非线性再生散度随机效应模型的极大似然估计及EM算法

非线性再生散度随机效应模型是指数族非线性随机效应模型和非线性再生散度模型的推广和发展．通过视模型中的随机效应为假想的缺失数据和应用Metropolis-Hastings（MH）算法,提出了模型参数极大似然估计的Monte-Carlo EM（MCEM）算法,并用模拟研究和实例分析说明了该算法的可行性．     

基于随机效应的兴安落叶松材积生长模拟

基于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和Logistic生长模型,分别考虑单木效应和样地效应,利用S-PLUS软件中的NLME过程拟合非线性材积生长模型,采用赤池信息准则(AIC)、贝叶斯信息准则(BIC)、对数似然值和似然比检验等模型评价指标对不同模型的精度进行比较.结果表明：当考虑单木效应影响时,b₁、b₂、b₃（分别代表Logistic模型中的渐进、尺度和形状的随机参数）同时作为随机参数时模型拟合效果最好; 当考虑样地效应影响时,b₁作为随机参数时模型拟合效果最好.基于单木效应和样地效应的混合模型的拟合精度高于基本模型（Logistic生长模型）,考虑单木效应影响的混合模型的精度高于考虑样地效应影响的模型.模型检验结果表明,随机效应模型不但能反映单木材积的总体平均变化趋势,还能反映个体之间的差异;随机效应模型通过校正随机参数值能提高模型的预测精度.     

数量性状主要基因随机效应的分析

数量性状主基因在不同环境或遗传背景中表现随机效应。本文提出数量性状基因随机效应分析的试验设计和统计模型,以及对基因的分离比、平均效应和随机方差进行假设测验的方法．所述方法可用于借助标记基因对数量性状基因效应作类似分析．     

随机森林模型在分类与回归分析中的应用

随机森林(random forest)模型是由Breiman和Cutler在2001年提出的一种基于分类树的算法。它通过对大量分类树的汇总提高了模型的预测精度,是取代神经网络等传统机器学习方法的新的模型。随机森林的运算速度很快,在处理大数据时表现优异。随机森林不需要顾虑一般回归分析面临的多元共线性的问题,不用做变量选择。现有的随机森林软件包给出了所有变量的重要性。另外,随机森林便于计算变量的非线性作用,而且可以体现变量间的交互作用(interaction)。它对离群值也不敏感。本文通过3个案例,分别介绍了随机森林在昆虫种类的判别分析、有无数据的分析(取代逻辑斯蒂回归)和回归分析上的应用。案例的数据格式和R语言代码可为研究随机森林在分类与回归分析中的应用提供参考。     

Crow-Kimura模型中位点突变率对误差阈的随机效应

为了补充Eigen模型和Crow-Kimura模型的随机效应研究,Crow-Kimura模型中的位点突变率被处理成高斯分布随机变量,从而研究误差阈值的特征以及误差阈值的扩展与随机突变率涨落强度之间的关系. 准物种浓度和群体序参数分析表明,在位点突变率涨落较大时,误差阈值不再是相变点,而是平滑的转变区域. 定量分析表明,随机Crow-Kimura模型中转变区宽度与涨落强度之间的关系是非线性的. 将Crow-Kimura模型与Eigen模型的随机特征进行比较发现,在两个模型中适应值随机化使得转变区域的宽度和随机变量涨落强度之间的关系是线性的,而位点突变率随机化中两者的关系是非线性的（指数）. 对于随机化的Crow-Kimura模型,适应值随机化与位点突变率随机化引起的误差阈扩展效应相当. 对于随机Eigen模型,误差阈的扩展效应则主要是由位点突变率的随机化引起的. 之后,本文概述了Eigen模型和Crow Kimura模型中适应值和位点突变率随机化对误差阈值随机效应的影响,并讨论了上述结果对抗病毒策略、癌症治疗和动植物育种的重要意义.     

