广义的Chapman-Richards函数及其在树木和林分生长中的应用

The generalized Chapman-Richards model was derived from the Chapman-Richards function in which parameters η,κ and m were unconstrained.Based on the structure of solutions and biological interpretations,the model could be classified into eight cases(three categories)at all and among them only 4 kinds of cases are suitable in forestry that represent four typical growth patterns of trees and stands.For each of 4 equations,the model properties and biological interpretations for parameters were discussed in detail.The generalized chapman-Richards model was capable of describing a wide range of growth curves that was asymptotic or nonasymptotic,with or without inflection point.In order to illustrate the versatility of the model,it was fitted to a group of data sets conceming the DBH growth of cryptomeria plantations with 4 initial densities and the DBH and height growth of natural Korean pine tree.Comparing the generalized Chapman-Richards function and the Sohnute model,it was found that the parameters and expressions of the two modets were interchangeable in theory,and the fitting results were explicitly identical in empirical applications.     

Growth models and site index table of natural Korean pine forests

IntroductionKoreanpine(PinuskOraiensisSieb.etZucc.)isoneofthemostimportanttimberspeciesanditisnaturaIIydistributedinHeilongjiang,JiIinandLiaon-ingprovincesinChina.ManyforestryresearchersmadeextensiveandprofoundstudiesonthisspeciesJiangYiyin(1985)studiedthegroWthandgrowthmodelsforpIantationsofKoreanpine.However,veryfewpaperswerefoundonthegroWthmodeIsofnaturalKoreanpineforest.Koreanpinehasa1onggroWthperiod.ForextensivelymanagingKoreanpineforest,itneedstheJorestrytabIeswithhighac-Curacy…     

Development of site index curves for Pinus kesiya in the Philippines

This study was conducted to develop a height–age growth model and site index curves for site quality evaluation of old secondary-growth stands of Pinus kesiya in the northern Philippines. The Chapman-Richards growth function was used in the guide curve method to generate anamorphic site index curves for this species. In order to evaluate the developed model, coefficient of determination (R ² ), root mean square error (RMSE), bias (ē), absolute mean difference (AMD) and mean percent bias (MPB) were used as statistical criteria. The Chapman-Richards model explained about 96.84% of the total variation of the dominant height. The value of ē was ?0.004 m, AMD was 2.566 m, MPB was 3.88% and RMSE was 3.331. The site index curves developed as a result of this study are significant for forest managers in predicting the growth patterns and classification of site productivities for Pinus kesiya stands.     

Genetic variation in height growth curves observed in three clonal tests of sugi (Cryptomeria japonica D. Don) in Kyushu

Genetic variation in the height growth curves was investigated by analyzing data from three clonal trials of sugi (Crytomeria japonica D. Don) in Kyushu. Average height of twelve clones measured at each of five years until 30 years of age were fitted to the Chapman-Richards function with two parameters model. Clonal variation in the two parameters (an upper asymptote and a rate of growth parameter) was statistically significant across the tests, indicating that height growth pattern is under genetic control. The type of growth curve was clearly classified with the two parameters and agreed with the empirical classifications of the growth habit of local varieties. The rate of growth parameter was correlated with total height up to 20 years of age, while the upper asymptote was correlated only with the last ten years’ increment from 21 to 30 years where the clonal repeatability was decreasing. This indicates that a clonal selection for long rotation management system would not be reliable unless the height is measured accurately with more advanced devices or it is adjusted by the current increment of diameter.     

THE CONSTRUCTION OF SOME FORESTRY TABLES FOR DAHURIAN LARCH PLANTATIONS

Plantationsofdahurianlarch(LarixgmeIini(Rupr)Rupr.)haveestablishbdandhavebecomeanimportanttimberspeciesintheforestreserveresourcesinthenortheastofChina.Soformingtheforesttableswhichhavehighprecisionformakinglogicalmanagementdecisionsha$beenimportantproblemstobesolvedquicklyinforestrypractice.Uptonow,thereisalackofsystematicforestrytablesfordahurianlarchplantations.Themainpurposeofthispaperistotrytoconstructaseriesofsomeforestrytablesfordahurianlarchplantations.MATERIALSANDMETHODSData…     

