关于单个种群的随机模型的周期解

1.引言众所周知,单个种群的Logistic模型为 dN/dt=N(b-cN), (1.1) 其中,N是种群密度,b和c均为正常数,b/c称为容纳量。(1.1)的平衡点是N=0和N=b/c。其中人们感兴趣的是平衡点N=b/c,它是渐近稳定的。即每个具有初值N(0)>0的解N(t)→b/c,当t→ ∞时。在[1]中,讨论了具有周期性的环境中的Logistic模型(1.1),这时b和c均为周期T的周期函数,[1]给出了存在唯一正周期解的充分条件。在自然界中,一般地说,种群赖以生活的环境都具有随机性。May考虑到环境的随机性提出了一     

红腹缢管蚜空间分布型及抽样技术研究

对红腹缢管蚜的空间分布型及抽样技术进行了研究。 11组样本各项指标均符合聚集分布的检定标准。应用 Taylor幂法则、Iwao回归分析法 ,测定出红腹缢管蚜的空间格局是基本成份为个体群的聚集分布 ,聚集强度随种群密度的升高而增加。聚集原因是昆虫本身行为和环境因素综合影响的结果。应用 Iwao提出的 N=t2D2 (α+1x +β- 1) )公式 ,确定了在一定精确水平下的理论抽样数。当 t=1,m0 =2时 ,序贯抽样的上、下限为 :T(n) =2 n± 6 .8577n。     

带年龄结构的非线性共生模型的稳定性

在[1]中讨论了一般形式的非线性共生模型的稳定性,其中N_1(t)和N_2(t)分别表示 dN_1(t)/dt=f(N_1(t),N_2(t))N_1(t), dN_2(t)/dt=g(N_1(t),N_2(t))N_2(t) (1) t时刻种群1和2的个体总数。这里我们把这个模型按自然方式推广到带年龄结构的两种群共生模型 (?)+μp+f(N_1(t),N_2(t))P_i=0, p(0,t)=integral from n=0 to m_i b_i(r)p(r,t)dr, p_i(r,0)=p_0(r), N(t)=integral from n=0 to m_i p_i(r,t)dr,i=1,2。 (2)     

中立型时滞LOTKA—VOLTERRA系统解的稳定性和振动性

一、引言考虑中立型时滞Lotka-Volterra系统 (t)=N(t)[a_i-sum from j=1 to n b_(ij) N_i(t—τ_(ij))-sum from j=1 to n c_(ij) (t-σ_(ij))],i=1,2,…,n,(E)其中τ_(ij),σ_(ij)∈(0,∞),a,b_(ij),c_(ij)∈R,i,j=1,2,…,n,对正常数平衡点N~*的稳定性和振动性。由于系统(E)是描述种群所组成的生态群落中种群之间互相作用的生态     

大仓鼠种群季节存活率的估算

本文依据夹捕法所获得的大仓鼠种群总数量和孕鼠数量等数据资料,探讨一种估算种群季节存活率的方法。其原理如下: 设NP_K、N_K和D_K分别为第K次取样时孕鼠数量、总数量和采样间隔,L为平均胎仔数,T_1为可见胚胎发育历期,T_2为从胚胎起至其被捕获的平均历期。 首先将各取样时刻的NP_K,N_K依次连接成折线,求出对应时刻t的NP(t)和N(t)。然后可得到t时刻新增加孕鼠数量NNP(t)为NP(t+h)/T_1,这里h=1NT(T_1/2),1NT表示取整函数。若S(t)为t时刻瞬时存活率,且P(t)=S(0)·S(1)……S(t-1),即P(t)为从t=0时刻至t=t时刻之间的总存活率,则有: N(t+1)= S(t)·[N(t)+NNP(t-T_2)·L·P(t)/P(t-T_2)]这样便可求出瞬时存活率S(t)。 将上述计算步骤编译成Basic程序,对1986和1988年河北饶阳县大仓鼠种群季节存活率作了估算。     

