Bayesian Inference of the Evolution of a Phenotype Distribution on a Phylogenetic Tree

The distribution of a phenotype on a phylogenetic tree is often a quantity of interest. Many phenotypes have imperfect heritability, so that a measurement of the phenotype for an individual can be thought of as a single realization from the phenotype distribution of that individual. If all individuals in a phylogeny had the same phenotype distribution, measured phenotypes would be randomly distributed on the tree leaves. This is, however, often not the case, implying that the phenotype distribution evolves over time. Here we propose a new model based on this principle of evolving phenotype distribution on the branches of a phylogeny, which is different from ancestral state reconstruction where the phenotype itself is assumed to evolve. We develop an efficient Bayesian inference method to estimate the parameters of our model and to test the evidence for changes in the phenotype distribution. We use multiple simulated data sets to show that our algorithm has good sensitivity and specificity properties. Since our method identifies branches on the tree on which the phenotype distribution has changed, it is able to break down a tree into components for which this distribution is unique and constant. We present two applications of our method, one investigating the association between HIV genetic variation and human leukocyte antigen and the other studying host range distribution in a lineage of Salmonella enterica, and we discuss many other potential applications.     

On the Discrete POISSON-Inverse GAUSSian Distribution

The discrete POISSON-inverse GAUssian distribution is obtained by compounding the POISSON distribution with the inverse-GAUssian distribution. The maximum likelihood of the parameter is discussed. Comparison with the POISSON, negative binomial, POISSON-LINDLEY and the generalized WARING distribution when fitting a distribution to accident statistics data is given.     

空间分布型的形成过程研究

具合影个研究了广义空间分布型和复合空间分布型的形成问题,解释了空间分布型的形成机理,并给出了１１种广义空间分布型和９种复事空间分布型;同时提出了空间分布型的３种判定方法：扩散系数法、空间相关法和参数变动法,它们以可用于区分常见的空间分布型,也可以用于判定分布型的形成过程;为研究空间分布型的形成机理和变化规模提供了有力的手段。以马尾松毛虫的空间分布型的研究结果表明,马尾松毛虫幼虫的空间分布型是复合负     

The generalized lambda distribution as a survival model: The generalized single hit model

The generalized single hit (GSH) distribution has been proposed as a survival distribution for modeling populations with decreasing hazard. This distribution is a member of Turner and Pruitt's [15] generic family of survival distributions. The equivalence of the GSH distribution and a member of the generalized Tukey's lambda distribution is demonstrated. In addition, the GSH is shown to be equivalent to other known distributions, such as Hjorth's IDB and Pearson's type VIII. The GSH is the result of compounding a gamma prior distribution on exponential failure times. Thus, from a modeling viewpoint, the GSH can be used when it is assumed that the population with decreasing hazard is made up of individuals with constant hazards. An example is presented fitting the GSH distribution to censored data by the method of maximum likelihood.     

Sample-Based Vegetation Distribution Information Synthesis

In constructing and visualizing a virtual three-dimensional forest scene, we must first obtain the vegetation distribution, namely, the location of each plant in the forest. Because the forest contains a large number of plants, the distribution of each plant is difficult to obtain from actual measurement methods. Random approaches are used as common solutions to simulate a forest distribution but fail to reflect the specific biological arrangements among types of plants. Observations show that plants in the forest tend to generate particular distribution patterns due to growth competition and specific habitats. This pattern, which represents a local feature in the distribution and occurs repeatedly in the forest, is in line with the “locality” and “static” characteristics in the “texture data”, making it possible to use a sample-based texture synthesis strategy to build the distribution. We propose a vegetation distribution data generation method that uses sample-based vector pattern synthesis. A sample forest stand is obtained first and recorded as a two-dimensional vector-element distribution pattern. Next, the large-scale vegetation distribution pattern is synthesized automatically using the proposed vector pattern synthesis algorithm. The synthesized distribution pattern resembles the sample pattern in the distribution features. The vector pattern synthesis algorithm proposed in this paper adopts a neighborhood comparison technique based on histogram matching, which makes it efficient and easy to implement. Experiments show that the distribution pattern synthesized with this method can sufficiently preserve the features of the sample distribution pattern, making our method meaningful for constructing realistic forest scenes.     

