质体在非均衡分裂下传递分配的概率

质体非均衡分裂时,其传递和分配情况复杂,重组状态多。本文分析了突变质体在各种分配情况下得到的概率,条件概率、联合概率和一细胞至少含m_0个突变质体的概率公式及计算示例。讨论了它们在生物学中的重要意义。     

On the Assessment of the Performance of Multiple Test Procedures

Based on the concept of the multiple level of significance two criteria for assessing the performance of multiple tests are proposed: The simultaneous power is defined as the probability of rejecting all false null hypotheses. The probability of a correct decision is defined as the probability of correctly rejecting all false null hypotheses and accepting all true ones. Both criteria are discussed for nonstagewise and stagewise procedures in case of independent test statistics. For the example of 5 independently and normally distributed test statistics the values of the two criteria are calcutated under reasonably simple alternatives.     

Maximum Parsimony and the Skewness Test: A Simulation Study of the Limits of Applicability

The maximum parsimony (MP) method for inferring phylogenies is widely used, but little is known about its limitations in non-asymptotic situations. This study employs large-scale computations with simulated phylogenetic data to estimate the probability that MP succeeds in finding the true phylogeny for up to twelve taxa and 256 characters. The set of candidate phylogenies are taken to be unrooted binary trees; for each simulated data set, the tree lengths of all (2n − 5)!! candidates are computed to evaluate quantities related to the performance of MP, such as the probability of finding the true phylogeny, the probability that the tree with the shortest length is unique, the probability that the true phylogeny has the shortest tree length, and the expected inverse of the number of trees sharing the shortest length. The tree length distributions are also used to evaluate and extend the skewness test of Hillis for distinguishing between random and phylogenetic data. The results indicate, for example, that the critical point after which MP achieves a success probability of at least 0.9 is roughly around 128 characters. The skewness test is found to perform well on simulated data and the study extends its scope to up to twelve taxa.     

The role of uncertainty in the conditioned-reflex learning behavior for selected cardiovascular functions]

As a contribution to quantitative analysis of exogenous stress action, the role of probability learning (probability stress, probability affirmation) for selected cardio-vascular functions was studied in 25 albino rats and 8 dogs. It has been shown in the rats learning with probability stress that a dependence exists between stress probability, on the one hand, and conditional-reflectory processes and systolic blood pressure rise, on the other, that is, the pathogenic action of probability stress increases from a probability of p = 1.0 to p = 0.5. An analogous picture was found with the probability affirmation being applied in dogs. While a probability affirmation with p = 1.0 promoted adaptational processes, a value of p = 0.5 led to experimental neurosis, tachycardia and ECG alterations. The results obtained are discussed in context with the information entropy and information theory of emotions.     

P300, probability,and the three-tone paradigm

The effects of stimulus probability on P300 from a 3-tone paradigm were examined in two experiments. Experiment 1 manipulated the probability of the non-target tone as 0.10, 0.45, or 0.80, while the target tone probability was always 0.10. Experiment 2 manipulated the probability of 3 tones as 0.10, 0.30, or 0.60, with one of the infrequent tones assigned as the target in each condition. Subjects were required to press a button in response to the target stimulus in both experiments. The results indicated that the P300 to the target and the non-target were both affected by the probability of the eliciting stimulus, such that component amplitude was inversely related to probability; no reliable P300 latency effects were found. Target tones elicited larger P300 amplitude than the non-target tones at the same probability. The findings suggest that probability effects on P300 amplitude are independent of responding to a specific target stimulus and are discussed with reference to the clinical utility of the 3-tone paradigm.     

Can we model the probability of presence of species without absence data?

In ecological studies, it is useful to estimate the probability that a species occurs at given locations. The probability of presence can be modeled by traditional statistical methods, if both presence and absence data are available. However, the challenge is that most species records contain only presence data, without reliable absence data. Previous presence‐only methods can estimate a relative index of habitat suitability, but cannot estimate the actual probability of presence. In this study, we develop a presence and background learning algorithm (PBL) that is successful in modeling the conditional probability of presence of a simulated species. The model is trained by two completely separate sets: observed presence and background data. Assuming that the probability of presence is one for ‘prototypical presence’ locations where the habitats are maximally suitable for a species, we can estimate a constant that can calibrate the trained model into the actual probability of presence. Experimental results show that the PBL method performs similarly to a presence‐absence method, and significantly better than the widely used maximum entropy method. The new algorithm enables us to model the probability that a species occurs conditional on environmental covariates without absence data. Hence, it has potential to improve modeling of the geographical distributions of species.     

