rhizobium on growth and nutrient concentration of these legumes. Seeds were planted in a greenhouse and inoculated with one of two species of AM and/or one of two strains of Rhizobium. Plants were harvested after 80 d and data taken on leaf and stem dry weight, root fresh weight, stem height, nodulation, AM colonization, and N, P, K, Ca, and Mg concentration. Inoculation with Rhizobium did not affect plant growth in Illinois bundleflower, but colonization by Glomus intraradices increased all plant growth variables except stem height. Nutrient concentration was unaffected by the presence of either endophyte. In contrast, inoculation of panicled tick clover with Rhizobium str. 41Z10 increased leaf dry weight (32%) compared to the control and root fresh weight (41%) compared to str. 32Z3, and colonization by G. intraradices increased leaf dry weight (35%) and stem height (26%). Both species of AM increased P and K concentration (41% and 55%, respectively) in panicled tick clover. Our results suggest that the growth of these legumes can be improved by the use of proper AM species and/or Rhizobium strains. However, additional research to identify the best Rhizobium and AM inoculates for these plant species is important in developing strategies for their use in agroforestry. This revised version was published online in June 2006 with corrections to the Cover Date.     

Regeneration growth in different light environments of mixed species, multiaged, mountainous forests of Romania

Growth of regenerating trees in different light environments was studied for the mountainous, mixed-species forests in the Carpathian Mountains of Romania. The primary species in these mixtures were silver fir (Abies alba Mill.), European beech (Fagus sylvatica L.) and Norway spruce (Picea abies (L.) Karst). Seedlings/saplings of these species were selected and measured in different stands from two different geographical locations. Regenerating trees were measured for height and diameter growth during the summer of 2002. For each seedling/sapling, percentage of above canopy light (PACL) and stand basal area (BA) were used to assess available and occupied growing space respectively. Regeneration growth was compared against these two variables and regression relationships were developed. Using these models, we predicted the dynamics of regeneration as both growth and species composition. Our results showed that in low-light environments (PACL<20–35%; BA>30 m²/ha), shade tolerant fir and beech clearly outcompeted the spruce. Therefore, in dense stands, spruce could be eliminated by the shade tolerant species. For intermediate levels of cover (PACL=35–70%; BA=15–35 m²/ha) the spruce grew at comparable rates as the beech and fir. All three species showed similar growth rates in open conditions (PACL>80–90%; BA<15–20 m²/ha) with the spruce having a tendency to outgrow the others. However, in terms of establishment, such conditions favor spruce and inhibit fir and beech.