A stochastic model of gene evolution with chaotic mutations

We develop here a new class of stochastic models of gene evolution in which the mutations are chaotic, i.e. a random subset of the 64 possible trinucleotides mutates at each evolutionary time t according to some substitution probabilities. Therefore, at each time t, the numbers and the types of mutable trinucleotides are unknown. Thus, the mutation matrix changes at each time t. The chaotic model developed generalizes the standard model in which all the trinucleotides mutate at each time t. It determines the occurrence probabilities at time t of trinucleotides which chaotically mutate according to three substitution parameters associated with the three trinucleotide sites. Two theorems prove that this chaotic model has a probability vector at each time t and that it converges to a uniform probability vector identical to that of the standard model. Furthermore, four applications of this chaotic model (with a uniform random strategy for the 64 trinucleotides and with a particular strategy for the three stop codons) allow an evolutionary study of the three circular codes identified in both eukaryotic and prokaryotic genes. A circular code is a particular set of trinucleotides whose main property is the retrieval of the frames in genes locally, i.e. anywhere in genes and particularly without start codons, and automatically with a window of a few nucleotides. After a certain evolutionary time and with particular values for the three substitution parameters, the chaotic models retrieve the main statistical properties of the three circular codes observed in genes. These applications also allow an evolutionary comparison between the standard and chaotic models.     

An Analytical Model of Gene Evolution with 9 Mutation Parameters: An Application to the Amino Acids Coded by the Common Circular Code

We develop here an analytical evolutionary model based on a trinucleotide mutation matrix 64× 64 with nine substitution parameters associated with the three types of substitutions in the three trinucleotide sites. It generalizes the previous models based on the nucleotide mutation matrices 4× 4 and the trinucleotide mutation matrix 64× 64 with three and six parameters. It determines at some time t the exact occurrence probabilities of trinucleotides mutating randomly according to these nine substitution parameters. An application of this model allows an evolutionary study of the common circular code of eukaryotes and prokaryotes and its 12 coded amino acids. The main property of this code is the retrieval of the reading frames in genes, both locally, i.e. anywhere in genes and in particular without a start codon, and automatically with a window of a few nucleotides. However, since its identification in 1996, amino acid information coded by has never been studied. Very unexpectedly, this evolutionary model demonstrates that random substitutions in this code and with particular values for the nine substitutions parameters retrieve after a certain time of evolution a frequency distribution of these 12 amino acids very close to the one coded by the actual genes.     

A Positive Stable Frailty Model for Clustered Failure Time Data with Covariate‐Dependent Frailty

Summary In this article, we propose a positive stable shared frailty Cox model for clustered failure time data where the frailty distribution varies with cluster‐level covariates. The proposed model accounts for covariate‐dependent intracluster correlation and permits both conditional and marginal inferences. We obtain marginal inference directly from a marginal model, then use a stratified Cox‐type pseudo‐partial likelihood approach to estimate the regression coefficient for the frailty parameter. The proposed estimators are consistent and asymptotically normal and a consistent estimator of the covariance matrix is provided. Simulation studies show that the proposed estimation procedure is appropriate for practical use with a realistic number of clusters. Finally, we present an application of the proposed method to kidney transplantation data from the Scientific Registry of Transplant Recipients.     

A Stochastic Compartmental Model with Long Lasting Infusion

Most of the compartmental models in current use to model pharmacokinetic systems are deterministic. Stochastic formulations of pharmacokinetic compartmental models introduce stochasticity through either a probabilistic transfer mechanism or the randomization of the transfer rate constants. In this paper we consider a linear stochastic differential equation (LSDE) which represents a stochastic version of a one‐compartment linear model when input function undergoes random fluctuations. The solution of the LSDE, its mean value and covariance structure are derived. An explicit likelihood function is obtained either when the process is observed continuously over a period of time or when sampled data are available, as it is generally feasible. We discuss some asymptotic properties of the maximum likelihood estimators for the model parameters. Furthermore we develop expressions for two random variables of interest in pharmacokinetics: the area under the time‐concentration curve, M₀(T), and the plateau concentration, x_ss. Finally the estimation procedure is illustrated by an application to real data.     

A Stochastic Epidemic Model with Seasonal Variations in Infection Rate

In this paper we consider a modification of Bailey's stochastic model for the spread of an epidemic when there are seasonal variations in infection rate. The resulting nonlinear model is analyzed by employing the diffusion approximation technique. We have shown that for a large population the process, on suitable scaling and normalization, converges to a non-stationary Ornstein-Uhlenbeck process. Consequently the number of infectives has in the steady state a gaussian distribution.     

