逻辑斯谛增长导致的复杂种群动态及其实验验证

教科书通常用“S”型曲线表示逻辑斯谛增长模型导致的种群动态,事实上,这一模型可以产生包括稳定平衡、周期性振荡、混沌等多种多样的种群动态模式。介绍了如何用Kicker图示的方法分析逻辑斯谛增长可能导致的种群动态模式。同时介绍了相关的实验研究案例,这些实验工作大都是以生活史周期较短的昆虫为材料在相对简单的实验室环境中完成的。     

逻辑斯谛曲线的一种拟合方法

一、前言 逻辑斯谛方程(Logistic equation)指出了有限空间种群增长的基本规律,是研究种群动态的重要工具。长期以来,人们运用逻辑斯谛方程处理实验数据,得出了种种曲线拟合的方法。然而,这些方法都存在着一定的缺点,使逻辑斯谛方程的应用受到某些限制。随着种群生态学的不断发展,对实验数据的处理要求更精确、更迅速,因此进一步探讨曲线拟合     

用麦夸方法最优拟合逻辑斯谛曲线

一般对非线性逻辑斯谛生长曲线的拟合是采用首先对原方程线性化以后用线性最小二乘的方法。此方法不是最优的。本文提出用麦夸方法对曲线进行拟合,并且比较了Gause、Andrewartha、May、Pearl、Krebs、万昌秀等人提出的方法与计算结果。麦夸方法对生物实验及生态学中诸多非线性曲线的参数估计具有普遍的意义。     

逻辑斯谛曲线拟合的一种数值方法

1、引言逻辑斯谛方程(Logistic equation)是研究有限空间内种群增长规律的重要工具之一,这是由荷兰生物数学家verhulst于1838年首先提出来的。迄今为止,人们利用逻辑斯谛方程处理实验数据已经提出了各种曲线拟合方法,其中比较曲型的有三点法,平均     

红花尔基沙地樟子松种群优势度增长动态及自疏规律的研究

用逻辑斯谛模型分析了红花尔基沙地不同类型樟子松种群胸高断面积增长规律,发现从坡底到坡顶,环境容纳量逐渐减小,种群内禀增长率降低,种群胸高断面积最大增长速度逐渐减小,种媾和的特征返回时间逐渐增大。樟子松种群自疏规律为：平均胸径与密度的关系符合负幂函数模型。     

云冷杉林建群种的种群优势度增长动态研究

 用有限空间种群增长的逻辑斯谛模型探讨了种群基面积增长规律,指出了云冷杉林建群种在不同状态下的基面积最大增长速度的径级范围,紫果云杉35—40cm,岷江冷杉50—55cm;在不同林分内,建群种具有不同的基面积最大增长期。     

棉花生长发育模拟模型的研究

本文是根据1984—1985年大田资料建立的一个棉花生长发育模型。模型利用光能辐射,叶面积指数,植株干重等来计算净光合产物,并在各器官之间进行分配。利用生理学时间来预测主茎节数,根据顶芽、腋芽分化的同步序列,来确定果枝数、果节数。单铃重随其生理时间而呈逻辑斯谛克曲线分布: BW=8.2842/(1+e5.2701-0.0073×PT) 并定出蕾铃潜在增长率,根据潜在增长率求出每米~2土地上蕾铃干物质需求量,从营养供求状况来控制雷铃脱落。 根据模型预测,可确定棉花不同生育时期最佳栽培措施;与棉虫动态模型偶联,可研究棉虫动态经济阈值。     

鼎湖山森林优势种群数量动态

本文分析研究了鼎湖山森林群落优势种群的数量动态,结果表明厚壳桂和黄果厚壳桂的增长曲线是与逻辑斯谛曲线相一致,椎栗的增长曲线则是一条近似的抛物曲线。拟合组建了种群增长方程(6)、(7)、(8)、(9)、(12),并论证了可信度及生态意义。     