种群增长的分段指数模型及其参数估计

本文给出了种群增长的分段指数模型其中N（t）是在时刻t种群的密度,No=N（t0）,r0和rl是群群的内禀增长率,t0是转变点,H（t-t0）=1,t≥t0,H（t-t0）=0,t＜t0．利用非线性模型的正割法（DUD,Doesn’tusederivatives）,可同时确定模型的所有参数（包括交点t0在内）．并用于描述长爪沙鼠种群动态．     

冷蒿种群在放牧干扰下遗传多样性的变化

通过随机扩增多态性 DNA(RAPD)方法检测了放牧干扰下冷蒿种群遗传多样性的变化。 17条 (组 )引物进行 RAPD分析 ,扩增共产生 2 5 4条带 ,其中 2 4 0条为多态性带 ,多态位点百分率达 94 .4 9%。随着放牧强度的增加 ,冷蒿种群多态位点百分数 ,Nei遗传多样性指数、Shannon信息指数均下降 ,种群内个体平均遗传一致度增加。放牧梯度上 4个冷蒿种群 H t=0 .2 116 ,Hs=0 .170 0 ,Dst=0 .0 4 16 ,种群间基因分化系数 Gst=0 .196 5 ,基因流 N*m=2 .0 4 5 1;同时随着放牧强度的增加 ,种群间的 Dst、Gst增加 ,N*m 降低。说明放牧限制了种群间的基因交流 ,使种群发生遗传分化。放牧梯度上的 4个冷蒿种群的遗传距离很小 ,但是随着放牧强度的增加 ,遗传距离在缓慢的增加 ,种群间的遗传一致度降低。根据遗传距离所构建的 U PGMA聚类图中冷蒿 4个种群随着牧压的增加 ,逐级聚在一起。这表明冷蒿种群的遗传分化与放牧强度的关系     

人口增长的数学模型探讨

本文根据人类种群与生物种群的共性与特点,给出一种人口增长的数学模型,并从生态学意义上作一些探讨。一、人口增长的确定性模型在人类种群的动态变化过程中,由于人类世代之间有重叠,因此宏观上可以认为种群数量是连续变化的,可以用一个实值连续函数x=x(t)表示t时刻人类种群的大小。人口运动的基本动态模型可表示为:     

物种多样性指数及其分形分析

提出了一个新的群落α多样性测度方法。定义物种多样性指数DIV =2S -∑Si =1(1/Ni) a,式中S为群落物种数 ,Ni 为种i的个体数 ,a为对个体数敏感程度的控制参数。物种丰富度指数只是DIV指数中参数a =0时的一个特例。在存在自相似性的尺度范围内 ,利用分形维数可以对任意尺度上的群落α多样性进行较为准确地定量描述。以广东黑石顶自然保护区常绿阔叶林作为应用实例进行分析 ,结果表明 ,DIV指数与取样尺度在双对数坐标上的线性相关系数明显高于常用的Shannon指数和Simpson指数。     

瑞士西部农田周围生态保留带中小型兽类种群结构特征及数量动态的初步研究

为了评价生态保留带对小型兽类种群的影响,2003年7月至2004年6月在瑞士西部Salavaux,chevmux和Montbrelloz 3个地区采用标志重捕方法对小型兽类种群进行了研究。在3个生态保留带中,共发现6种1206只小型兽类,其中普通田鼠、小林姬鼠、中麝晌捕获数量多。普通田鼠为优势种。普通田鼠的种群数量在生态保留带间有差异,但具有相同的季节性波动趋势,一般种群数量随着植被覆盖度和食物丰富度的增加,春季末开始出现增加,仲夏达到最高水平。种群中雌雄个体年龄结构之间有明显的差异,成体和亚成体的数量比幼体多,雄性亚成体的数量比雌性多,雌性成体数量比雄性多（X^2=44．09,df=10,P〈0．001,N=203）。普通田鼠种群中雌雄个体体重之间有明显的差异,雄性的体重比雌性大（t一检验：t=5．011,df=162,P〈0．05,N=213）。种群性比之间有明显的月间变化,雌性的捕获次数比雄性大。普通田鼠只在短距离范围内活动,在生态保留带中的巢区为350～400m^2,雌雄个体的巢区大小之间没有显著性差异。     

A study of a Malthusian parameter in relation to some stochastic models of human reproduction

