Markov Model of Haploid Random Mating with Given Distribution of Population Size

An exact Markov chain model is formulated and computed for random mating in a haploid gamete pool. There are two versions of the gamete, and there is a finite number of diploid monoecious organisms. The founder population is given, and the subsequent generations allow a prescribed statistical distribution over different population sizes. The non-homogeneous Markov chain works on the haploid gamete level provided the probability of self-fertilization is 1/n, where n is the number of diploid individuals. Standard deviations of gamete frequencies and fixation probabilities are calculated. Effective population sizes for different population size distributions are estimated, including periodic bottlenecks.     

A Markov Chain Model for Newcastle Disease and its Relevance to the Intracerebral Pathogenicity Index

By modelling the progression of the avian disease caused by Newcastle disease virus (NDV) as a one‐step, time homogeneous Markov Chain (MC) it is possible to set the intracerebral pathogenicity index (ICPI) in a statistical context. Previous assessments of ICPI values for different viruses ignore the fact that the same ICPI value may occur via different sequences of disease status. However, the MC model approach takes into account the state transitions by which an animal came to obtain its particular contribution to the ICPI value. Because the probability that an animal remains normal approaches zero as time increases, the MC model suggests a pathogenicity index based on the multiplying factor that determines this probability's approach to zero. Numerical examples are given with data from NDV pathogenicity trials.     

A Multiple Binary Markov Chain Model for Explaining the Behaviour of Diverse Biological Phenomena

The behaviour of many biological systems can be attributed to that of a large number of units, with each unit swinging between two competing states. During the past few years efforts have been made (e.g., Chung and Kennedy , 1996) to describe such discrete systems using a multiple binary Markov chain model. Here we explore the gamut of these models and classify their behaviour into five qualitatively distinct types, corresponding to subregions of the parameter space. It is suggested that these model behaviours may correspond to behaviours observed in nature. A simple method for fitting the model to data is presented.     

Use of Growth Indices in Markov Chain Models for Crop Yield Forecasting

An improved Markov chain model has been developed for forecasting of sugarcane yields in which growth indices of biometrical characters based on data from two stages simultaneously have been utilised. Comparisons were also made with the models in use viz. the regression model and the first order Markov chain model.     

Bayesian analysis of discrete survival data with a hidden Markov chain

This paper considers the discrete survival data from a Bayesian point of view. A sequence of the baseline hazard functions, which plays an important role in the discrete hazard function, is modeled with a hidden Markov chain. It is explained how the resultant model is implemented via Markov chain Monte Carlo methods. The model is illustrated by an application of real data.     

A Clustering Method for the States of a Markov Chain with an Application to Primate Communication

In some applications clustering problems in stochastic processes arise when the experimenter wants to improve the insight into the structure of the observed system by lumping its states into clusters. As measure of goodness of a cluster solution we choose the rate of predictability of the forthcoming events which can be quantified by means of the entropy of the lumped process. The entropy in turn can be estimated by making use of a Shannon-McMillan-type theorem. We will establish some asymptotic results for the estimate of entropy in the case where the underlying stochastic process is a Markov chain. Our main tool will be a representation of functions of Markov chains which is due to Blackwell (1957). The method proposed here is applied to data on communication processes in monkeys. The object of our analysis will be to find a subgroup structure in the animal group.     

On the estimation of mean parameter with random number of observations on each unit

In this paper an attempt has been made to estimate the population parameter, mean, of a normal population when the number of observations taken on each unit is a random variable and is supposed to follow a Truncated POISSON Distribution.     

A Multiple‐Absorbent Markov Process in Survival Studies: Application to Breast Cancer

A Markov process with several absorbent states is applied for analyzing a breast cancer dataset. The study examines the evolution of patients until death, and shows that two well‐differentiated ways can be considered in the evolution of patients towards the death state: those who relapse and those who not. The risk groups we have considered are determined by the application of treatments radiotherapy and chemotherapy, which are introduced as covariates. Four states are distinguished: no relapse, relapse, death after metastasis, and death without metastasis, the last two absorbent. We apply a methodology that uses algorithmic procedures, avoiding differential equations. The transition probability functions and the likelihood function in the model are calculated. For the dataset, the survival functions and the mean times in states for the different group of risks are determined. We show that the metastasis is the main cause of death in this cohort, but the number of deaths by relapse is not negligible.     