Assessing the Ideal Free Distribution: Do Guppies Use Aggression as Public Information about Patch Quality?

Aggression can be costly to foragers, yet some recent research suggests that foragers should use aggression as a cue to patch quality (the attractive aggression hypothesis). If aggression is predictive of patch quality, then the attractive aggression hypothesis predicts that the distribution of foragers should follow the distribution of aggression. If, instead, aggression is repulsive because it is costly, then the distribution of foragers should diverge from the distribution of aggression. We tested the attractive aggression hypothesis using female guppies, Poecilia reticulata , and found that the distribution of foragers followed the distribution of food, but was unaffected by the distribution of aggression. These data do not support the attractive aggression hypothesis, but instead suggest that the distribution of aggression is a consequence of the distribution of foragers, and that aggression is not used as public information about patch quality.     

The Non-Central Negative Binomial Distribution

The non-central negative binomial distribution is derived by mixing the POISSON distribution with a certain BESSEL function distribution, or the negative binomial distribution with the POISSON distribution. Some properties of the distribution are discussed, including a characterization. The fitting of the distribution to some data are given together with the efficiency for various procedures of estimation.     

Modeling menstrual cycle length using a mixture distribution

In reproductive health studies, epidemiologists are often interested in examining the effects of covariates on menstrual cycle length which is a convenient, noninvasive measure of women's ovarian and reproductive function. Previous literature (Harlow and Zeger, 1991) suggests that the distribution of cycle length is a mixture of a major symmetric distribution and a component featuring a long right tail. Motivated by the shape of this marginal distribution, we propose a mixture distribution for cycle length, representing standard cycles from a Normal distribution and nonstandard cycles from a shifted Weibull distribution. The parameters are estimated using an estimating equation derived from the score function of an independence working model. The fitted mixture distribution agrees well with the distribution estimated using nonparametric approaches. We propose two measures to help determine whether a cycle is standard or nonstandard, developing tools necessary to identify characteristics of the menstrual cycles that are biologically indicative of ovarian dysfunction. We model the effect of a woman's age on the mean and variation of both standard and nonstandard cycle lengths using multiple measurements of women.     

A novel generalized normal distribution for human longevity and other negatively skewed data

Negatively skewed data arise occasionally in statistical practice; perhaps the most familiar example is the distribution of human longevity. Although other generalizations of the normal distribution exist, we demonstrate a new alternative that apparently fits human longevity data better. We propose an alternative approach of a normal distribution whose scale parameter is conditioned on attained age. This approach is consistent with previous findings that longevity conditioned on survival to the modal age behaves like a normal distribution. We derive such a distribution and demonstrate its accuracy in modeling human longevity data from life tables. The new distribution is characterized by 1. An intuitively straightforward genesis; 2. Closed forms for the pdf, cdf, mode, quantile, and hazard functions; and 3. Accessibility to non-statisticians, based on its close relationship to the normal distribution.     

Several appropriate background distributions for entropy-based protein sequence conservation measures

Amino acid background distribution is an important factor for entropy-based methods which extract sequence conservation information from protein multiple sequence alignments (MSAs). However, MSAs are usually not large enough to allow a reliable observed background distribution. In this paper, we propose two new estimations of background distribution. One is an integration of the observed background distribution and the position-specific residue distribution, and the other is a normalized square root of observed background frequency. To validate these new background distributions, they are applied to the relative entropy model to find catalytic sites and ligand binding sites from protein MSAs. Experimental results show that they are superior to the observed background distribution in predicting functionally important residues.     

Analysis of temperature factor distribution in high-resolution protein structures.