The paper is divided into six sections and is devoted to a study of a Malthusian parameter in relation to some stochastic models of human reproduction. In Section 1, some of the motivations underlying the study are discussed, and in Section 2 some literature on the stochastic model of population growth underlying the foundations of the paper is briefly reviewed. Section 3, which lays the foundations for the study of a more complicated model in Section 4, is devoted to the study of the Malthusian parameter in relation to a stochastic model of human reproduction formulated as a terminating renewal process. In Section 4 the Malthusian parameter is studied in relation to a terminating Markov renewal model of human reproduction, stemming from the work of Perrin and Sheps (1964). Among the mathematical results of independent interest in this section is a complete spectral decomposition of the Laplace-Stieltjes transform of the semi-Markov transition matrix in the model of Perrin and Sheps. Section 5 is devoted to the discussion of a mathematical method which allows accomodating in the model the time taken by an individual to reach reproductive age, and Section 6 ends the paper by supplying bounds for the Malthusian parameter which are valid under quite general conditions. Possible applications of the results in evaluating what influences a population policy may have on population growth are also discussed.     

The diffusion process approach to one-compartmental stochastic models: A mathematical note

We consider the one-dimension (one-compartment) exponential model using a diffusion process approach. In particular, we summarize the known results in the case where the stochastic component of the model is a Gaussian white noise process with mean zero and variance σ². Finally, we briefly illustrate a number of cases where similar forms of model arise.     

A computational model for telomere-dependent cell-replicative aging

Telomere shortening provides a molecular basis for the Hayflick limit. Recent data suggest that telomere shortening also influence mitotic rate. We propose a stochastic growth model of this phenomena, assuming that cell division in each time interval is a random process which probability decreases linearly with telomere shortening. Computer simulations of the proposed stochastic telomere-regulated model provides good approximation of the qualitative growth of cultured human mesenchymal stem cells.     

A study of some diffusion models of population growth

The stochastic differential equations of many diffusion processes which arise in studies of population growth in random environments can be transformed, if the Stratonovich stochastic calculus is employed, to the equation of the Wiener process. If the transformation function has certain properties then the transition probability density function and quantities relating to the time to first attain a given population size can be obtained from the known results for the Wiener process. Some other random growth processes can be derived from the Ornstein-Uhlenbeck process. These transformation methods are applied to the random processes of Malthusian growth, Pearl-Verhulst logistic growth and a recent model of density independent growth due to Levins.     

A Model for Mortality in a Self-thinning Plant Population

A model for mortality process in a self-thinning plant populationis proposed. It considers the spacial process but does not requirepositional information of each individual plant due to the assumptionsthat plants with interacting neighbours all greater than themselvesare the first to die and neighbours' sizes are mutually independentat each growth stage. Mortality of plants of size x at age t,M(t, x), is given as M(t, x) = m{P(t, x)}ⁿ where P(t, x) isthe proportion of plants of size greater than x at age t, andm and n are parameters. This model fits data from an experimentalplantation of Abies sachalinensis and will be useful for furtherdevelopment of the theoretical study of plant population growth. Abies sachalinensis Fr. Schm., self-thinning, mortality, size distribution, neighbourhood effect, spacial process model     

A new mathematical model for combining growth and energy intake in animals: The case of the growing pig

A simultaneous model for analysis of net energy intake and growth curves is presented, viewing the animal's responses as a two dimensional outcome. The model is derived from four assumptions: (1) the intake is a quadratic function of metabolic weight; (2) the rate of body energy accretion represents the difference between intake and maintenance; (3) the relationship between body weight and body energy is allometric and (4) animal intrinsic variability affects the outcomes so the intake and growth trajectories are realizations of a stochastic process. Data on cumulated net energy intake and body weight measurements registered from weaning to maturity were available for 13 pigs. The model was fitted separately to 13 datasets. Furthermore, slaughter data obtained from 170 littermates was available for validation of the model. The parameters of the model were estimated by maximum likelihood within a stochastic state space model framework where a transform-both-sides approach was adopted to obtain constant variance. A suitable autocorrelation structure was generated by the stochastic process formulation. The pigs’ capacity for intake and growth were quantified by eight parameters: body weight at maximum rate of intake (149-281 kg); maximum rate of intake (25.7-35.7 MJ/day); metabolic body size exponent (fixed: 0.75); the daily maintenance requirement per kg metabolic body size (0.232-0.303 MJ/(day×kg^0.75)); reciprocal scaled energy density ; a dimensional exponent, θ₆ (0.730-0.867); coefficient for animal intrinsic variability in intake (0.120-0.248 MJ^0.5) and coefficient for animal intrinsic variability in growth (0.029-0.065 kg^0.5). Model parameter values for maintenance requirements and body energy gains were in good agreement with those obtained from slaughter data. In conclusion, the model provides biologically relevant parameter values, which cannot be derived by traditional analysis of growth and energy intake data.     