Secondary Nothofagus dombeyi forests: site index curves and dominant height in the Coastal Range of south-central Chile

Nothofagus dombeyi is distributed on very diverse sites in the temperate forests of Chile and Argentina. In Chile, studies on its dynamics and productivity in forests, where it is the dominant species, have been carried out mainly in the foothills of the Andes, but the productivity and growth of these forests in the Coastal Range are almost unknown. The objective of this study was to evaluate the construction of a single dominant height/age growth model for two homogeneous edaphoclimatic zones (ZEH 2 and 5) previously defined for this species in the Coastal Range of south­central Chile. The results showed that the Chapman-Richards model was the best candidate function, in terms of goodness of fit and predictive capabilities. Using this function, specific parameters (a, b and c) were obtained for each zone, from which site models were constructed by the Algebraic Difference Approach method for a base age of 35 years. This model is intended to contribute to better estimations of site productivity for N. dombeyi forests in the Coastal Range of south-central Chile, and thus facilitate private and public decisions regarding their management.     

直径生长潜力模型的研究

文章运用理查德生长曲线构成的遵守加法组合和乘法组合的非线性模型，对日本落叶松等3个树种进行了立地质量评价的尝试。结果表明，在森林立地质量评价的诸多方法之中，直径生长潜力仍然不失为一种应用简便和行之有效的方法。     

Financial performance of using genetically improved regeneration material of Scots pine (<Emphasis Type="Italic">Pinus sylvestris</Emphasis> L.) in Finland

The financial viability of using improved seed material of Scots pine was assessed in Finnish conditions. Based on a few dozen field trials, a range of genetic gains for height growth was incorporated into a stand simulator. Technically genetic gain was modelled into individual growth models by applying the Chapman-Richards type function and using genetic gain estimates as asymptotic scaling parameters. Stand projections, including the effect of genetic gain, were further converted into monetary terms by calculating bare land values, i.e. BLVs according to the Faustman rotation model. Following this, the financial attractiveness of using improved seed material from Scots pine was determined by comparing the BLVs between stands with and without genetic gain. The study focused on the private forest owner’s point of view, reflecting the primary demand conditions for improved seed material. Comparisons between BLVs indicated that using improved seed material of Scots pine would be financially viable for private forest owners in most parts of Finland, the discount rate being 3%. The main results were robust, with pertinent changes in silvicultural costs and stumpage prices. This study demonstrates the need for financial analysis in decision-making in the context of regeneration material.     

吉林蛟河针阔混交林主要树种树高-胸径模型

[目的]建立吉林蛟河针阔混交林主要树种不同竞争强度个体的树高-胸径关系模型,并探讨竞争强度对树高-胸径关系的影响。[方法]采用蛟河42 hm2成熟林固定样地中4个树种的树高-胸径数据,用Chapman-Richards、Logistic、Korf和Weibull模型这4种应用广泛的经验模型进行树高-胸径曲线拟合,选出适合的最佳模型。[结果]表明:(1)4个树种的12组个体中有7个组的最佳模型形式是Weibull模型,4个组的最佳模型形式为Chapman-Richards模型,只有1组为Korf模型。(2)同一树种的低竞争强度个体和高竞争强度个体的最优模型形式不同。(3)用独立样本数据对最优模型进行检验,模型表现良好。[结论]Weibull模型能够很好地拟合4个树种各竞争强度的树高-胸径关系,能够适用于本地区针阔混交林的树高-胸径模拟,并且竞争强度会影响树高-胸径关系,将各竞争强度个体分别进行树高-胸径拟合可以提高模型预测能力。     

Das Wachstum von Pinus pinaster (Aiton) in Abhängigkeit vom Standraum

Summary Spacing trials were established inPinus pinaster, in plantations in the Southern and South-Western Cape Province in South Africa. Eight spacings, with nominal initial stem numbers between 125 and 3000 were tested in each of the two trials, with a single replicate in each experiment. The Chapman-Richards growth model was applied to mean diameter, mean height and basal area/ha. For diameter and height, the assumption m=0 holds true, but for basal area/ha, this parameter is related to initial stem number. The volume growth of each sample plot was estimated from equations with basal area and mean height and their interaction as predictor-variables. The regression model also included constraints for basal area and height, to prevent anomalies for the estimated volume per hectare at young age. Each of the trials contained a number of plots, thinned after the onset of competition. The growth rates in these plots was statistically significantly greater than that of the same stand density in the unthinned plots.      

