东北过伐林区主要森林类型林分蓄积量生长模型

以吉林省汪清林业局金沟岭林场的主要森林类型为对象,基于小班调查数据,利用R ichards、Logistic、单分子、Gompertz和Korf 5种理论生长方程,建立了林分蓄积量生长模型,采用模型拟合统计量、误差及残差分布对模型进行评价和检验。结果表明:白桦林、人工混交林、天然针阔混交林用R ichards模型最好,人工落叶松林、阔叶混交林、天然针叶混交林用Logistic模型最好。研究结果为该地区森林生长预测和经营优化提供了参考和依据。     

辽宁冰砬山地区蒙古栎生长过程研究

在辽宁冰砬山地区不同立地条件的蒙古栎林分中设置5块样地进行各项因子调查,在每个样地内伐取1株蒙古栎平均木进行树干解析,解析木年龄为50～63 a,树干解析数据表明:胸径连年生长量高峰值出现在15 a,平均生长量高峰值出现在20 a;树高连年生长量高峰值出现在15 a,平均生长量高峰值出现在15～20 a;材积连年生长量和平均生长量在35 a前增长较快,45 a后有所减缓,从生长量变化趋势来看,数量成熟龄应在60 a左右。选用5个生长模型对胸径、树高、材积的总生长过程进行了拟合,结果表明Richards曲线拟合效果最好,可以用其作为胸径、树高、材积的生长预估模型。     

云南松优势木胸径生长模型研究

以云南省金沙江流域永仁县的云南松天然次生林优势木胸径为研究对象,选择Logistics、Gompertz、Richards、Korf、Levakovic、严格苏马克和Hossfld模型对其进行拟合.通过对总相对误差、平均相对误差、平均相对误差绝对值和预估精度的分析,从中选出最优生长模型.研究结果显示,这些生长模型对云南松天然次生林优势木胸径生长拟合的精度基本相近.最优生长模型为Gompertz模型.     

Evaluation of unconstrained and constrained mathematical functions to model girth growth of rubber trees (Hevea brasiliensis) using young age measurements

No attempt has been made to date to model growth in girth of rubber tree (Hevea brasiliansis). We evaluated the few widely used growth functions to identify the most parsimonious and biologically reasonable model for describing the girth growth of young rubber trees based on an incomplete set of young age measurements. Monthly data for girth of immature trees (age 2 to 12 years) from two locations were subjected to modelling. Reparameterized, unconstrained and constrained growth functions of Richards (RM), Gompertz (GM) and the monomolecular model (MM) were fitted to data. Duration of growth was the constraint introduced. In the first stage, we attempted a population average (PA) model to capture the trend in growth. The best PA model wasfitted as a subject specific (SS) model. We used appropriate error variance-covariance structure to account for correlation due to repeated measurements over time. Unconstrained functions underestimated the asymptotic maximum that did not reflect the carrying capacity of the locations. Underestimations were attributed to the partial set of measurements made during the early growth phase of the trees. MM proved superior to RM and GM. In the random coefficient models, both Gf and G0 appeared to be influenced by tree level effects. Inclusion of diagonal definite positive matrix removed the correlation between random effects.The results were similar at both locations. In the overall assessment MM appeared as the candidate model for studying the girth-age relationships in Hevea trees. Based on the fitted model we conclude that, in Hevea trees, growth rate is maintained at maximum value at t0, then decreases until the final state at dG/dt ≥ 0, resulting in yield curve with no period of accelerating growth. One physiological explanation is that photosynthetic activity in Hevea trees decreases as girth increases and constructive metabolism is larger than destructive metabolism.     

遗传算法对5种理论生长方程的最优拟合研究

利用北美林肯小区黄杉6个分期的数据,选择Logistic、Richards、Korf、Gompertz和Mitscherlich 5种生长方程建立胸径随年龄变化的生长模型.分别利用遗传算法和传统拟合方法确定参数,并对拟合效果进行对比分析.研究结果显示：遗传算法对于Richards和Korf方程的拟合精度要明显高于传统拟合方法,对于Logistic、Gompertz以及Mitscherlich方程的拟合精度几乎一致.通过将检验数据带入由遗传算法拟合的方程中,除拟合后不符合生物学意义的Korf方程外,发现由剩下4种方程计算得到的预测值与实际值无明显差异（P值均大于0.05）.最终表明遗传算法对生长方程的最优拟合较传统拟合方法更有优势.     