Stochastic model of an influenza epidemic with drug resistance

A continuous-time Markov chain (CTMC) model is formulated for an influenza epidemic with drug resistance. This stochastic model is based on an influenza epidemic model, expressed in terms of a system of ordinary differential equations (ODE), developed by Stilianakis, N.I., Perelson, A.S., Hayden, F.G., [1998. Emergence of drug resistance during an influenza epidemic: insights from a mathematical model. J. Inf. Dis. 177, 863-873]. Three different treatments-chemoprophylaxis, treatment after exposure but before symptoms, and treatment after symptoms appear, are considered. The basic reproduction number, R(0), is calculated for the deterministic-model under different treatment strategies. It is shown that chemoprophylaxis always reduces the basic reproduction number. In addition, numerical simulations illustrate that the basic reproduction number is generally reduced with realistic treatment rates. Comparisons are made among the different models and the different treatment strategies with respect to the number of infected individuals during an outbreak. The final size distribution is computed for the CTMC model and, in some cases, it is shown to have a bimodal distribution corresponding to two situations: when there is no outbreak and when an outbreak occurs. Given an outbreak occurs, the total number of cases for the CTMC model is in good agreement with the ODE model. The greatest number of drug resistant cases occurs if treatment is delayed or if only symptomatic individuals are treated.     

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.     

Testing concordance of clinical characteristics in familial studies with application to inflammatory bowel diseases

The etiology of chronic Inflammatory Bowel Diseases (IBD) remains unknown, with both genetic and environmental risk factors having been implicated. A recent collaborative study of IBD provides clinical data from families with three or more affected first-degree relatives. The scientific question is whether specific clinical characteristics aggregate among affected individuals within families. Gastroenterological researchers have examined the number of concordant familial pairs in familial aggregation studies, but methods and results have been discrepant. This article investigates concepts of concordance and gives a comprehensive statistical treatment for testing concordance of various clinical traits in familial studies. For dichotomous traits, the distribution of this statistic under the null hypothesis of no familial aggregation is obtained by three methods: asymptotic, probability generating function, and permutation. The permutation method is extended to analyze aggregation for non-dichotomous traits and co-aggregations between two traits. We apply the permutation method to analyze the aforementioned multiply-affected IBD family data. Evidence is found for familial clustering of various traits, some of which are not revealed in existing studies. Such analyses provide a basis for investigating the dependence of trait aggregation upon genetic or environmental risk factors.     

A Mathematical Model for the Effect of Water Pollutants on the Growth Pattern of Pollen

The heavy metals as water pollutants had some adverse effects on the growth pattern of pollen grains of the aquatic macrophytes viz. Ottelia, Vallisneria, Hyderilla and Eichhornia. The germination of pollen grains were inversely proportional and the abnormality of pollen tube and the flowering time were directly proportional to the concentration of the heavy metal. In this paper we have presented a mathematical model that is the germinability and the abnormality changes with the log-value of concentration in a straight line fashion. Also the flowering time changes with treatment time in an exponential pattern.     

应用马尔可夫链模型预测长爪沙鼠和黑线仓鼠种群数量

依据1984～2004年21年在呼和浩特郊区对长爪沙鼠(Meriones unguiculatus)和黑线仓鼠(Cricetulus barabansis)种群数量动态的调查数据,结合优选法(0.618法),应用加权马尔可夫链预测模型,建立了长爪沙鼠和黑线仓鼠种群数量预测模型。应用此模型分别预测了长爪沙鼠和黑线仓鼠2004年的种群数量,预测值与实测值相符,预测准确。同时,预测了未来三年(2005～2007年)长爪沙鼠和黑线仓鼠的种群数量。结果表明,此方法计算简便、准确、可靠,为鼠类种群数量的预测提供了新的方法。     

广义隐Markov模型在基因识别中的应用

广义隐Markov模型(GHMM)是基因识别的一种重要模型,但是其计算量比传统的隐Markov模型大得多,以至于不能直 接在基因识别中使用。根据原核生物基因的结构特点,提出了一种高效的简化算法,其计算量是序列长度的线性函数。在此 基础上,构建了针对原核生物基因的识别程序GeneMiner,对实际数据的测试表明,此算法是有效的。     

有限群体中基因频率概率分布的模拟实验

本文采用计算机模拟的方法,对有限群体中基因频率的概率分布进行了研究。 The probability distribution of gene frequency was studied by simulative method in finite population.     

具年龄结构的种群在破碎化生境中的空间分布模型

随着人类和其他生物赖以生存的环境破碎化程度的加剧,许多以前是连续分布的物种,目前不得不在破碎化生境(斑块)中求生存,所以,种群在破碎化生境(斑块)中分布问题的研究对生物保护和生境重建意义重大．本文运用Leslie矩阵和Markov链建立了一个具年龄结构的种群在破碎化生境中随时间动态变化的分布模型,讨论了种群在该生境中持续存在以及灭绝的条件．