A test of the accuracy of two individual tree growth functions for Picea abies

The accuracy of two distant‐independent diameter growth functions for individual trees of Picea abies L. (Karst.) are tested on plots older than 55 years b.h., and with relatively few trees per hectare. Both functions (I1 and I2) have site index, stand basal area, and individual tree basal area as explanatory variables; in addition age at breast height is used in Function I1. Relative to mean measured increment, Functions I1 and I2 underestimate the growth of the test plots by 4.4% and 10.9% respectively; Function I1 shows a root mean squared deviation of 29.2% for single plot predictions, and 5.4% for mean of all plots. Function II predicts the growth as well as some stand functions frequently in use in Norway. Function I2 is unacceptable because age is not an independent variable.     

Application of the logistic, gompertz, and richards growth functions to gentan probability analysis

In a previous paper, a stochastic model complying with a state-dependent growth rate function was proposed for Gentan probability estimation. The growth function applied was the so-called Mitscherlich type of growth function. In this paper, application of other growth functions,i.e., the logistic, Gompertz and Richards growth functions, is addressed. Assuming growth dynamics as a function of time and state, an alternative stochastic model is derived with the above three growth dynamics. In the proposed model, the time is assumed to be continuous and the state to be discrete. Like in the previous paper, the sum of the Gentan probabilities derived from the proposed model with three growth functions over time is proved to be always unity. This is because the state-dependent part of the growth dynamics is a linear function of the state, which is the same as in the Mitscherlich growth function. This leads to the binomial probability law for a stochastic process, satisfying the unity requirement of the sum of the Gentan probabilities. This research was supported by a Grant-in-Aid for Scientific Research (No.11660155) from the Ministry of Education, Culture, Science, Sports, and Technology of Japan.     

雷州半岛不同桉树品系树冠生长预测模型研究

应用阶跃函数模型,对雷州半岛4个不同桉树品系人工林的冠幅生长与树龄关系进行了回归分析与研究,并对不同品系桉树人工林冠幅生长的阶跃模型方程进行了比较分析。结果表明,阶跃函数模型在桉树林分树冠生长过程中的应用效果良好,巨尾桉无性系ECl的树冠生长遵循指数生长的阶跃模型,尾叶桉无性系U6的树冠生长遵循一元幂生长的阶跃模型,尾叶桉实生林与刚果12号桉无性系W5的树冠生长遵循严格苏玛克生长的阶跃模型。利用已建立的阶跃函数模型可以有效地预测不同桉树品系人工林树冠生长动态,为桉树人工林的合理经营提供科学依据。     

基于VAR模型的森林生态系统适应性管理与经济发展动态关联分析———以黑龙江省大小兴安岭森林生态功能区为例

将衡量森林生态功能区森林生态系统适应性管理效果的指标分解为气候调节、生态保持、产品供给、休闲服务4项,通过主成分分析计算得到各个指标的重要性; 利用VAR模型分析黑龙江省大小兴安岭森林生态系统适应性管理与经济发展的相互影响; 根据脉冲响应函数分析得到森林生态系统适应性管理与经济发展之间的动态关联关系,据此给出若干提高森林生态系统服务水平和促进经济发展的对策和建议。     

An empirical cohort model for management of Terra Firme forests in the Brazilian Amazon

A model to project forest growth in the Terra Firme forests of the eastern Amazon is described. It is based on 12–17 years measurements from experimental plots at Jarí and Tapajós. Forest stands are represented by cohorts of species group, diameter, and defect. There are 54 species groups, with a robust diameter increment function fitted to each, tables of mortality by crown and defect status, and recruit lists by disturbance level and locality. Stand level functions partition trees by crown status, and modify growth for stand density. Recruitment is a function of basal-area losses. Evaluation compares model performance with two experiments involving heavy felling in Tapajos State Forest. At one site, total bole volume growth of all species over 45 cm DBH was 2.56 m³ ha⁻¹ year⁻¹ over 17 years, whereas the model projected 3.13 m³ ha⁻¹ year⁻¹. At the other site, actual growth over 12 years was 0.39 m³ ha⁻¹ year⁻¹, with the model giving an identical result. Both felled and control plots are compared in the study and accurately simulated. Some weaknesses in the model are discussed.     

