基于混合效应的兴安落叶松树高与胸径关系模拟

以黑龙江省带岭林业局大青川林场和永翠林场的兴安落叶松人工林为研究对象,基于41块样地调查数据和Richards模型,构建了含有林分变量的树高与胸径关系模型。利用混合效应模型方法拟合常规Richards模型yij=(β1+bi1)(1-e-(β2+bi2)xij)(β3+bi3)+εij和含有林分变量的模型yij=(β1+bi1)(Dq)(β2+bi2)(1-e-(β3+bi3)(N(β4+bi4))xij)+εij。结果表明:当对Richards混合效应模型拟合时,引入随机参数b1、b2时模型拟合最好;当对含有林分变量的Richards混合效应模型拟合时,引入随机参数b2、b4时模型拟合最好。模型检验表明:当随机抽取独立样本时,混合模型误差小于固定效应模型。如果随机抽取4个样本校正时,混合模型的误差和均方根误差降低71.8%和42.1%。     

用度量误差模型方法编制相容的生长过程表和材积表

指出了按照常规方法建立的生长模型和材积模型不相容的原因、利用两阶段度量误差模型方法估计生长模型和材积模型的参数,进而编制相容的生长过程表和材积表．     

Richards方程的数学属性及其在兽类生长过程中的应用

通过对Richards方程数学属性的分析表明 ,该方程具有变动的拐点值 ,因而在描绘兽类多种多样的生长过程时具有良好的可塑性。依据其方程参数n取值的不同 ,Richards方程包含了Spillman ,Logistic,Gompertz以及Bertalanffy方程。为了评估Richards方程对兽类生长过程的拟合优度 ,作者引用 1 0组哺乳动物兽类生长数据 ,将它与一些经典的生长模型如Spillman ,Logistic,Gompertz以及Bertalanffy方程共同进行了拟合比较。结果表明 ,Richards方程具有良好的拟合优度 ,适于描绘多种多样的兽类生长模式。     

望天树种群动态的初步研究

本文采用空间代替时间的方法组建了我国热带雨林的重要优势种望天树(Parashorea chinensis)种群的静态生命表,并建立了种群结构动态模型,种群材积动态模型和种群自疏模型。结果表明望天树种群现阶段足稳定型种群,具不断扩大的潜力;种群材积约170年前符合logistic增长,170年后材积下降;种群的自疏指数约为-2.1。     

天然云杉相容性生物量估算模型

基于150株天然云杉实测材积和生物量数据,利用非线性度量误差方法,建立相容性立木材积与生物量方程,并采用总量直接控制方案和分级联合控制方案研建了地上总生物量与4个分项(干材、干皮、树枝、树叶)的相容性方程系统,其中又采取了独立估计和联合估计两种处理方法进行地上生物量的估计.结果表明: 所建一元、二元相容性立木材积和地上生物量模型的材积和生物量决定系数均在0.85以上,最高达0.99,在胸径基础上增加树高变量能显著提高材积的预估效果,但对生物量的预估效果改进不大.就总量与分量相容性模型而言,分级联合控制方案所建的一元模型好于总量直接控制所建的一元模型,两种方案所建的二元模型效果相当.对一元、二元相容性生物量模型的拟合效果进行对比,结果显示,解释变量的增加明显提高了树枝和树叶生物量的拟合效果,对其他几个分量的拟合效果改善不大.对独立估计和联合估计的对比分析显示,两种估计方法几乎没有差异.     

森林流域坡面流与壤中流耦合模型的构建与应用

采用饱和入渗理论、Saint-Venant方程和Richards方程构建了以有限差分法求解的坡面流与壤中流耦合模型,并模拟了不同坡度和不同雨强下的坡面产汇流室内实验.结果表明：该模型模拟的坡面流和壤中流过程与实测过程基本一致,峰现时间、径流历时、峰值流量、出流总量模拟值与实测值的相对误差均较小,基本小于10%.模型的模拟精度较高,实用性较强,为深入研究壤中流机制和改进流域降雨-径流模型提供了理论依据.     

陕北白桦个体生长过程的谐波分析

利用波谱分析方法中的谐波分析原理, 对陕北白桦个体生长过程进行了不同层次的分析。结果表明:白桦个体的树高、胸径和材积生长动态波动规律与Logistic 模型不完全相同, 树高在20 年后与Logistic 模型吻合, 胸径整个过程均不吻合, 但材积生长与Logistic 模型基本一致;应用波谱分析方法分析树木生长过程的动态规律, 比Logistic 模型更准确。     

陕北白桦个体生长过程的谐波分析

利用波谱分析方法中的谐波分析原理,对陕北白桦个体生长过程进行了不同层次的分析。结果表明：白桦个体的树高、胸径和材积生长动态波动规律与Ｌogistic模型不完全相同,树高在２０年后与Ｌogistic模型吻合,胸径整个过程均不吻合,但材积生长与Ｌogistic模型基本一致,应用波谱分析方法分析树木生长过程的动态规律,比Ｌogistic模型更准确。     

三种预测林木生长量方法的比较

本研究选择了三种方法灰色GM(1,1)模型法、回归法、灰色线性回归组合模型法,经过数据的加载,灰色GM(1,1)为Ⅱ级合格模型,发展系数|a|＜0.3可用于中长期预测;在回归法中选用5个模型进行拟合,以Richards方程的复相关系高,残差平方和最小,被选中;灰色线性回组合模型达到Ⅲ级勉强可用模型.用三个模型分别对32、34龄阶的生长量进行预测,其平均相对精度分别为94.64%、80.68%、92.41%.     

