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     

二个新的种群增长方程

本文提出了二个新的种群增长方程,方程Ⅰ和方程Ⅱ．对Gause的草履虫实验数据的拟合结果表明,这二个方程与逻辑斯谛方程相比,可以有效地降低拟合的残差平方和．     

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。     

滞后—逻辑斯谛方程振动的充要条件

一、引言本文研究方程杨正清7卷的振动性。(1)产是物种自身调节反馈变滞后一逻辑斯谛方程。这是一类很重要的生态方程。它是研究有限空间内种群增长规律的重要工具之一。     

浅评逻辑斯蒂方程

一、一个重要而被滥加引用的方程1838年Verhulst提出的逻辑斯蒂方程,被人们广泛地引用。不仅在自然科学中,甚至在社会科学中亦如此。Deevey认为这种增长型可能是最普遍的,在生态学上,由于逻辑斯蒂方程与因种群密度制约因素而形成的负反馈机制有联系,因而有人说,逻辑斯蒂方程是种群生态学中的核心理论之一,可见,逻辑斯蒂方程处于十分重要地位。(1)利用逻辑斯蒂方程表征种群数量动态:著名的经典实验有Pearl(1927)的果蝇;chapman(1931)的拟谷盗;Gause(1934)     

褐飞虱种群的广义逻辑斯谛曲线模型的研究

用广义逻辑斯谛曲线模型及预测饱和增长趋势,解释了该模型包含的实际生物学意义,并给出了相应的参数估计算法,对褐飞虱Nilaparvatalugens（Stal）种群资料进行具体的分析,结果与其它模型相比,拟合程度高,用广义逻辑斯谛曲线模型作为预报,可以提高预测的效果。     

两种异养性鞭毛虫实验种群数量动态的比较研究

1999年4－8月从武昌东湖PFU样本中分离纯化了两种异养性鞭毛虫,对四种不同浓度Ceraphyl培养液中的种群增长进行了比较研究,结果表明这两种异养性鞭毛虫种群的数量动态显著不同,聚滴虫在四种浓度Ceraphyl培养液中均呈逻辑斯谛增长;而舞行波豆虫在四种浓度Ceraphyl培养液中的增长曲线均为抛物线。拟合组建了种群增长方程,并论证了方程可信度及其参数的生态学意义。     

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。     

介绍两种逻辑曲线拟合的方法

凡是具有峰形曲线增长的生物种群,大体上可归纳为前峰形、中峰形和后峰形,完全像逻辑斯蒂曲线增长的不多。因而,采用逻辑斯蒂曲线拟合的方法拟合峰形曲线就有些不太理想。本文介绍两种拟合峰形曲线较理想的方法,一种是累加生成拟合,另一种是灰色逻辑斯蒂曲线拟合。第一种方法是通过一次累加生成弱化原始数据中的随机性和波动性,以适应于逻辑曲线的拟合。第二种是采用灰色系统理论的方法,采用     

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。     

Vibration analysis on incubating eggs and its relation to embryonic development

Coucke (1998) was the first to use acoustic resonance analysis to monitor embryo development in chicken eggs. He remarked that at around 100 hours of incubation, the course of the resonant frequency and damping changed abruptly in the case of fertile eggs. He also showed that these changes were related to a physiologic event during early embryonic development. The objective of our study is to monitor the course of the vibration parameters during the early incubation of chicken eggs and to relate these changes to egg and embryo characteristics. A total of 72 Hybro eggs were incubated vertically in a small incubator at standard conditions. Several egg parameters were measured before incubation. During the early stages of incubation the vibration behavior of these eggs was monitored. The time at which the damping of the vibration suddenly changed, the diameter of the eggs and their interaction were found to be significant explanatory variables in order to predict hatching time. A correlation coefficient r of 0.72 was obtained.     

A comparison of quantitative structure-activity relationships for the effect of benzoic and cinnamic acids on Listeria monocytogenes using multiple linear regression,artificial neural network and fuzzy systems

The ability of artificial neural networks (ANN), fuzzy systems (FS) and multiple linear regression (MLR) to fit the biological activity surface describing the inhibition of Listeria monocytogenes by benzoic and cinnamic acid derivatives was compared. MLR and ANN were also compared for their ability to select the properties that best describe the biological activity of the compounds. The criteria used for comparing surface fits of all models were the coefficient of determination r2 and the standard deviation of the error, s(e). The ANN method gave a better correlation, r2 = 0.96, compared with either MLR, r2 = 0.81, or FS, r2 = 0.92, and also a lower standard error, possibly indicating non-linearity in the data. The ANN was shown to generalize better than MLR using the leave-one-out method. The ANN selection algorithm for the selection of the parameters that contributed most to the biological activity of the phenols (log K and pKa) agreed with the selected parameters of the MLR system.     