一类具有随机周期移民扰动的非线性人口发展方程随机周期解的存在唯一性

本文给出了一类具有随机周期移民扰动的非线性m增生人口发展方程随机周期解的存在性和唯一性结论。     

单和同类随机效应模型的局部影响判断

利用局部影响方法对线性模型中的单向分类随机效应模型进行了讨论。这种方法的优点在于避免了线性模型中有些参数估计不便于进行单点删除的诊断分析。     

随机Lotka-Volterra系统的稳定性

利用Lyapunov方法与K．lto公式及鞅的理论,研究了随机Lotka-Volterra系统正平衡点的全局渐近稳定性．得到了随机全局渐近稳定的主要定理,并以确定性系统的全局稳定性作为定理的推论．     

利用随机效应模型模拟东北三省胡桃楸地位指数

通过精确模拟东北三省胡桃楸多形地位指数混合效应模型,为胡桃楸立地质量评价提供科学依据,本研究在辽宁、吉林和黑龙江三省23个典型区域内,采用样圆法布设样地197块,测定样地内胡桃楸树高-年龄数据,共得到数据1537组,同时将立地因子进行划分和赋值,应用方差分析和模型拟合进行计算。结果表明: 坡位是影响胡桃楸优势木生长最显著的因素,其次为土壤深度、坡度和坡向等;对8种常见基础模型进行拟合与分析,发现逻辑斯蒂模型H=a/[1+exp(b+cA)]为最优基础模型(R²=0.70),平均绝对误差(MAE)为2.52;对4种主要影响因素进行随机组合,得到随机组合因素最优地位指数模型M_8.15,其R²=0.90,提高了基础模型的拟合精度;采用K均值聚类分组法进一步将初始的立地类型划分为6个立地类型组,按6个立地类型组建立的非线性混合效应模型M_final,即H=(20.1837+u_i)/[1+exp (1.7352-0.0961A)]+ε_ij,其R²=0.92,AIC=912.65,模型的拟合度和精确度显著提高,可以用于东北三省复杂立地类型下胡桃楸立地质量的准确评价。     

单向分类随机效应模型的局部影响判断

利用局部影响方法对线性模型中的单向分类随机效应模型进行了讨论.这种方法的优点在于避免了线性模型中有些参数估计不便于进行单点删除的诊断分析.     

Details of local dispersion improve the fit of neighborhood competition models

I performed a series of greenhouse experiments to explore how patterns in the dispersion of local competitors affect the reproductive performance of Capsella bursa-pastoris, Poa annua and Senecio vulgaris. I manipulated the density and relative frequency of competitors in each of three concentric rings surrounding a central plant, thereby creating a variety patterns by which local competitors were distributed. Neighborhood competition models were used to predict the seed output of these central plants. For both Senecio vulgaris and Capsella bursa-pastoris, I found that models which incorporated the dispersion of competitors, as well as the relative emergence date of plants, performed substantially better than those that considered only the distance between the central plant and each of its competitors. I was unable to measure the seed output of Poa annua but neither emergence data nor the dispersion of competitors were important in determining its final dry-weight. Present address: Department of Biology, Box 1137, Washington University, 1 Brookings Drive, St. Louis, MO 63130, USA     

Langmuir wave in weakly inhomogeneous relativistic plasma

The evolution of a Langmuir wave in a weakly inhomogeneous relativistic plasma with a positive density gradient is considered. It is shown that, at relativistic phase velocities, the wave evolution even at the tail of the electron distribution, where it is close to linear in the nonrelativistic case, results in the wave transformation into a hybrid of two waves with different spatial periods. Nonlinear dispersion relations for different stages of the wave evolution are derived.     

Overman, A.R. and Scholtz, R.V. III. Mathematical models of crop growth and yield

This book comprises six chapters: Introduction (34 pp.), Seasonalresponse models (60 pp.), Growth response models (91 pp.), Mathematicalcharacteristics of models (97 pp.), Pasture systems (22 pp.)and Nonlinear regression for mathematical models (20 pp.). Eachchapter ends with exercises and references. The book has a subjectindex. I found     

An intuitive formulation for the reproductive number for the spread of diseases in heterogeneous populations

The thresholds for mathematical epidemiology models specify the critical conditions for an epidemic to grow or die out. The reproductive number can provide significant insight into the transmission dynamics of a disease and can guide strategies to control its spread. We define the mean number of contacts, the mean duration of infection, and the mean transmission probability appropriately for certain epidemiological models, and construct a simplified formulation of the reproductive number as the product of these quantities. When the spread of the epidemic depends strongly upon the heterogeneity of the populations, the epidemiological models must account for this heterogeneity, and the expressions for the reproductive number become correspondingly more complex. We formulate several models with different heterogeneous structures and demonstrate how to define the mean quantities for an explicit expression for the reproductive number. In complex heterogeneous models, it seems necessary to define the reproductive number for each structured subgroup or cohort and then use the average of these reproductive numbers weighted by their heterogeneity to estimate the reproductive number for the total population.     