An approximation method for solving the steady-state probability distribution of probabilistic Boolean networks

MOTIVATION: Probabilistic Boolean networks (PBNs) have been proposed to model genetic regulatory interactions. The steady-state probability distribution of a PBN gives important information about the captured genetic network. The computation of the steady-state probability distribution usually includes construction of the transition probability matrix and computation of the steady-state probability distribution. The size of the transition probability matrix is 2(n)-by-2(n) where n is the number of genes in the genetic network. Therefore, the computational costs of these two steps are very expensive and it is essential to develop a fast approximation method. RESULTS: In this article, we propose an approximation method for computing the steady-state probability distribution of a PBN based on neglecting some Boolean networks (BNs) with very small probabilities during the construction of the transition probability matrix. An error analysis of this approximation method is given and theoretical result on the distribution of BNs in a PBN with at most two Boolean functions for one gene is also presented. These give a foundation and support for the approximation method. Numerical experiments based on a genetic network are given to demonstrate the efficiency of the proposed method.     

Waiting for invasions: a framework for the arrival of nonindigenous species

The process of nonindigenous species (NIS) arrival has received limited theoretical consideration despite importance in predicting and preventing the establishment of NIS. We formulate a mechanistically based hierarchical model of NIS arrival and demonstrate simplifications leading to a marginal distribution of the number of surviving introduced individuals from parameters of survival probability and propagule pressure. The marginal distribution is extended as a stochastic process from which establishment emerges with a waiting time distribution. This provides a probability of NIS establishment within a specified period and may be useful for identifying patterns of successful invaders. However, estimates of both the propagule pressure and the individual survival probability are rarely available for NIS, making estimates of the probability of establishment difficult. Alternatively, researchers are able to measure proportional estimates of propagule pressure through models of NIS transport, such as gravity models, or of survival probability through habitat-matching indexes measuring the similarity between potentially occupied and native NIS ranges. Therefore, we formulate the relative waiting time between two locations and the probability of one location being invaded before the other.     

基于ArcView-WOE的下辽河平原地下水生态系统健康评价

地下水生态系统是生态系统的重要类型,随着社会经济的发展,地下水资源与环境压力日益增大,地下水生态系统健康问题已经成为人类重点关注的环境问题之一。以ArcView为平台,以下辽河平原硝酸盐氮浓度为响应因子,并从地下水系统结构特征、区域自然条件、外界压力、资源与保护和生态环境5个方面建立证据因子的图层数据库,利用证据权重法(WOE)对下辽河平原地下水生态系统健康进行评价,得到硝酸盐氮后验概率分布图。结果表明:下辽河平原的西北、东北部、东南部及抚顺和辽阳地区地下水生态系统健康处于相对高和较高概率区,东部山前冲洪积平原及下辽河平原的周边地区处于中等概率区,下辽河平原的中部平原、南部滨海平原地区处于相对低和较低概率区。将地下水水质监测点硝酸盐氮含量与后验概率分布图进行对比分析,发现二者对应性较好,这说明WOE可以用于地下水生态系统健康评价,其概率表现形式能够有效的弥补传统生态系统健康评价结果是一个具体值(或等级)而无法反映生态系统健康不确定性的不足。     

Properties of average score distributions of SEQUEST: the probability ratio method

High throughput identification of peptides in databases from tandem mass spectrometry data is a key technique in modern proteomics. Common approaches to interpret large scale peptide identification results are based on the statistical analysis of average score distributions, which are constructed from the set of best scores produced by large collections of MS/MS spectra by using searching engines such as SEQUEST. Other approaches calculate individual peptide identification probabilities on the basis of theoretical models or from single-spectrum score distributions constructed by the set of scores produced by each MS/MS spectrum. In this work, we study the mathematical properties of average SEQUEST score distributions by introducing the concept of spectrum quality and expressing these average distributions as compositions of single-spectrum distributions. We predict and demonstrate in the practice that average score distributions are dominated by the quality distribution in the spectra collection, except in the low probability region, where it is possible to predict the dependence of average probability on database size. Our analysis leads to a novel indicator, the probability ratio, which takes optimally into account the statistical information provided by the first and second best scores. The probability ratio is a non-parametric and robust indicator that makes spectra classification according to parameters such as charge state unnecessary and allows a peptide identification performance, on the basis of false discovery rates, that is better than that obtained by other empirical statistical approaches. The probability ratio also compares favorably with statistical probability indicators obtained by the construction of single-spectrum SEQUEST score distributions. These results make the robustness, conceptual simplicity, and ease of automation of the probability ratio algorithm a very attractive alternative to determine peptide identification confidences and error rates in high throughput experiments.     