Morphological analysis of the division cycle of two Escherichia coli substrains during slow growth.

Morphological parameters of the cell division cycle have been examined in Escherichia coli B/r A and K. Whereas the shape factor (length of newborn cell/width) of the two strains was the same at rapid growth (doubling time, tau, less than 60 min), with decreasing growth rate the dimensions of the two strains did change so that B/r A cells became more rounded and B/r K cells became more elongated. The process of visible cell constriction (T period) lasted longer in B/r A than in B/r K during slow growth, reaching at tau = 200 min values of 40 and 17 min, respectively. The time between termination of chromosome replication and cell division (D period) was found to be longer in B/r A than in B/r K. As a result, in either strain completion of chromosome replication seemed always to occur before initiation of cell constriction. Nucleoplasmic separation did not coincide with termination as during rapid growth but occurred in both strains within the T period, about 10 min before cell division.     

Evolutionary predictions should be based on individual-level traits

Recent theoretical studies have analyzed the evolution of habitat specialization using either the logistic or the Ricker equation. These studies have implemented evolutionary change directly in population-level parameters such as habitat-specific intrinsic growth rates r or carrying capacities K. This approach is a shortcut to a more detailed analysis where evolutionary change is studied in underlying morphological, physiological, or behavioral traits at the level of the individual that contribute to r or K. Here we describe two pitfalls that can occur when such a shortcut is employed. First, population-level parameters that appear as independent variables in a population dynamical model might not be independent when derived from processes at the individual level. Second, patterns of covariation between individual-level traits are usually not conserved when mapped to the level of demographic parameters. Nonlinear mappings constrain the curvature of trade-offs that can sensibly be assumed at the population level. To illustrate these results, we derive a two-habitat version of the logistic and Ricker equations from individual-level processes and compare the evolutionary dynamics of habitat-specific carrying capacities with those of underlying individual-level traits contributing to the carrying capacities. Finally, we sketch how our viewpoint affects the results of earlier studies.     

Parameter optimization by using differential elimination: a general approach for introducing constraints into objective functions

Background

The investigation of network dynamics is a major issue in systems and synthetic biology. One of the essential steps in a dynamics investigation is the parameter estimation in the model that expresses biological phenomena. Indeed, various techniques for parameter optimization have been devised and implemented in both free and commercial software. While the computational time for parameter estimation has been greatly reduced, due to improvements in calculation algorithms and the advent of high performance computers, the accuracy of parameter estimation has not been addressed.

Results

We propose a new approach for parameter optimization by using differential elimination, to estimate kinetic parameter values with a high degree of accuracy. First, we utilize differential elimination, which is an algebraic approach for rewriting a system of differential equations into another equivalent system, to derive the constraints between kinetic parameters from differential equations. Second, we estimate the kinetic parameters introducing these constraints into an objective function, in addition to the error function of the square difference between the measured and estimated data, in the standard parameter optimization method. To evaluate the ability of our method, we performed a simulation study by using the objective function with and without the newly developed constraints: the parameters in two models of linear and non-linear equations, under the assumption that only one molecule in each model can be measured, were estimated by using a genetic algorithm (GA) and particle swarm optimization (PSO). As a result, the introduction of new constraints was dramatically effective: the GA and PSO with new constraints could successfully estimate the kinetic parameters in the simulated models, with a high degree of accuracy, while the conventional GA and PSO methods without them frequently failed.

Conclusions

The introduction of new constraints in an objective function by using differential elimination resulted in the drastic improvement of the estimation accuracy in parameter optimization methods. The performance of our approach was illustrated by simulations of the parameter optimization for two models of linear and non-linear equations, which included unmeasured molecules, by two types of optimization techniques. As a result, our method is a promising development in parameter optimization.

     

The kinetics and thermodynamics of the reaction of solid-state fully reduced membrane-bound cytochrome oxidase with carbon monoxide as studied by dual-wavelength multichannel spectroscopy and flash photolysis.

1. The results of non-linear optimization studies on the mechanism of reaction of solid-state fully reduced membrane-bound cytochrome oxidase with CO over the 178--203 K range are presented. The analysis is carried out on data obtained by dual-wavelength multichannel spectroscopy at three wavelength pairs (444--463 nm, 590--630 nm and 608--630 nm), which yield three distinct progress curves. The only model that satisfies the triple requirement of a standard deviation within the standard error of the data, a random distribution of residuals and good determination of the optimized parameters is a two-species sequential mechanism: flash photolysis yields unliganded cytochrome oxidase and free CO, which then recombine to form species Ic; Ic is then converted into species IIc, which is identical with the cytochrome oxidase-CO complex existing before flash photolysis. All the thermodynamic parameters describing this model are calculated. 2. On the basis of the data obtained from this paper, together with data from potentiometric studies, magnetic susceptibility measurements and i.r. spectroscopy, the chemical identity of the species is suggested.     