逻辑斯谛Logistic模型研究进展

阐述了经典的逻辑斯谛(Logistic)模型的类型,分析了Logistic模型中存在的局限性,根据其局限性,学者们提出了各种各样的数学模型。这些数学模型对于实际中的模型选择和拟合有一定的启示作用,而且,进一步加强了对种群数量变动的理解。     

半天然杉阔混交林优势种群的增长规律

采用有限空间种群增长的逻辑斯谛模型,研究半天然杉阔混交林群落中主要种群（杉木,米槠）氏面积增长规律,指出杉木,米槠在不同类型群落中的底面积的最大增长速度的径级范围。     

关于农药消解模型参数拟合优化算法的研究

参数拟合是数学建模的重要方面．本文对农药消解模型参数拟合的算法进行优化,用麦夸方法最优拟合消解方程y=c0e～-kt,给出参数和半衰期的数值解．理论和实例计算均表明：用麦夸方法得到的消解模型的预测值与实测值拟合度优于其他方法．优化的麦夸算法简便实用,且具有普遍适用性．     

基于人工神经网络的农业病虫害预测模型及其效果检验

选取与病虫害有关的因子作为样本的输入特征,建立了农业病虫害年分类预测的Ｂ－Ｐ人工神经网络模型。该方法应用于稻瘟病的预测建模结果的拟合率为１００％,预留样本检验报率为８３％。     

Applying geographic profiling used in the field of criminology for predicting the nest locations of bumble bees

We tested whether geographic profiling (GP) can predict multiple nest locations of bumble bees. GP was originally developed in the field of criminology for predicting the area where an offender most likely resides on the basis of the actual crime sites and the predefined probability of crime interaction. The predefined probability of crime interaction in the GP model depends on the distance of a site from an offender's residence. We applied GP for predicting nest locations, assuming that foraging and nest sites were the crime sites and the offenders’ residences, respectively. We identified the foraging and nest sites of the invasive species Bombus terrestris in 2004, 2005, and 2006. We fitted GP model coefficients to the field data of the foraging and nest sites, and used GP with the fitting coefficients. GP succeeded in predicting about 10-30% of actual nests. Sensitivity analysis showed that the predictability of the GP model mainly depended on the coefficient value of buffer zone, the distance at the mode of the foraging probability. GP will be able to predict the nest locations of bumble bees in other area by using the fitting coefficient values measured in this study. It will be possible to further improve the predictability of the GP model by considering food site preference and nest density.     

冷却猪肉中气单胞菌生长预测模型的建立和检验

为探讨冷却猪肉中气单胞菌的生长规律,将气单胞茵接种到经过80℃无菌水灭菌的冷却猪肉中,构建Gompertz和Baranyi初级模型来描述气单胞菌在不同温度下的生长状况。结果表明：修正的Gompertz模型对气单胞菌生长曲线的拟合效果优于Baranyi模型,R2均在0．97以上。应用平方根模型和Arrhenius模型对由修正的Gompertz模型得出的最大比生长速率进行拟合,所得平方根模型拟合效果略优于Arrhenius模型。实验所建二级模型能预测0-35℃贮藏条件下气单胞菌的生长。     

THE TEMPO AND MODE OF EVOLUTION OF TRANSPOSABLE ELEMENTS AS REVEALED BY MOLECULAR PHYLOGENIES RECONSTRUCTED FROM MOSQUITO GENOMES

Although many mathematical models exist predicting the dynamics of transposable elements (TEs), there is a lack of available empirical data to validate these models and inherent assumptions. Genomes can provide a snapshot of several TE families in a single organism, and these could have their demographics inferred by coalescent analysis, allowing for the testing of theories on TE amplification dynamics. Using the available genomes of the mosquitoes Aedes aegypti and Anopheles gambiae, we indicate that such an approach is feasible. Our analysis follows four steps: (1) mining the two mosquito genomes currently available in search of TE families; (2) fitting, to selected families found in (1), a phylogeny tree under the general time‐reversible (GTR) nucleotide substitution model with an uncorrelated lognormal (UCLN) relaxed clock and a nonparametric demographic model; (3) fitting a nonparametric coalescent model to the tree generated in (2); and (4) fitting parametric models motivated by ecological theories to the curve generated in (3).     