长白山岳桦种群格局的地统计学分析

应用地统计学的原理和方法研究了长白山岳桦种群空间分布格局及其空间相关关系,首先通过样方调查数据计算岳桦材积的半变异函数,拟合半变异函数模型,然后根据拟合的最优半变异函数模型,进行空间数据插值、绘制岳桦材积的克立拉图,最后对所得到的不同海拔质海拔岳桦材积的半变异函数图和克立格图进行分析。结果表明,在海拔1650－1700m岳桦材积的半变异函数曲线为球形,其空间分布格局为聚集型,种群呈衰退趋势;海拔1750－2000m岳桦材积的半变异函数曲线为直线形,其空间分布格局为随机型,种群较稳定;在海拔2000－2150m岳桦材积的半变异函数曲线为球形,其空间分布格局为聚集型,种群呈增长趋势,这说明长白山桦整体上有一种向上迁移的趋势,尤其是过渡带中的岳桦表现则为更为明显。     

Plant Growth Analysis: The Use of the Richards Function as an Alternative to Polynomial Exponentials

The derived quantities in plant growth analysis, obtained byfitting the Richards function on the one hand and polynomialexponential functions on the other hand, are compared, usingtwo sets of experimental data. Results show that, although thereis rarely a statistical difference between the quantities derivedfrom the two types of function, the time trends are often morebiologically meaningful when derived from Richards functionfittings. Further, use of the Richards function does not entaila problem of choice, as occurs in the use of polynomial exponentialswhen particular members of the family must be selected for givendata sets; on the other hand, the Richards function will notfit those few sets of growth data which show insufficient curvaturetowards an upper asymptote. It is recommended that, wheneverpossible, the Richards function be used in plant growth analysisinstead of polynomial exponentials. Triticum aestivum L., wheat, Helianthus annuus L., sunflower, growth analysis, Richards function     

Richards's equation and nonlinear mixed models applied to avian growth: why use them?

Postnatal growth is an important life‐history trait that varies widely across avian species, and several equations with a sigmoidal shape have been used to model it. Classical three‐parameter models have an inflection point fixed at a percentage of the upper asymptote which could be an unrealistic assumption generating biased fits. The Richards model emerged as an interesting alternative because it includes an extra parameter that determines the location of the inflection point which can move freely along the growth curve. Recently, nonlinear mixed models (NLMM) have been used in modeling avian growth because these models can deal with a lack of independence among data as typically occurs with multiple measurements on the same individual or on groups of related individuals. Here, we evaluated the usefulness of von Bertalanffy, Gompertz, logistic, U₄ and Richards's equations modeling chick growth in the imperial shag Phalacrocorax atriceps. We modelled growth in commonly used morphological traits, including body mass, bill length, head length and tarsus length, and compared the performance of models by using NLMM. Estimated adult size, age at maximum growth and maximum growth rates markedly differed across models. Overall, the most consistent performance in estimated adult size was obtained by the Richards model that showed deviations from mean adult size within 5%. Based on AICc values, the Richards equation was the best model for all traits analyzed. For tarsus length, both Richards and U₄ models provided indistinguishable fits because the relative inflection value estimated from the Richards model was very close to that assumed by the U₄ model. Our results highlight the bias incurred by three‐parameter models when the assumed inflection placement deviates from that derived from data. Thus, the application of the Richards equation using the NLMM framework represents a flexible and powerful tool for the analysis of avian growth.     

Modelling avian growth with the Unified‐Richards: as exemplified by wader‐chick growth

Postnatal growth in birds is traditionally modelled by fitting three‐parameter models, namely the logistic, the Gompertz, or the von Bertalanffy models. The purpose of this paper is to address the utility of the Unified‐Richards (U‐Richards) model. We draw attention to two forms of the U‐Richards and lay down a set of recommendations for the analysis of bird growth, in order to make this model and the methods more accessible. We examine the behaviour of the four parameters in each model form and the four derived measurements, and we show that all are easy to interpret, and that each parameter controls a single curve characteristic. The two parameters that control the inflection point, enable us to compare its placement in two dimensions, 1) inflection value (mass or length at inflection) and 2) inflection time (time since hatching), between data sets (e.g. between biometrics or between species). We also show how the parameter controlling growth rate directly presents us with the relative growth rate at inflection, and we demonstrate how one can compare growth rates across data sets. The three traditional models, where the inflection value is fixed (to a specific percentage of the upper asymptote), provide incompatible growth‐rate coefficients. One of the two forms of the U‐Richards model makes it possible to fix not only the upper asymptote (adult value), but also the intersection with the y‐axis (hatching value). Fitting the new model forms to data validates the usefulness of interpreting the inflection placement in addition to the growth rate. It also illustrated the advantages and limitations of constraining the upper asymptote (adult value) and the y‐axis intersection (hatching value) to fixed values. We show that the U‐Richards model can successfully replace some of the commonly used growth models, and we advocate replacing these with the U‐Richards when modelling bird growth.     

