A Stochastic Model for Estimating Adolescent Sterility

In this article, a simple stochastic model for the time to first conception of a cohort of married women is developed, by identifying three states, ‘adolescent sterile’, ‘ovulating’ and ‘conceived‘, into which they can be placed. It is demonstrated that the model provides a close fit to observed data. The estimates of the parameters in the model, can be used to calculate the number of women in each state at different points of time and also to obtain estimates of the probabilities of conception for the two categories of women, adolescent sterile and biologically mature.     

A Stochastic Model for Coupled Enzyme System

The molecular biology of transformed cancer cells singles out key enzymes as sensitive targets of anti-cancer drugs. Here we use one substrate–one intermediate–one final product model for a coupled enzyme system. The transfer rates for the mechanism are taken as continuous but subject to random fluctuations. Explicit formulae for the first moments of the distribution of the process are obtained. These formulae allow us to take into account not only the variability between the subjects, but also the variability of the process for a single subject. The present results allow us also to build the prediction interval for a particular time period given the observations for some preceding moments.     

单位点孢子体-配子体互作模型中不育基因的位置和效应的估计方法

水稻籼粳亚种间杂交F1通常表现为高度不育,这种不育性的一种遗传学解释称为单位点孢子体-配子体互作模型.为了研究这种不育性,提出了一种统计方法,可以估计单位点孢子体-配子体互作模型中不育基因位点的位置和效应.该方法利用回交群体中呈现异常分离的标记位点,用最大似然法对不育基因与标记位点之间的重组率和雌配子存活率进行估计.由于所依据的是非连续变异的遗传标记的分离,而不是连续分布的配子育性指标,因此可以避免由育性直接估计所带来的重组率结果的不稳定.     

A Derivative Matching Approach to Moment Closure for the Stochastic Logistic Model

Continuous-time birth-death Markov processes serve as useful models in population biology. When the birth-death rates are nonlinear, the time evolution of the first n order moments of the population is not closed, in the sense that it depends on moments of order higher than n. For analysis purposes, the time evolution of the first n order moments is often made to be closed by approximating these higher order moments as a nonlinear function of moments up to order n, which we refer to as the moment closure function. In this paper, a systematic procedure for constructing moment closure functions of arbitrary order is presented for the stochastic logistic model. We obtain the moment closure function by first assuming a certain separable form for it, and then matching time derivatives of the exact (not closed) moment equations with that of the approximate (closed) equations for some initial time and set of initial conditions. The separable structure ensures that the steady-state solutions for the approximate equations are unique, real and positive, while the derivative matching guarantees a good approximation, at least locally in time. Explicit formulas to construct these moment closure functions for arbitrary order of truncation n are provided with higher values of n leading to better approximations of the actual moment dynamics. A host of other moment closure functions previously proposed in the literature are also investigated. Among these we show that only the ones that achieve derivative matching provide a close approximation to the exact solution. Moreover, we improve the accuracy of several previously proposed moment closure functions by forcing derivative matching.     

A Stochastic Model for Oviposition Tactics in the Bean Weevil

In a recent paper, MITCHELL (1975) experimentally investigated the oviposition behavior of weevils on mung beans. In this paper, we develop a stochastic model to study the oviposition tactics of the female weevils on beans.     

Stochastic analogues of deterministic single-species population models

Although single-species deterministic difference equations have long been used in modeling the dynamics of animal populations, little attention has been paid to how stochasticity should be incorporated into these models. By deriving stochastic analogues to difference equations from first principles, we show that the form of these models depends on whether noise in the population process is demographic or environmental. When noise is demographic, we argue that variance around the expectation is proportional to the expectation. When noise is environmental the variance depends in a non-trivial way on how variation enters into model parameters, but we argue that if the environment affects the population multiplicatively then variance is proportional to the square of the expectation. We compare various stochastic analogues of the Ricker map model by fitting them, using maximum likelihood estimation, to data generated from an individual-based model and the weevil data of Utida. Our demographic models are significantly better than our environmental models at fitting noise generated by population processes where noise is mainly demographic. However, the traditionally chosen stochastic analogues to deterministic models--additive normally distributed noise and multiplicative lognormally distributed noise--generally fit all data sets well. Thus, the form of the variance does play a role in the fitting of models to ecological time series, but may not be important in practice as first supposed.     

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.     

随机时滞Lotka-Volterra模型数值解的收敛性

通常情况下,随机时滞Lotka-Volterra模型没有解析解,因而数值逼近方法是研究其性质的有效工具.本文根据Euler数值方法,利用鞅不等式和Ito公式讨论了一类随机时滞Lotka-Volterra模型数值解的收敛性,给出了数值解收敛于解析解的条件.最后通过数值算例对数值计算方法进行了验证.     

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 Spatial Dynamical Model for Aedes Aegypti

We develop a stochastic spatial model for Aedes aegypti populations based on the life cycle of the mosquito and its dispersal. Our validation corresponds to a monitoring study performed in Buenos Aires. Lacking information with regard to the number of breeding sites per block, the corresponding parameter (BS) was adjusted to the data. The model is able to produce numerical data in very good agreement with field results during most of the year, the exception being the fall season. Possible causes of the disagreement are discussed. We analyzed the mosquito dispersal as an advantageous strategy of persistence in the city and simulated the dispersal of females from a source to the surroundings along a 3-year period observing that several processes occur simultaneously: local extinctions, recolonization processes (resulting from flight and the oviposition performed by flyers), and colonization processes resulting from the persistence of eggs during the winter season. In view of this process, we suggest that eradication campaigns in temperate climates should be performed during the winter time for higher efficiency.     