The temperature factors obtained from X-ray refinement of proteins at high resolution show large variations from one structure to another. However, the B-values expressed in units of standard deviation about their mean value (B'-factor) at the C alpha atoms show remarkably characteristic frequency distribution. In all of the 110 proteins examined in this study, the frequency distribution exhibited a bimodal distribution. The peaks in the B'-factor frequency distribution occur at -1.1 and 0.4 for a bin size of 0.5. The peak at lower temperature factor corresponds largely to buried residues, whereas the peak at larger value corresponds to exposed residues. The distribution could be accurately described as a superposition of two Gaussian functions. The parameters describing the distribution are therefore characteristic of protein structures. The frequency distribution for a given amino acid over all the proteins also shows a similar bimodal distribution, although the areas under the two Gaussians differ from one amino acid to another. The area under the frequency distribution curve for any interval in B'-factor represents the propensity of the amino acid to occur in that interval. This propensity is related both to the hydrophilicity/hydrophobicity of the residue and the tendency of the residue to impose a different degree of rigidity on the polypeptide chain. The frequency distribution of stretches of high B'-factors departs appreciably from that expected for a random distribution. The correlation in the B-values of sequentially proximal residues is probably responsible for the bimodal distribution.     

Modeling the simple epidemic with deterministic differential equations and random initial conditions

In a simple epidemic the only transition in the population is from susceptible to infected and the total population size is fixed for all time. This paper investigates the effect of random initial conditions on the deterministic model for the simple epidemic. By assuming a Beta distribution on the initial proportion of susceptibles, we define a distribution that describes the proportion of susceptibles in a population at any time during an epidemic. The mean and variance for this distribution are derived as hypergeometric functions, and the behavior of these functions is investigated. Lastly, we define a distribution to describe the time until a given proportion of the population remains susceptible. A method for finding the quantiles of this distribution is developed and used to make confidence statements regarding the time until a given proportion of the population is susceptible.     

A simple method for the determination of DNA molecular weight distribution

A method is described for the molecular weight distribution of DNA which is determined from sedimentation-velocity analysis. Knowing the distribution of sedimentation coefficients for a single DNA concentration it is possible to extrapolate such a distribution to infinite dilution of the solute in a simple way. Two versions (using two or three terms of a series) of extrapolating equations are considered and discussed in detail. The sedimentation coefficients distribution calculated from these equations differs only insignificantly with that obtained in a conventional way.     

Optimal nitrogen distribution within a leaf canopy under direct and diffuse light

Nitrogen distribution within a leaf canopy is an important determinant of canopy carbon gain. Previous theoretical studies have predicted that canopy photosynthesis is maximized when the amount of photosynthetic nitrogen is proportionally allocated to the absorbed light. However, most of such studies used a simple Beer's law for light extinction to calculate optimal distribution, and it is not known whether this holds true when direct and diffuse light are considered together. Here, using an analytical solution and model simulations, optimal nitrogen distribution is shown to be very different between models using Beer's law and direct–diffuse light. The presented results demonstrate that optimal nitrogen distribution under direct–diffuse light is steeper than that under diffuse light only. The whole‐canopy carbon gain is considerably increased by optimizing nitrogen distribution compared with that in actual canopies in which nitrogen distribution is not optimized. This suggests that optimization of nitrogen distribution can be an effective target trait for improving plant productivity.     

GEOGRAPHIC DISTRIBUTION AND POTENTIAL DISTRIBUTION ESTIMATION OF PSEUDOTAXUS CHIENII

 利用Diva-Gis软件对东亚特有单种属植物白豆杉(Pseudotaxus chienii)的地理分布格局进行研究。结合海拔图层和植被图层绘制白豆杉的分布图, 并用Diva-Gis中整合的Bioclim和Domain两个生态模型估测了白豆杉的潜在分布区。结果表明, 白豆杉分布在长江以南地区中低海拔450~1 500 m山区山坡林下、沟谷地带及溪边灌丛中, 浙江地区为白豆杉分布最为密集的地区。白豆杉的分布与植被类型和海拔有着密切的关系, 分布区的植被类型为常绿灌木林、阔叶林及常绿针阔叶混交林; 由东到西, 分布的最低海拔升高, 海拔范围缩小, 白豆杉资源量减少。白豆杉潜在分布区为浙、闽、粤、赣、湘、桂及黔几省及其交界处, 从浙江南部山区沿武夷山山系至南岭山系(向北到湘赣交界的罗宵山系甚至可以延伸到大别山系)至大瑶山山系(向北沿雪峰山)。保护方式应以就地保护为主, 同时兼顾其未来潜在的分布区, 关键是对白豆杉的适生区生境的保护。     