A RE-EVALUATION OF SPHENACODONTID SYNAPSID MATERIAL FROM THE LOWER PERMIAN FISSURE FILLS NEAR RICHARDS SPUR, OKLAHOMA

Abstract:  Early Permian terrestrial vertebrate faunal assemblages of Laurasia are dominated by large ophiacodontid, sphenacodontid, and edaphosaurid synapsids. This pattern contrasts with the fauna recovered from the Early Permian fissure fill deposits near Richards Spur, Oklahoma, where derived nontherapsid synapsids are rare. The fragmentary remains of Thrausmosaurus serratidens constitute the only published report of Sphenacodontidae from this locality. Here, we re-evaluate T. serratidens in light of new information on the faunal assemblage of this locality. We confirm that the type material of T. serratidens cannot be assigned to Sphenacodontidae and conclude that it pertains to an indeterminate varanopid. We also describe new material, including a partial maxilla, several isolated jaw fragments with teeth, an isolated precaniniform tooth and a posterior cervical vertebra that represents unequivocal sphenacodontid remains from the Richards Spur assemblage. This material is the first definitive record of a eupelycosaurian synapsid other than a varanopid from this important locality. Faunal similarities between Richards Spur and the Bromacker Quarry, Germany, may be reflective of upland terrestrial communities during the Early Permian.     

Estimating Initial Epidemic Growth Rates

The initial exponential growth rate of an epidemic is an important measure of disease spread, and is commonly used to infer the basic reproduction number $\mathcal{R}_{0}$ . While modern techniques (e.g., MCMC and particle filtering) for parameter estimation of mechanistic models have gained popularity, maximum likelihood fitting of phenomenological models remains important due to its simplicity, to the difficulty of using modern methods in the context of limited data, and to the fact that there is not always enough information available to choose an appropriate mechanistic model. However, it is often not clear which phenomenological model is appropriate for a given dataset. We compare the performance of four commonly used phenomenological models (exponential, Richards, logistic, and delayed logistic) in estimating initial epidemic growth rates by maximum likelihood, by fitting them to simulated epidemics with known parameters. For incidence data, both the logistic model and the Richards model yield accurate point estimates for fitting windows up to the epidemic peak. When observation errors are small, the Richards model yields confidence intervals with better coverage. For mortality data, the Richards model and the delayed logistic model yield the best growth rate estimates. We also investigate the width and coverage of the confidence intervals corresponding to these fits.     

Choosing the right sigmoid growth function using the unified‐models approach

Growth of the young is an important part of the life history in birds. However, modelling methods have paid little attention to the choice of regression model used to describe its pattern. The aim of this study was to evaluate whether a single sigmoid model with an upper asymptote could describe avian growth adequately. We compared unified versions of five growth models of the Richards family (the four‐parameter U‐Richards and the three‐parameter U‐logistic, U‐Gompertz, U‐Bertalanffy and U4‐models) for three traits (body mass, tarsus‐length and wing‐length) for 50 passerine species, including species with varied morphologies and life histories. The U‐family models exhibit a unified set of parameters for all models. The four‐parameter U‐Richards model proved a good choice for fitting growth curves to various traits – its extra d‐parameter allows for a flexible placement of the inflection point. Which of the three‐parameter U‐models was the best performing varied greatly between species and between traits, as each three‐parameter model had a different fixed relative inflection value (fraction of the upper asymptote), implying a different growth pattern. Fixing the asymptotes to averages for adult trait value generally shifted the model preference towards one with lower relative inflection values. Our results illustrate an overlooked difficulty in the analysis of organismal growth, namely, that a single traditional three‐parameter model does not suit all growth data. This is mostly due to differences in inflection placement. Moreover, some biometric traits require more attention when estimating growth rates and other growth‐curve characteristics. We recommend fitting either several three‐parameter models from the U‐family, where the parameters are comparable between models, or only the U‐Richards model.     

红松单木高生长模型的研究

１引言生长模型是定量研究树木生长过程的有效手段。它既可对林木生长作出现实的评价,也可用来预估将来各测树因子的变化;既是编制修订各种数表的基础,也是森林经营中各种措施实施的依据。在林学上,生长模型主要包括单木生长模型和林分生长模型,其中单木生长模型是林...