Parameter-free testing of the shape of a probability distribution

The Kolmogorov-Smirnov test determines the consistency of empirical data with a particular probability distribution. Often, parameters in the distribution are unknown, and have to be estimated from the data. In this case, the Kolmogorov-Smirnov test depends on the form of the particular probability distribution under consideration, even when the estimated parameter-values are used within the distribution. In the present work, we address a less specific problem: to determine the consistency of data with a given functional form of a probability distribution (for example the normal distribution), without enquiring into values of unknown parameters in the distribution. For a wide class of distributions, we present a direct method for determining whether empirical data are consistent with a given functional form of the probability distribution. This utilizes a transformation of the data. If the data are from the class of distributions considered here, the transformation leads to an empirical distribution with no unknown parameters, and hence is susceptible to a standard Kolmogorov-Smirnov test. We give some general analytical results for some of the distributions from the class of distributions considered here. The significance level and power of the tests introduced in this work are estimated from simulations. Some biological applications of the method are given.     

Complete Numerical Solution of the Diffusion Equation of Random Genetic Drift

A numerical method is presented to solve the diffusion equation for the random genetic drift that occurs at a single unlinked locus with two alleles. The method was designed to conserve probability, and the resulting numerical solution represents a probability distribution whose total probability is unity. We describe solutions of the diffusion equation whose total probability is unity as complete. Thus the numerical method introduced in this work produces complete solutions, and such solutions have the property that whenever fixation and loss can occur, they are automatically included within the solution. This feature demonstrates that the diffusion approximation can describe not only internal allele frequencies, but also the boundary frequencies zero and one. The numerical approach presented here constitutes a single inclusive framework from which to perform calculations for random genetic drift. It has a straightforward implementation, allowing it to be applied to a wide variety of problems, including those with time-dependent parameters, such as changing population sizes. As tests and illustrations of the numerical method, it is used to determine: (i) the probability density and time-dependent probability of fixation for a neutral locus in a population of constant size; (ii) the probability of fixation in the presence of selection; and (iii) the probability of fixation in the presence of selection and demographic change, the latter in the form of a changing population size.     

A Bayesian framework for the analysis of cospeciation

Abstract.— Information on the history of cospeciation and host switching for a group of host and parasite species is contained in the DNA sequences sampled from each. Here, we develop a Bayesian framework for the analysis of cospeciation. We suggest a simple model of host switching by a parasite on a host phylogeny in which host switching events are assumed to occur at a constant rate over the entire evolutionary history of associated hosts and parasites. The posterior probability density of the parameters of the model of host switching are evaluated numerically using Markov chain Monte Carlo. In particular, the method generates the probability density of the number of host switches and of the host switching rate. Moreover, the method provides information on the probability that an event of host switching is associated with a particular pair of branches. A Bayesian approach has several advantages over other methods for the analysis of cospeciation. In particular, it does not assume that the host or parasite phylogenies are known without error; many alternative phylogenies are sampled in proportion to their probability of being correct.     

Characteristics of the Internal Representation of the Probability Structure of the Environment in Certain Mental Illnesses

In 1935, Pavlov advanced the hypothesis that certain depressive states might be traceable to the subject's incorrect assessment of the probability that some threatening event, for example, a bolt of lightning, would occur.* Recent attempts to verify this hypothesis empirically and to apply it clinically by distinguishing the interacting influences of the real probability and the biological significance of an event have encountered considerable difficulties of a methodological nature. One possible approach to the solution of this problem and to working out equivalent assessments of these two factors is to compare the speed with which conditioned responses to various appropriate ecological stimuli are developed and extinguished (D. A. Biryukov) when the probability of the reinforcement is adequate (D. N. Menitskii, 1964). Another approach is to compare motor reaction times (I. M. Feigenberg). Moreover, the process of decision making and the overall reaction of the organism can be regarded as two discrete steps: (1) construction of a probability model of the environment (perception), and (2) evaluation of the "utility function" (motivation). The two steps are effected by different neurological mechanisms.     