Predicting Human Preferences Using the Block Structure of Complex Social Networks

With ever-increasing available data, predicting individuals'' preferences and helping them locate the most relevant information has become a pressing need. Understanding and predicting preferences is also important from a fundamental point of view, as part of what has been called a “new” computational social science. Here, we propose a novel approach based on stochastic block models, which have been developed by sociologists as plausible models of complex networks of social interactions. Our model is in the spirit of predicting individuals'' preferences based on the preferences of others but, rather than fitting a particular model, we rely on a Bayesian approach that samples over the ensemble of all possible models. We show that our approach is considerably more accurate than leading recommender algorithms, with major relative improvements between 38% and 99% over industry-level algorithms. Besides, our approach sheds light on decision-making processes by identifying groups of individuals that have consistently similar preferences, and enabling the analysis of the characteristics of those groups.     

基于线性混合模型的红松人工林一级枝条大小预测模拟

基于黑龙江省孟家岗林场60株人工红松955个标准枝数据,采用线性混合效应模型理论和方法,考虑树木效应,利用SAS软件中的MIXED模块拟合红松人工林一级枝条各因子(基径、枝长、着枝角度)的预测模型.结果表明： 通过选择合适的随机参数和方差协方差结构能够提高模型的拟合精度;把相关性结构包括复合对称结构CS、一阶自回归结构AR(1)及一阶自回归与滑动平均结构ARMA(1,1)加入到一级枝条大小最优混合模型中,AR(1)可显著提高枝条基径和角度混合模型的拟合精度,但3种结构均不能提高枝条角度混合模型的精度.为了描述混合模型构建过程中产生的异方差现象,把CF₁和CF₂函数加入到枝条混合模型中,CF₁函数显著提高了枝条角度混合模型的拟合效果,CF₂函数显著提高了枝条基径和长度混合模型拟合效果.模型检验结果表明：对于红松人工林一级枝条大小预测模型,混合效应模型的估计精度比传统回归模型估计精度明显提高.
     

基于BP人工神经网络的兴安落叶松天然林全林分生长模型的研究

以大兴安岭地区兴安落叶松天然林为研究对象,基于688块固定标准地数据,采用MATLAB中log-sigmoid型函数(logsig)和线性函数(purelin)为神经元的作用函数,依据全林分生长模型的概念,以年龄（A）、地位级指数（SCI）和林分密度指数（SDI）作为输入变量,以林分每公顷蓄积量（M）作为输出变量,构建和训练了全林分生长的BP人工神经网络模型,并与常规建模方法进行了对比研究。结果表明,BP人工神经网络模型的拟合精度高达99.6%,检验精度为98.9%,说明与其它建模方法相比人工神经网络建模具有较高的拟合精度和适应性,对林分生长具有更好的预测能力。     

基于遗传算法和支持向量机的乳杆菌发酵过程建模

由于生化反应过程的复杂性和高度非线性,多数简单的数学模型不能准确描述。该文基于Matlab软件,利用改进的支持向量机(υ-SVR)对植物乳酸杆菌发酵这一典型生化过程进行研究,应用遗传算法估计模型最优参数,建立植物乳杆菌的菌体密度预测模型。同时建立传统的logistic动力学模型以进行比较。结果表明,采用结合遗传算法的υ-SVR预测模型拟合误差小,皮尔森相关系数(R)更高,可以较好地预测乳酸杆菌的发酵过程,为其优化控制及放大提供依据。     

A general Akaike-type criterion for model selection in robust regression

Akaike's procedure (1970) for selecting a model minimises anestimate of the expected squared error in predicting new, independentobservations. This selection criterion was designed for modelsfitted by least squares. A different model-fitting technique,such as least absolute deviation regression, requires an appropriatemodel selection procedure. This paper presents a general Akaike-typecriterion applicable to a wide variety of loss functions formodel fitting. It requires only that the function be convexwith a unique minimum, and twice differentiable in expectation.Simulations show that the estimators proposed here well approximatetheir respective prediction errors.