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 Model of Gene Evolution with Time Dependent Pseudochaotic Mutations

We develop here a new class of stochastic models of gene evolution in which a random subset of the 64 possible trinucleotides mutates at each evolutionary time t according to some time dependent 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. This pseudochaotic 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 pseudochaotically mutate according to 3 time dependent substitution parameters associated with the 3 trinucleotide sites. The main result proves that under suitable assumptions, this pseudochaotic model converges to a uniform probability vector identical to that of the standard model. Furthermore, an application of this pseudochaotic model allows an evolutionary study of the 3 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 time dependent functions for the 3 substitution parameters, precisely an exponential decrease in the 1st and 2nd trinucleotide sites and an exponential increase in the 3rd one, this pseudochaotic model retrieves the main statistical properties of the 3 circular codes observed in genes. Furthermore, it leads to a circular code asymmetry stronger than the standard model (nonpseudochaotic) and, therefore, to a better correlation with the genes.     

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.     

Stochastic models for cell motion and taxis

Certain biological experiments investigating cell motion result in time lapse video microscopy data which may be modeled using stochastic differential equations. These models suggest statistics for quantifying experimental results and testing relevant hypotheses, and carry implications for the qualitative behavior of cells and for underlying biophysical mechanisms. Directional cell motion in response to a stimulus, termed taxis, has previously been modeled at a phenomenological level using the Keller-Segel diffusion equation. The Keller-Segel model cannot distinguish certain modes of taxis, and this motivates the introduction of a richer class of models which is nevertheless still amenable to statistical analysis. A state space model formulation is used to link models proposed for cell velocity to observed data. Sequential Monte Carlo methods enable parameter estimation via maximum likelihood for a range of applicable models. One particular experimental situation, involving the effect of an electric field on cell behavior, is considered in detail. In this case, an Ornstein- Uhlenbeck model for cell velocity is found to compare favorably with a nonlinear diffusion model.     

A Leap-frog Algorithm for Stochastic Dynamics

Abstract

A third-order algorithm for stochastic dynamics (SD) simulations is proposed, identical to the powerful molecular dynamics leap-frog algorithm in the limit of infinitely small friction coefficient γ. It belongs to the class of SD algorithms, in which the integration time step Δt is not limited by the condition Δt ≤ γ^?1, but only by the properties of the systematic force. It is shown how constraints, such as bond length or bond angle constraints, can be incorporated in the computational scheme. It is argued that the third-order Verlet-type SD algorithm proposed earlier may be simplified without loosing its third-order accuracy. The leap-frog SD algorithm is proven to be equivalent to the verlet-type SD algorithm. Both these SD algorithms are slightly more economical on computer storage than the Beeman-type SD algorithm.     

主要农作物细胞质雄性不育系育性恢复基因研究进展

提升作物产量、抗逆性和品质的主要手段之一是利用杂种优势,其中细胞质雄性不育/恢复(CMS/Rf)系统是应用最广的雄性不育系统。研究细胞质雄性不育系育性恢复机理是"三系"法选育的重要分子遗传学基础。目前,各个作物已经创制了不同类型的不育系。随着分子技术、基因组学和测序技术的深入,大量育性恢复基因已被定位,且部分已被克隆和功能鉴定。针对主要作物中恢复基因的遗传模式,分子标记定位、克隆及CMS/Rf系统在杂交育种中的应用进行了系统总结。希望本文能为今后恢复系分子标记辅助选育,或利用转基因、基因编辑手段创制新恢复系提供思路。     

A Stochastic Model for Surname Evolution

Surnames are inherited in much the same way as biological traits like alleles of one locus. Assuming the heritability of surnames, a simple stochastic model for X, the total number of occurrences of a surname, the Consul distribution defined by the probability mass function: for x = 1, 2, 3,… and zero otherwise and where either (i) m is a positive integer when 0 ≤ θ ≤ 1 such that θ ≦ mθ ≦ 1, or (ii) m≤0, θ ≤0 such that mθ 1, can be arrived at by considering the branching process mechanism. Some applications of the model to real data are also considered.     

Proliferation and Death in a Binary Environment: A Stochastic Model of Cellular Ecosystems

The activation, growth and death of animal cells are accompanied by changes in the chemical composition of the surrounding environment. Cells and their microscopic environment constitute therefore a cellular ecosystem whose time-evolution determines processes of interest for either biology (e.g. animal development) and medicine (e.g. tumor spreading, immune response). In this paper, we consider a general stochastic model of the interplay between cells and environmental cellular niches. Niches may be either favourable or unfavourable in sustaining cell activation, growth and death, the state of the niches depending on the state of the cells. Under the hypothesis of random coupling between the state of the environmental niche and the state of the cell, the rescaled model reduces to a set of four non-linear differential equations. The biological meaning of the model is studied and illustrated by fitting experimental data on the growth of multicellular tumor spheroids. A detailed analysis of the stochastic model, of its deterministic limit, and of normal fluctuations is provided.     

数量性状的基因型值计算

提出了在数量遗传中基因具有固定的量值—基因值的假设;假设认为基因值由基因的分子结构所决定而与所在的杂交组合无关．由此推导出以双亲的基因值向量为变量,数量性状的基因型值为结果的新的数量遗传模型．并给出了具体的计算方法和应用举例．     

刺五加经济产量估测的数学模型

一、前言生物生产量的研究是60年代以来,生态学中一个崭新的领域,随着生产的发展和对自然资源开发利用的需要,愈来愈引起人们的注意,并成为当代生物学研究的中心问题之一。这类研究是以有机物的重量或能量(即生物量和生产力)为指标,研究各生态系统中物质与能量的数量及其固定、消耗、分配、积累与转化的特点,并探讨其与生态因素