一个具有统计稳定参数的综合生长量模型

一、问题的提出在森林资源数据实行计算机管理以后,小班资源数据的更新和预测工作已变得越来越重要。对于有直接经营活动的小班,资源数据的改变可以由键盘输入等方式来解决,但对于大量的没有直接经营活动的小班的数据更新,采用全面清查的办法显然是不可能的,这只有借助于模型处理加以解决。模型的好坏,也即模型对数据的适合程度,将直接影响更新数据的准确性。已经使用的生长量模型有很多,如理查德、龚帕茨、逻辑斯蒂生长量模型,等等。对于     

Diameter and height growth curves for widely-spaced trees in European agroforestry

Predicting timber volume can be important for decision- making. Conventional forest growth models are generally based on mensuration data acquired in fully stocked homogeneous tree stands, and do not consider the wide spacings often adopted in European agroforestry. In order to test the possibility of adapting conventional forestry growth models, diameter and height growth were measured on widely spaced trees. Parameters of a Gompertz double exponential function were adjusted for several tree species planted at wide spacings. Spacing, vegetation control, and individual tree shelters affected the parameters. At wide spacings, the asymptote for diameter growth was larger, and the asymptote for height growth smaller, compared to conventional forestry. This revised version was published online in June 2006 with corrections to the Cover Date.     

Modelling dominant height growth from national forest inventory individual tree data with short time series and large age errors

We developed dominant height growth models for Norway spruce (Picea abies (L.) Karst.) and Scots pine (Pinus sylvestris L.) in Norway using national forest inventory (NFI) data. The data were collected for a different purpose which potentially causes problems for dominant height growth modelling due to short time series and large age errors. We used the generalized algebraic difference approach and fitted 15 different models using nested regression techniques. Despite the potential problems of NFI data the models fitted to these data were unbiased for most of the age and site index range covered by the NFI data when tested against independent data from long-term experiments (LTE). Biased predictions for young stands and better site indices that are better represented in the LTE data, led us to fit models to a combined data set for unbiased predictions across the total data range. The models fitted to the combined data that were unbiased with little residual variation when tested against an independent data set based on stem analysis of 73 sample trees from southeastern Norway. No indications of regional differences in dominant height growth across Norway were detected. We tested whether the better growing conditions during the short time series (22 years) of the NFI data had affected our dominant height growth models relative to long-term growing conditions, but found only minor bias. The combination with LTE data that have been collected during a longer period (91 years) reduced this potential bias. The dominant height growth models presented here can be used as potential height growth models in individual tree-based forest growth models or as site index models.     

红松高生长模型的研究(英文)

高生长模型是定量研究树木生长过程的有效途径,本文应用双曲线方程、Logistic方程、三个参数的Richards方程及四个参数的Richards方程对红松的高生长进行了研究。结果表明四个参数的Richards方程在模拟红松高生长时最为合适,且当其参数取不同的数值时,该方程可转化为其它理论方程。在使用四个参数的Richards方程时,可根据立地条件事先给定树高最大值,这样可使模型更符合实际情况。此外,文中还对一种以固定年龄时实际树高为参数值的模型进行了讨论,该模型对于计算给定树木的高生长将更为有效。     

内蒙古大青山华北落叶松人工林生长模型研究

利用内蒙古大青山32株华北落叶松解析木数据,分析研究华北落叶松人工林的树高、胸径、年龄、材积之间的关系,并选取对数模型、理查德模型、考尔夫方程和逻辑斯蒂方程等4个常用的生长模型对树高、胸径、材积生长量进行拟合.结果表明：效果好的生长模型分别为胸径对数模型y=-24.03＋ 11.28×Log（x＋1.99）,树高理查德模型Y=27.27×[1-Exp（-0.041 ×x）]△1 5735,材积理查德模型y=7495.55×[1-Exp（-0.001×x）]△3.13.经F检验（F ＜0.05） =6.94,呈显著.3个预测模型的标准误差、平均百分误差、平均绝对百分误差都非常小,平均相对误差均在±2.5％以内,预测值与实测值无显著差异（p=0.05）.     