Reduced rank proportional hazards model for competing risks

Competing events concerning individual subjects are of interest in many medical studies. For example, leukemia-free patients surviving a bone marrow transplant are at risk of developing acute or chronic graft-versus-host disease, or they might develop infections. In this situation, competing risks models provide a natural framework to describe the disease. When incorporating covariates influencing the transition intensities, an obvious approach is to use Cox's proportional hazards model for each of the transitions separately. A practical problem then is how to deal with the abundance of regression parameters. Our objective is to describe the competing risks model in fewer parameters, both in order to avoid imprecise estimation in transitions with rare events and in order to facilitate interpretation of these estimates. Suppose that the regression parameters are gathered into a p x K matrix B, with p and K as the number of covariates and transitions, respectively. We propose the use of reduced rank models, where B is required to be of lower rank R, smaller than both p and K. One way to achieve this is to write B = AGamma(intercal) with A and Gamma matrices of dimensions p x R and K x R, respectively. We shall outline an algorithm to obtain estimates and their standard errors in a reduced rank proportional hazards model for competing risks and illustrate the approach on a competing risks model applied to 8966 leukemia patients from the European Group for Blood and Marrow Transplantation.     

Three-dimensional biofilm image reconstruction for assessing structural parameters

Parameters representing three-dimensional (3D) biofilm structure are quantified from confocal laser-scanning microscope (CLSM) images. These 3D parameters describe the distribution of biomass pixels within the space occupied by a biofilm; however, they lack a direct connection to biofilm activity. As a result, researchers choose a handful of parameters without there being a consensus on a standard set of parameters. We hypothesized that a select 3D parameter set could be used to reconstruct a biofilm image and that the reconstructed and original biofilm images would have similar activities. To test this hypothesis, an algorithm was developed to reconstruct a biofilm image with parameters identical to those of the original CLSM image. We introduced an objective method to assess the reconstruction algorithm by comparing the activities of the original and reconstructed biofilm images. We found that biofilm images with identical structural parameters showed nearly identical activities and substrate concentration profiles. This implies that the set containing all common structural parameters can successfully describe biofilm structure. This finding is significant, as it opens the door to the next step, of finding a smaller standard set of biofilm structural parameters that can be used to compare biofilm structure.     

Interaction of colchicine with human serum albumin investigated by spectroscopic methods

We investigated the interaction between colchicine and human serum albumin (HSA) by fluorescence and UV-vis absorption spectroscopy. In the mechanism discussion, it was proved that the fluorescence quenching of HSA by colchicine is a result of the formation of colchicines-HSA complex; van der Waals interactions and hydrogen bonds play a major role in stabilizing the complex. The modified Stern-Volmer quenching constant K(a) and corresponding thermodynamic parameters deltaH, deltaG, deltaS at different temperatures were calculated. The distance r between donor (Trp214) and acceptor (colchicine) was obtained according to fluorescence resonance energy transfer (FRET).     

Different Clustering of Genomes Across Life Using the A-T-C-G and Degenerate R-Y Alphabets: Early and Late Signaling on Genome Evolution?

In this study, we have calculated distances between genomes based on our previously developed compositional spectra (CS) analysis. The study was conducted using genomes of 39 species of Eukarya, Eubacteria, and Archaea. Based on CS distances, we produced two different consensus dendrograms for four- and two-letter (purine-pyrimidine) alphabets. A comparison of the obtained structure using purine-pyrimidine alphabet with the standard three-kingdom (3K) scheme reveals substantial similarity. Surprisingly, this is not the case when the same procedure is based on the four-letter alphabet. In this situation, we also found three main clusters-but different from those in the 3K scheme. In particular, one of the clusters includes Eukarya and thermophilic bacteria and a part of the considered Archaea species. We speculate that the key factor in the last classification (based on the A-T-G-C alphabet) is related to ecology: two ecological parameters, temperature and oxygen, distinctly explain the clustering revealed by compositional spectra in the four-letter alphabet. Therefore, we assume that this result reflects two interdependent processes: evolutionary divergence and superimposed ecological convergence of the genomes, albeit another process, horizontal transfer, cannot be excluded as an important contributing factor.