价值工程在空调设计方案选择中的应用

价值工程用于多方案选择时,能全面、客观地分析产品的功能与成本的关系,分析结果直接、可靠,具有较强的说服力。空调系统不同的方案,都有其各自的特点。本文提出运用价值工程的方法对4种空调冷热源组合方案进行技术经济的全面比较,以确定最满意方案。价值工程在工程应用过程中,运用功能评价系数来描述,因此产品的功能定义应力求准确,成本分析应着眼于产品的全寿命周期成本。     

Comparison of stand structure and growth between artificial and natural forests of Pinus sylvestiris var, mongolica on sandy land

Mongolian pine (Pinus sylvestiris Linnaeus var. mongolica Litvinov) as a valuable conifer tree species has been broadly introduced to the sandy land areas in “Three North” regions (North, northwest and northeast of China), but many prob-lems occurred in the earliest Mongolian pine plantations in 7hanggutai, 7hangwu County, Liaoning Province (ZZL). In order to clarify the reason, comprehensive investigations were carried out on differences in structure characteristics, growth processes and ecological factors between artificial stands (the first plantation established in ZZL in 1950s) and natural stands (the origin forests of the tree species in Honghuaerji, Inner Mongolia) on sandy land. The results showed that variation of diameter-class distributions in artificial stands and natural stands could be described by Weibull and Normal distribution models, respectively.Chapman-Richards growth model was employed to reconstruct the growth process of Mongolian pine based on the data from field investigation and stem analysis. The ages of maximum of relative growth rate and average growth rate of DBH, height, and volume of planted trees were 11,22 years, 8, 15 years and 35, 59 years earlier than those of natural stand trees, respectively. In respect of the incremental acceleration of volume, the artificial and natural stands reached their maximum values at 14 years and 33 years respectively. The quantitative maturity ages of artificial stands and natural stands were 43 years and 102 years respectively. It was concluded that the life span of the Mongolian pine trees in natural stands was about 60 years longer than those in artificial stands. The differences mentioned above between artificial and natural Mongolian pine forests on sandy land were partially attributed to the drastic variations of ecological conditions such as latitude, temperature, precipitation, evaporation and height above sea level. Human beings‘‘ disturbances and higher density in plantation forest may be ascribed as additional reasons. Those results may be potentially useful for the management and afforestation of Mongolian pine plantations on sandy land in arid and semi-arid areas.     

森林生长模型库系统的研究与设计

通过对现有森林生长模型的系统分析,提出通过设计构建一个森林生长模型库系统,以实现对其生长模型进行分类管理和维护,支持模型的生成、存储、查询、运行和分析应用。据此阐述了森林生长模型库系统的设计思想,模型库系统的总体框架和基本功能结构,并对模型库系统可以实现的功能,进行了初步的分析。     

Finding the appropriate level of complexity for a simulation model: An example with a forest growth model

The topic of model complexity is fundamental to model developers and model users. In this study, we investigate how over- and under-fitting of a driving function in a simulation model influences the predictive ability of the model. Secondly, we investigate whether model selection approaches succeed in selecting driving functions with the best predictive ability. We address these issues through an example with the forest simulator SORTIE-ND. Utilizing maximum likelihood methods and individual tree growth data we parameterize five growth functions of increasing complexity. We then incorporate each growth function into the simulation model SORTIE-ND and test predicted growth against independent data. Compared to the independent data, the simplest and the most complex growth functions had the poorest predictive ability while functions of intermediate complexity had the best predictive ability. The poor predictive ability of the simplest model is caused by poor approximation of the system while the poor predictive ability of the most complex model is caused by biased parameter estimates. A growth function of intermediate complexity was the most parsimonious model where error due to approximation and error due to estimation were simultaneously minimized. The model selection criteria AIC and BIC were found to select complex functions that were over-fitted according to the independent data comparison. BIC was closer to choosing the model that minimized prediction error than AIC. In this example, BIC is the more appropriate model selection criterion. It is important that both model developers and models users remember that more complex models do not always result in better predictive models.