A Stochastic Model of Oscillatory Blood Testosterone Levels

A continuous-time, discrete-state stochastic model of testosterone secretion in men is considered. Blood levels of testosterone in men fluctuate periodically with a period of 2–3 h. The deterministic model, on which the stochastic model considered here is based, is well studied and has been shown to have a globally stable fixed point. Thus, no sustained oscillations are possible in the deterministic case. However, the stochastic model does observe periodic, pulsatile behavior. This demonstrates how oscillations can occur due to a switching behavior dependent on the random degradation of testosterone molecules in the system. The Gillespie algorithm is used to simulate the hormone secretion model. Important parameters of the model are discussed and results from the model are compared to experimental observations.     

A Dynamic Logistic Regression Model for Multiple Spell Failure Time Data

The paper deals with discrete-time regression models to analyze multistate-multiepisode failure time data. The covariate process may include fixed and external as well as internal time dependent covariates. The effects of the covariates may differ among different kinds of failures and among successive episodes. A dynamic form of the logistic regression model is investigated and maximum likelihood estimation of the regression coefficients is discussed. In the last section we give an application of the model to the analysis of survival time after breast cancer operation.     

具有混合时滞和脉冲效应的随机反应扩散Cohen-Grossberg神经网络的指数稳定性

研究了一类具有混合时滞和脉冲效应的随机反应扩散Cohen—Grossberg神经网络模型,应用M-矩阵,It微分公式和分析技巧,得到了模型平衡点的全局均方指数稳定性的充分条件,所得结果推广了已有的工作．     

Covariation of Mitochondrial Genome Size with Gene Lengths: Evidence for Gene Length Reduction During Mitochondrial Evolution

Reduction of genome size and gene shortening have been observed in a number of parasitic and mutualistic intracellular symbionts. Reduction of coding capacity is also a unifying principle in the evolutionary history of mitochondria, but little is known about the evolution of gene length in mitochondria. The genes for cytochrome c oxidase subunits I–III, cytochrome b, and the large and small subunit rRNAs are, with very few exceptions, always found on the mitochondrial genome. These resident mitochondrial genes can therefore be used to test whether the reduction in gene lengths observed in a number of intracellular symbionts is also seen in mitochondria. Here we show that resident mitochondrial gene products are shorter than their corresponding counterparts in -proteobacteria and, furthermore, that the reduction of mitochondrial genome size is correlated with a reduction in the length of the corresponding resident gene products. We show that relative genomic AT content, which has been identified as a factor influencing gene lengths in other systems, cannot explain gene length/genome size covariance observed in mitochondria. Our data are therefore in agreement with the idea that gene length evolves as a consequence of selection for smaller genomes, either to avoid accumulation of deleterious mutations or triggered by selection for a replication advantage.     

一类灰色项时间序列模型及其应用

利用灰色系统理论与时间序列分析,提出了带灰色项的时间序列模型,对这类模型进行了分析,给出了建模与预报方法,并将其应用于我国农业产值问题的预报与研究之中,模型的正确性得到了检验．     

以比生长速率时间曲线为基础的生物群体生长数学模型

构建了一个描述限制性环境条件下生物群体生长规律的数学模型。模型中比生长速率(μ)是时间(t)的函数。模型可以很好地拟合多种生物或生物细胞群体生长的延迟期、指数期和稳定期。该模型参数少,模型参数生物学意义明确,计算简单。     

A Stochastic Model for the Synthesis and Degradation of Natural Organic Matter. Part I. Data Structures and Reaction Kinetics

Here we present a stochastic biogeochemical model for the formation, transformation and mineralization of natural organic matter (NOM). The model is agent-based, with each software agent representing a single molecule of defined composition. Molecular properties and reactivities are estimated from composition and environmental parameters. Environmental parameters including temperature, pH, light intensity, dissolved O₂, moisture and enzyme activities are user controlled. Time is treated in discrete steps, and during each step potential reaction probabilities are evaluated for each molecule based on its structure and the environmental parameters. When reactions occur, the molecular composition is modified accordingly. The model uses small natural products and biopolymers for inputs, and the composition of the molecules produced is constrained only by the inputs and reaction stoichiometries, not by pre-defined structures. Example simulations using the program AlphaStep are presented, in which the breakdown of biopolymers and the condensation of small molecules both lead to molecular assemblages with elemental composition and average properties similar to those of aquatic NOM. This batch-reactor model can be expanded to include spatial information and environmental feedback.     

A Stochastic Population Dynamics Model for Aedes Aegypti: Formulation and Application to a City with Temperate Climate

Aedes aegypti is the main vector for dengue and urban yellow fever. It is extended around the world not only in the tropical regions but also beyond them, reaching temperate climates. Because of its importance as a vector of deadly diseases, the significance of its distribution in urban areas and the possibility of breeding in laboratory facilities, Aedes aegypti is one of the best-known mosquitoes. In this work the biology of Aedes aegypti is incorporated into the framework of a stochastic population dynamics model able to handle seasonal and total extinction as well as endemic situations. The model incorporates explicitly the dependence with temperature. The ecological parameters of the model are tuned to the present populations of Aedes aegypti in Buenos Aires city, which is at the border of the present day geographical distribution in South America. Temperature thresholds for the mosquito survival are computed as a function of average yearly temperature and seasonal variation as well as breeding site availability. The stochastic analysis suggests that the southern limit of Aedes aegypti distribution in South America is close to the 15^∘C average yearly isotherm, which accounts for the historical and current distribution better than the traditional criterion of the winter (July) 10°C isotherm.     