长白山杨桦次生林生长过程与演替动向分析

以长白山金沟岭林场的杨桦次生林为研究对象,根据山杨、白桦解析木资料,利用Richards方程拟合了白桦和山杨的胸径、树高和材积的生长方程,分别编制了二者的生长过程表;同时根据径阶组划分标准,统计各树种在不同径阶组中的株数及其所占的比例,从而对林分内各乔木树种的演替动向进行分析.研究结果表明:山杨和白桦作为林分内的先锋树种,处于衰退趋势;红松、冷杉与云杉为地带性顶级树种,将在地带性顶级群落中占据为优势树种;其他树种在演替过程中变化不明显.     

Application of theoretical growth functions for Mongolian oak (Qurcus mongolica)

Four alternative functions are used for fitting tree height and diameter growth models for mongolian oak. (Quercus mongolica Fisch. et Turcz.). The data set includes 1250 random trees and 755 dominant trees coming from 510 temporary plots. The resultsshow that the Richards function is the best model for predicting height. diameter at breast height (DBH) and dominant height from age. The average growth curve of dominant height is used as a guide curve for the construction of a site index table which is partially validated using an independent data set. The Mitscherlich function is the best model for estimating height and dominant height from DBH. (Responsible Editor: Chai Ruihai)     

6种生长方程在杉木人工林林分直径结构上的应用

对Richards等6种生长方程的数学解析性及其应用于杉木人工林林分直径结构模拟的理论依据进行了分析和探索,并应用此6种生长方程模拟了林分直径累积分布。发现在描述林分直径累积分布时,Richards方程绝大多数表现为Logistic型,Weibull方程的参数c均大于1,曲线存在拐点;除Mitscherlich式外,各生长方程的模拟精度均相当高,Richards、Weibull、Logistic、Gompertz、Mitscherlich、Kod等6种生长方程样本选优率依次降低;Richards、Logistic、Weibull、Gopertz、Korf及Mitscherlich等6种生长方程总体模拟精度依次降低;相对生长率表现为变量指数函数方程的精度较相对生长率表现为变量幂函数方程的精度高,且3参数方程的精度较2参数的高。     

Comparison of the modified Weibull and Richards growth function for developing site index equations

A site index model based on the Weibull cumulative distribution function was fitted to three stem analysis data sets of black spruce (Picea mariana (Mill) BSP), white spruce (Picea glauca (Moench) Voss) and aspen (Populus tremuloides Michx.). The resulting equations were compared with those based on the modified Richards' (1959) biological growth function (Ek 1971; Payandeh 1977, 1978). The Weibull-type model performed as well as or better than the biological growth function for white spruce and aspen, respectively, but it performed less accurately in the case of black spruce. The Weibull-type model appears to behave better, i.e., it produces more realistic height growth patterns, than the Richards function upon extrapolation particularly at young ages.     

Modelling biomass and leaf area index in a sub-arctic Scandinavian mountain area

Estimates of biomass and leaf area index (LAI) are important variables in ecological and climate models. However, very little is known about the biomass and LAI of the vegetation in the Scandinavian mountain area. In this study, extensive field data consisting of diameter at breast height for 13?000 trees and height for 550 trees were collected. Furthermore, biomass and leaf area (LA) measurements for 46 mountain birch trees [Betula pubescens ssp. czerepanovii (Orlowa) Hämet-Ahti] and biomass and LA measurements for shrubs (e.g. Salix spp., Betula nana) at 36 sample plots were carried out. Multiplicative linear models for trees were fitted to tree biomass and LA measurements using basal area at breast height, height, crown diameter and diameter at stump height as explanatory variables. Additive linear models were fitted to shrub biomass and LAI measurements using coverage of shrubs, topographic variables and soil type as explanatory variables. The functions were then used to predict the biomass and LAI for trees and shrubs for the entire test area, which covers an area of 84 km² and is located at latitude 68° N. The mean total biomass estimates were 27?493 kg ha^?1 for the forest and 7650 kg ha^?1 for snow-protected heath and meadow vegetation. The LAIs were 2.06 and 0.52, respectively. For monitoring biomass and LAI in the Scandinavian mountain area, the functions could also be applied to data from traditional field-based inventories and the estimates might further be improved by combining the estimates from the test area with auxiliary information such as remote sensing images.     