GIS在野生动物空间分布格局研究中的应用

地理信息系统(GIS)在绘制动物分布图、确定物种丰富度、预测动物的空间分布格局、建立物种分布数据库等方面都有极大的应用价值。本文介绍了GIS技术在野生动物空间分布格局研究中的应用,并探讨了今后GIS技术在野生动物生态学领域的应用前景。     

Exponentiated Exponential Family: An Alternative to Gamma and Weibull Distributions

In this article we study some properties of a new family of distributions, namely Exponentiated Exponential distribution, discussed in Gupta , Gupta , and Gupta (1998). The Exponentiated Exponential family has two parameters (scale and shape) similar to a Weibull or a gamma family. It is observed that many properties of this new family are quite similar to those of a Weibull or a gamma family, therefore this distribution can be used as a possible alternative to a Weibull or a gamma distribution. We present two real life data sets, where it is observed that in one data set exponentiated exponential distribution has a better fit compared to Weibull or gamma distribution and in the other data set Weibull has a better fit than exponentiated exponential or gamma distribution. Some numerical experiments are performed to see how the maximum likelihood estimators and their asymptotic results work for finite sample sizes.     

A first principles derivation of animal group size distributions

Several empirical studies have shown that the animal group size distribution of many species can be well fit by power laws with exponential truncation. A striking empirical result due to Niwa is that the exponent in these power laws is one and the truncation is determined by the average group size experienced by an individual. This distribution is known as the logarithmic distribution. In this paper we provide first principles derivation of the logarithmic distribution and other truncated power laws using a site-based merge and split framework. In particular, we investigate two such models. Firstly, we look at a model in which groups merge whenever they meet but split with a constant probability per time step. This generates a distribution similar, but not identical to the logarithmic distribution. Secondly, we propose a model, based on preferential attachment, that produces the logarithmic distribution exactly. Our derivation helps explain why logarithmic distributions are so widely observed in nature. The derivation also allows us to link splitting and joining behavior to the exponent and truncation parameters in power laws.     

An Estimation Procedure for the Joint Distribution of Spatial Direction and Thickness of Flat Bodies Using Vertical Sections Part I: Theoretical Considerations

In soil micromorphology fissures are considered in vertical sections. To get information about the properties of the soil the joint distribution of spatial direction and width is of interest. The fissures are mathematically generalized to flat bodies which form a stationary weighted surface process with the weight “thickness”. Because of stationarity a joint distribution of spatial direction and thickness exists in a “typical point” of the surface process. A suitable parametric family of distributions is assumed. The corresponding parameters can be estimated from measurements on the vertical sections. But on the sections only the visible thickness and the visible angle of a fissure can be measured. Therefore the joint distribution of these variables is expressed by the joint spatial distribution of spatial direction and thickness. This derived distribution depends on the same parameters. The Chi-Square method is proposed for the parameter estimation. The estimation procedure is demonstrated using the Bingham-Mardia distribution for the direction and the lognormal distribution for the thickness and by defining a way to correlate the mean thickness and the direction.     

公平视角下护理人员绩效工资分配的改善策略

描述了医疗机构护理人员绩效工资分配办法的现状,在提出基本工资发放存在显性不公平的基础上,进一步揭露了绩效工资分配中的隐性不公平问题,即基本工资较高一方侵占了工资较低一方的部分绩效工资。同时,提出绩效工资分配中隐性不公平程度与护理人员的工资差距和低工资护理人员的数量密切相关。针对传统分配办法的隐性不公平现象,提出了改善绩效工资分配不公平的策略并对改进的效果进行了验证。最后,指出了新型绩效工资分配办法的主要功能主要在于改进公平,而不是提高效率,并应用利益相关者分析方法,对新型分配制度的可行性进行了分析和讨论。