Multivariate multilevel nonlinear mixed effects models for timber yield predictions

Nonlinear mixed effects models have become important tools for growth and yield modeling in forestry. To date, applications have concentrated on modeling single growth variables such as tree height or bole volume. Here, we propose multivariate multilevel nonlinear mixed effects models for describing several plot-level timber quantity characteristics simultaneously. We describe how such models can be used to produce future predictions of timber volume (yield). The class of models and methods of estimation and prediction are developed and then illustrated on data from a University of Georgia study of the effects of various site preparation methods on the growth of slash pine (Pinus elliottii Engelm.).     

Multiple states in river and lake ecosystems

Nonlinear models of ecosystem dynamics that incorporate positive feedbacks and multiple, internally reinforced states have considerable explanatory power. However, linear models may be adequate, particularly if ecosystem behaviour is primarily controlled by external processes. In lake ecosystems, internal (mainly biotic) processes are thought to have major impacts on system behaviour, whereas in rivers, external (mainly physical) factors have traditionally been emphasized. We consider the hypothesis that models that exhibit multiple states are useful for understanding the behaviour of lake ecosystems, but not as useful for understanding stream ecosystems. Some of the best-known examples of multiple states come from lake ecosystems. We review some of these examples, and we also describe examples of multiple states in rivers. We conclude that the hypothesis is an oversimplification; the importance of physical forcing in rivers does not eliminate the possibility of internal feedbacks that create multiple states, although in rivers these feedbacks are likely to include physical as well as biotic processes. Nonlinear behaviour in aquatic ecosystems may be more common than current theory indicates.     

Modelling time to population extinction when individual reproduction is autocorrelated

In nature, individual reproductive success is seldom independent from year to year, due to factors such as reproductive costs and individual heterogeneity. However, population projection models that incorporate temporal autocorrelations in individual reproduction can be difficult to parameterise, particularly when data are sparse. We therefore examine whether such models are necessary to avoid biased estimates of stochastic population growth and extinction risk, by comparing output from a matrix population model that incorporates reproductive autocorrelations to output from a standard age‐structured matrix model that does not. We use a range of parameterisations, including a case study using moose data, treating probabilities of switching reproductive class as either fixed or fluctuating. Expected time to extinction from the two models is found to differ by only small amounts (under 10%) for most parameterisations, indicating that explicitly accounting for individual reproductive autocorrelations is in most cases not necessary to avoid bias in extinction estimates.     

Indices of reproductive skew depend on average reproductive success

Several indices of reproductive skew, which quantify the degree of unequal partitioning of reproductive output among members in an animal society, have been proposed. Here we point out the drawbacks of these indices. The most serious problem is the dependence of the indices on mean reproductive success: skew values tend to be larger, as average numbers of offspring decrease, due to random sampling error in numbers of offspring. Thus it is difficult to compare societies with different average lifetime reproductive success using these indices, even though we have presented methods to calculate the expected reproductive skew caused by random sampling error, especially when average numbers of offspring are small, as is often the case with cooperatively breeding vertebrates. As an alternative, we propose using the spatial dispersion indices of population ecology (Morisita's index or its standardized version) for the measurement of reproductive skew. These indices are almost independent of average fecundity and have their own method of testing for random variation in offspring numbers. This revised version was published online in July 2006 with corrections to the Cover Date.     

Minimizing Bias in Biomass Allometry: Model Selection and Log‐Transformation of Data

Nonlinear regression is increasingly used to develop allometric equations for forest biomass estimation (i.e., as opposed to the traditional approach of log‐transformation followed by linear regression). Most statistical software packages, however, assume additive errors by default, violating a key assumption of allometric theory and possibly producing spurious models. Here, we show that such models may bias stand‐level biomass estimates by up to 100 percent in young forests, and we present an alternative nonlinear fitting approach that conforms with allometric theory.