Impulsive Vaccination of an SEIRS Model with Time Delay and Varying Total Population Size

Pulse vaccination is an effective and important strategy for the elimination of infectious diseases. A delayed SEIRS epidemic model with pulse vaccination and varying total population size is proposed in this paper. We point out, if R* < 1, the infectious population disappear so the disease dies out, while if R _*; > 1, the infectious population persist. Our results indicate that a long period of pulsing or a small pulse vaccination rate is sufficient condition for the permanence of the model.     

一类具有非线性发生率的带时滞的SIR传染病模型的局部渐近稳定性

基于传统的SIR传染病模型,本文提出了一类具有非线性发生率的带时滞的传染病模型,得出了当S0〈T= μ2＋λ/β,对任意的时间滞后^,无病平衡点岛是局部渐近稳定的;当S0〉 μ2＋λ/β,无病平衡点E0是不稳定的,此时,正平衡点E＋是局部渐近稳定的．     

一个具选择、突变、迁移的群体的遗传差分模型

假设一个群体是由“单位点—双基因”的个体所组成的,在该群体内存在选择、突变、迁移、生死等效应的作用。本文给出了在上述假设下并满足:(1)世代重叠,选择、突变、迁移、生死等效应的作用均在世代遗传之间完成;(2)群体适当大,个体间交配随机,符合孟德尔式遗传;(3)没有任何意外的灾祸等约定的群体遗传的数学模型。通过模型分析,我们能够进一步用数学语言来解释一些生命现象。模型分析指出:虽然某些群体不满足Hardy-Weinberg定律所叙述的条件,但可能具有和Hardy-Weinberg定律的结论相似的结果。该文中还就几个主要参数的变化讨论了群体遗传和进化的某些性质,如平衡等。最后,我们给出了该模型的一个数值例子。     

Synonymous Mutations at the Beginning of the Influenza A Virus Hemagglutinin Gene Impact Experimental Fitness

The fitness effects of synonymous mutations can provide insights into biological and evolutionary mechanisms. We analyzed the experimental fitness effects of all single-nucleotide mutations, including synonymous substitutions, at the beginning of the influenza A virus hemagglutinin (HA) gene. Many synonymous substitutions were deleterious both in bulk competition and for individually isolated clones. Investigating protein and RNA levels of a subset of individually expressed HA variants revealed that multiple biochemical properties contribute to the observed experimental fitness effects. Our results indicate that a structural element in the HA segment viral RNA may influence fitness. Examination of naturally evolved sequences in human hosts indicates a preference for the unfolded state of this structural element compared to that found in swine hosts. Our overall results reveal that synonymous mutations may have greater fitness consequences than indicated by simple models of sequence conservation, and we discuss the implications of this finding for commonly used evolutionary tests and analyses.     

沙坡头人工植被区陆气耦合模式及生物结皮与植被演变的机理研究

论述了研究陆气相互作用的意义和现状。在以前工作基础上,针对腾格里沙漠人工植被区陆气水热传输过程,提出了一个多层陆气耦 .人出了导水率的计算模型和修正后的根系吸水,考虑了结皮层对于土壤水分入渗的影响以及植被演变的过程。陆气耦 地大气,植被,土壤作多层划分,以助于细致了解沿高度分布的各物理量。同时,介绍了当地气候概况和野外观测情况。利用本模式对中国科学院沙坡头沙漠站人工植被区陆气水热交换过程进行了数值模拟,模拟结果与实测值吻合较好,可为当地合理利用水热资源和治理沙漠提供科学依据。     

揭秘鸟类合作繁殖的进化:以青藏高原特有物种地山雀作为模式系统的一项长期努力

鸟类合作繁殖系统的进化机制是行为生态学和进化生态学领域的热点,许多基本理论问题依然悬而未决.青藏高原草甸荒漠气候恶劣、植被贫乏,是地球上独特的生态地理区域.自2004年以来,我们以此极端环境的特有物种地山雀(Parus humilis)为模式系统,探讨合作繁殖系统的特征和适应方式.在掌握合作系统基本结构的基础上,将继续进行长期数据的积累.通过比较帮助者和独立繁殖者的终生适合度,检验亲属选择理论;建立时空尺度上合作繁殖与气候因子的关系,揭露生态压力的作用机制;理清不同种群合作繁殖与婚外父权的关系,阐明遗传单配制作为合作繁殖行为进化的驱动力;联系外源与内源因素,确定合作繁殖物种种群动态的调节机理.地山雀社会系统的神秘需要研究者用不懈的努力去探索.