Statistical properties of ion channel records. Part II: estimation from the macroscopic current

Macroscopic ion channel current is the summation of the stochastic records of individual channel currents and therefore relates to their statistical properties. As a consequence of this relationship, it may be possible to derive certain statistical properties of single channel records or even generate some estimates of the records themselves from the macroscopic current when the direct measurement of single channel currents is not applicable. We present a procedure for generating the single channel records of an ion channel from its macroscopic current when the stochastic process of channel gating has the following two properties: (I) the open duration is independent of the time of opening event and has a single exponential probability density function (pdf), (II) all the channels have the same probability to open at time t. The application of this procedure is considered for cases where direct measurement of single channel records is difficult or impossible. First, the probability density function (pdf) of opening events, a statistical property of single channel records, is derived from the normalized macroscopic current and mean channel open duration. Second, it is shown that under the conditions (I) and (II), a non-stationary Markov model can represent the stochastic process of channel gating. Third, the non-stationary Markov model is calibrated using the results of the first step. The non-stationary formulation increases the model ability to generate a variety of different single channel records compared to common stationary Markov models. The model is then used to generate single channel records and to obtain other statistical properties of the records. Experimental single channel records of inactivating BK potassium channels are used to evaluate how accurately this procedure reconstructs measured single channel sweeps.     

A stochastic two-phase growth model

This article proposes a stochastic growth model that starts as a Yule process and is subsequently joined with a Prendiville process when the population attains certain prescribed critical size. In other words, the model assumes exponential growth in an early stage and logistic growth later on to reflect growth retardation caused by overcrowding. In the case that the population starts with a single unit, closed form expressions are given for the distribution of the population size and for the mean and variance functions of the process. Numerical solutions are briefly discussed for the process that starts with more than one unit.     

A Simple,Realistic Stochastic Model of Gastric Emptying

Several models of Gastric Emptying (GE) have been employed in the past to represent the rate of delivery of stomach contents to the duodenum and jejunum. These models have all used a deterministic form (algebraic equations or ordinary differential equations), considering GE as a continuous, smooth process in time. However, GE is known to occur as a sequence of spurts, irregular both in size and in timing. Hence, we formulate a simple stochastic process model, able to represent the irregular decrements of gastric contents after a meal. The model is calibrated on existing literature data and provides consistent predictions of the observed variability in the emptying trajectories. This approach may be useful in metabolic modeling, since it describes well and explains the apparently heterogeneous GE experimental results in situations where common gastric mechanics across subjects would be expected.     

A biological and computational model of megakaryocyte development as a stochastic branching process

The purpose of this paper is to describe a model of megakaryocytopoiesis as a branching process with stochastic processes regulating critical control points of differentiation along the stem cell megakaryocyte platelet axis. Progress of cells through these critical control points are regulated by transitional probabilities, which in turn are regulated by influences such as growth factors. The critical control points include transition of resting megakaryocytic stem cells (CFU-meg) into proliferating stem cells, the cessation of cytokinesis, and the cessation of DNA synthesis. A computerized computational method has been developed for directly fitting the stochastic branching model to colony growth data. The computational model has allowed transitional probabilities to be derived from colony size data. The model provides a unifying explanation for much of the heterogeneity of stages of maturation within populations of megakaryocytes and is fully compatible with historical data supporting the stochastic nature of hematopoietic stem cell regulation and with modern molecular concepts about control of the cell cycle.