Bayesian Modeling of the Level and Duration of Fertility in the Menstrual Cycle

Time to pregnancy studies that identify ovulation days and collect daily intercourse data can be used to estimate the day-specific probabilities of conception given intercourse on a single day relative to ovulation. In this article, a Bayesian semiparametric model is described for flexibly characterizing covariate effects and heterogeneity among couples in daily fecundability. The proposed model is characterized by the timing of the most fertile day of the cycle relative to ovulation, by the probability of conception due to intercourse on the most fertile day, and by the ratios of the daily conception probabilities for other days of the cycle relative to this peak probability. The ratios are assumed to be increasing in time to the peak and decreasing thereafter. Generalized linear mixed models are used to incorporate covariate and couple-specific effects on the peak probability and on the day-specific ratios. A Markov chain Monte Carlo algorithm is described for posterior estimation, and the methods are illustrated through application to caffeine data from a North Carolina pregnancy study.     

Lines of descent and the coalescent

Some results of Kingman, Griffiths, and Ewens are unified in a probability distribution for the genealogical structure of a random sample of genes. The sample is partitioned into equivalence classes of two types, “old” and “new.” Old classes of genes are each descended from founder genes in a reference ancestral population without mutation, while new classes descend from more-recent mutant founders. From the probability distribution of the partition, some old and some new results are derived concerning allele frequencies in samples.     

On the prediction of simultaneous inbreeding coefficients at multiple loci

A new deterministic method for predicting simultaneous inbreeding coefficients at three and four loci is presented. The method involves calculating the conditional probability of IBD (identical by descent) at one locus given IBD at other loci, and multiplying this probability by the prior probability of the latter loci being simultaneously IBD. The conditional probability is obtained applying a novel regression model, and the prior probability from the theory of digenic measures of Weir and Cockerham. The model was validated for a finite monoecious population mating at random, with a constant effective population size, and with or without selfing, and also for an infinite population with a constant intermediate proportion of selfing. We assumed discrete generations. Deterministic predictions were very accurate when compared with simulation results, and robust to alternative forms of implementation. These simultaneous inbreeding coefficients were more sensitive to changes in effective population size than in marker spacing. Extensions to predict simultaneous inbreeding coefficients at more than four loci are now possible.     

Predicting the probability of slip in gait: methodology and distribution study

The likelihood of a slip is related to the available and required friction for a certain activity, here gait. Classical slip and fall analysis presumed that a walking surface was safe if the difference between the mean available and required friction coefficients exceeded a certain threshold. Previous research was dedicated to reformulating the classical slip and fall theory to include the stochastic variation of the available and required friction when predicting the probability of slip in gait. However, when predicting the probability of a slip, previous researchers have either ignored the variation in the required friction or assumed the available and required friction to be normally distributed. Also, there are no published results that actually give the probability of slip for various combinations of required and available frictions. This study proposes a modification to the equation for predicting the probability of slip, reducing the previous equation from a double-integral to a more convenient single-integral form. Also, a simple numerical integration technique is provided to predict the probability of slip in gait: the trapezoidal method. The effect of the random variable distributions on the probability of slip is also studied. It is shown that both the required and available friction distributions cannot automatically be assumed as being normally distributed. The proposed methods allow for any combination of distributions for the available and required friction, and numerical results are compared to analytical solutions for an error analysis. The trapezoidal method is shown to be highly accurate and efficient. The probability of slip is also shown to be sensitive to the input distributions of the required and available friction. Lastly, a critical value for the probability of slip is proposed based on the number of steps taken by an average person in a single day.     

The Probability Distribution of the Amount of an Individual''s Genome Surviving to the following Generation

The probability that at least p% of an individual's genome is passed on collectively to his children is calculated. With data availability the consideration of the chromosome as a whole rather than discrete loci becomes of increasing practical importance. Assuming the genomic continuum model, which allows for recombination, the crossover process in a chromosome pedigree is viewed as a continuous-time Markov random walk on the vertices of a hypercube with time parameter map distance along the chromosome. The desired probability corresponds to the probability of sojourn times of the process in a small set of vertices, which are well approximated via the Poisson clumping heuristic. Results are given for the human genome. It is very likely that an individual with at least four children passes on at least 90% of his genome. There exists no ``equivalent' number of independently segregating loci for this distribution.