桂林岩溶石山阴香幼苗生长动态的初步研究

探讨了广西桂林岩溶石山阴香幼苗的形态因子和生物量的生长动态,并运用数理统计学理论建立了它们与苗龄之间的回归方程。结果表明,随着苗龄的增加,阴香幼苗的形态因子和器官生物量均不断增大,但在不同时期它们的增长速率不同;幼苗的株高与苗龄之间符合二次曲线模型,基径与苗龄之间符合三次曲线模型,而叶面积以及器官生物量与苗龄之间符合线性模型。     

Distance-independent tree basal area growth models for Norway spruce,Douglas-fir and Japanese larch in Southern Belgium

This paper presents new harmonized distance-independent individual tree basal area growth models for Norway spruce, Douglas-fir and Japanese larch in pure even-aged stands in Southern Belgium. The selected model was originally developed for Norway spruce and Douglas-fir in neighboring France. New formulations are proposed for some of the model components in order to lower the number of fitted parameters and facilitate the fitting procedure. The resulting models integrate the most recent corresponding top-height growth models and use four simple and usually collected explanatory variables: stand age, top-height, total basal area and tree girth at breast height. The modified formulations maintain similar fitting performances and make it easier to interpret the influence of the explanatory variables on tree growth. Parameters estimates were fitted on thousands of growth measurements gathered from several monitoring plots, forest management inventories and silvicultural field experiments that represent the wide range of site conditions and of forest management scenarios applied to coniferous stands in Southern Belgium. Cross-validation of the models revealed no bias and highlighted their consistent behavior over the entire range of girth at breast height, age, top-height, site index and density represented in our dataset. Combining utility and robust performances, these models represent useful forest management tools, purposely ideal for forest simulation software development. Moreover, the flexibility and generic capabilities of the model formulation should make it easily adjustable for other species in even-aged stands.     

Bridging process-based and empirical approaches to modeling tree growth

The gulf between process-based and empirical approaches to modeling tree growth may be bridged, in part, by the use of a common model. To this end, we have formulated a process-based model of tree growth that can be fitted and applied in an empirical mode. The growth model is grounded in pipe model theory and an optimal control model of crown development. Together, the pipe model and the optimal control model provide a framework for expressing the components of tree biomass in terms of three standard inventory variables: tree height, crown height and stem cross-sectional area. Growth rates of the inventory variables and the components of biomass are formulated from a carbon balance. Fundamentally, the parameters of the model comprise physiological rates and morphological ratios. In principle, the values of these parameters may be estimated by lower-level process models. Alternatively, the physiological and morphological parameters combine, under reasonable assumptions, into a set of aggregate parameters, whose values can be estimated from inventory data with a statistical fitting procedure.     

Study on height growth model ofPinus koraiensis

Growth model is an efficient way to study growing process of some factors of plants quantitatively. Height growth of Korean pine (Pinus koraiensis) was studied by using Hyperbola equation, Logistic equation, Richards equation with three parameters, and Richards equation with four parameters in this paper. The results showed that Richards equation with four parameters was the most suitable and could be turned into other theoretical equations when some parameters were given different value. The maximum height of trees could be given in advance when using Richards equation with four parameters, and it was even more corresponding to reality. In addition, a height growth model with real height of fixed age as a parameter was discussed in this paper. This kind of growth model could be used to calculate height growth of a given tree effectively. Foundation item: This paper was supported by Great Item National Natural Science Foundation of China (39899370) and National Natural Science Foundation of China (NSFC39970123), and Changbai Mountain Open Research Station. Biography: DENG Hong-bing (1971-), male, Ph. Doctor, assistant research fellow in Institute of Applied Ecology, Chinese Academy of Sciences, Shenyang 110015, Post-doctor in Institute of Hydrobiology, Chinese Academy of Sciences. P. R. China. Responsible editor: Song Funan     

朝阳县油松、刺槐、华北落叶松树高生长模型研究

收集朝阳县主要造林树种油松、刺槐和华北落叶松的解析木数据,按照不同立地类型对数据进行分类整理,运用6种高生长模型对树高生长进行拟合和研究.结果表明,大部分树种高生长用Logistic模型最佳,油松在阴坡厚土层和阳坡厚土层的高生长用Richards方程最佳.相对生长方程在刺槐阳坡中土层和阳坡厚土层的高生长模拟也取得了满意的结果.