Neutral Models with Generalised Speciation

Hubbell’s neutral theory claims that ecological patterns such as species abundance distributions can be explained by a stochastic model based on simple assumptions. One of these assumptions, the point mutation assumption, states that every individual has the same probability to speciate. Etienne et al. have argued that other assumptions on the speciation process could be more realistic, for example, that every species has the same probability to speciate (Etienne, et al. in Oikos 116:241–258, 2007). They introduced a number of neutral community models with a different speciation process, and conjectured formulas for their stationary species abundance distribution. Here we study a generalised neutral community model, encompassing these modified models, and derive its stationary distribution, thus proving the conjectured formulas.     

A framework for estimating the fixation time of an advantageous allele in stepping-stone models

Determining how population subdivision increases the fixation time of an advantageous allele is an important problem in evolutionary genetics as this influences many processes. Here, I lay out a framework for calculating the fixation time of a positively selected allele in a subdivided population, as a function of the number of demes present, the migration rate between them and the manner in which they are connected. Using this framework, it becomes clear that a beneficial allele's fixation time is significantly reduced through migration continuously introducing copies of the allele into a newly colonized subpopulation, increasing its frequency within these demes. The effect that migration has on allele frequency needs to be explicitly taken into account to produce a realistic estimate of fixation time. This behaviour is most prominent when demes are arranged on a two-dimensional torus, in comparison with populations where demes are arranged in a circle. This is because each subpopulation is connected to several neighbours over a torus, so that there are multiple paths that an allele can take in order to fix. As a consequence, some demes experience a greater influx and efflux of migrants than others. Analytical results are found to be very accurate when compared to stochastic simulations, and are generally robust if there are a large number of demes, or if the allele is weakly selected for.     

Spatial Stochastic Models for Cancer Initiation and Progression

The multistage carcinogenesis hypothesis has been formulated by a number of authors as a stochastic process. However, most previous models assumed “perfect mixing” in the population of cells, and included no information about spatial locations. In this work, we studied the role of spatial dynamics in carcinogenesis. We formulated a 1D spatial generalization of a constant population (Moran) birth–death process, and described the dynamics analytically. We found that in the spatial model, the probability of fixation of advantageous and disadvantageous mutants is lower, and the rate of generation of double-hit mutants (the so-called tunneling rate) is higher, compared to those for the space-free model. This means that the results previously obtained for space-free models give an underestimation for rates of cancer initiation in the case where the first event is the generation of a double-hit mutant, e.g. the inactivation of a tumor-suppressor gene.     

A spatiotemporal stochastic process model for species spread

We use a spatiotemporal Markov process to model the spread of an ecological population through its environment over time. Available habitat is divided into sites, and a parametric function of spatial variables is used to model the probability that one site is colonized from another. This allows us both to make predictions about the future spread of a population, and to determine which are the important factors governing colonizations. The model evolves in discrete time, allowing the population distribution to change seasonally in accordance with breeding patterns. Discrete time formulations are natural for ecological populations, but are problematic due to difficulties of fitting and predicting over irregular time intervals. The model described here can accommodate years of missing data and can therefore fit and predict at irregular intervals. Two methods of approximating the likelihood are described and applied to ornithological survey data for the woodlark, Lullula arborea, from Thetford Forest in the U.K.     

常用大鼠发热模型研究

目的探讨干酵母、2,4-二硝基酚、脂多糖（LPS）、细菌内毒素引起SD大鼠实验性发热的过程和特点,比较不同浓度外致热原对大鼠发热过程的影响。方法建立大鼠干酵母（2 g/kg、1 g/kg）、2,4-二硝基酚（30mg/kg、15 mg/kg）、LPS（100μg/kg、20μg/kg）、细菌内毒素（120 EU/kg、60 EU/kg）发热模型,记录不同时间点大鼠升温值,绘制各模型平均升温曲线,比较不同大鼠发热模型的发热特点。结果皮下注射干酵母混悬液,注射后2～3 h开始升温,6～7 h达峰值,升温持续20 h;皮下注射2,4-二硝基酚溶液,注射后20 min开始升温,1～1.5 h达峰值,升温持续3～5 h;腹腔注射LPS、细菌内毒素,注射后30 min开始升温,此后升温曲线表现为双相热或三相热,升温持续5～8 h。结论不同外致热原所致SD大鼠发热的过程和特点不同;外致热原浓度不同,所致大鼠发热过程和特点不同。解热试验中,应根据受试药物本身特点选用合适的大鼠发热模型。     

Evolutionary branching of virulence in a single-infection model

This study explores the evolutionary dynamics of pathogen virulence in a single-infection model with density-dependent mortality. Although virulence is not an adaptation of the pathogen per se, it is generally believed to be an inevitable by-product of a pathogen's need to propagate and transmit to new hosts: an increase in virulence will parallel an increase in transmission efficacy. The exact characteristics of the trade-off curve defined by this relationship are important with respect to possible evolutionary scenarios. We conduct a critical function analysis, a method that exposes the evolutionary outcome resulting from trade-offs of arbitrary shape, and find that this simple model can display a wide variety of evolutionary dynamics; comprising multiple stable attractors, evolutionary repellors, and most notably, evolutionary branching points. We identify the conditions under which the different evolutionary outcomes are realised. Our analysis furthermore considers the evolution of coexisting strains, and identifies the trade-off characteristics that will support an evolutionarily stable dimorphic state. We find that an evolutionarily stable dimorphism may exist also in the absence of a branching point in the monomorphic state. The analysis reveals that an evolutionarily stable dimorphism will always be attracting and that no further branching is possible under this model. We discuss our results in relation to the dimension of the environmental feedback inherent in the model, and to results from previous studies and models of evolution of virulence.     

Mathematical Models for Hantavirus Infection in Rodents

Hantavirus pulmonary syndrome is an emerging disease of humans that is carried by wild rodents. Humans are usually exposed to the virus through geographically isolated outbreaks. The driving forces behind these outbreaks is poorly understood. Certainly, one key driver of the emergence of these viruses is the virus population dynamics within the rodent population. Two new mathematical models for hantavirus infection in rodents are formulated and studied. The new models include the dynamics of susceptible, exposed, infective, and recovered male and female rodents. The first model is a system of ordinary differential equations while the second model is a system of stochastic differential equations. These new models capture some of the realistic dynamics of the male/female rodent hantavirus interaction: higher seroprevalence in males and variability in seroprevalence levels.     

New Multicentre Point Charge Models for Molecular Electrostatic Potentials from Semiempirical M0-Calculations

Two quasi-multipole electrostatic models for molecular charge distributions are presented. They assign arrays of point charges to nonhydrogen atoms on the basis of hybrid orbitals or localised molecular orbitals. When used with common semiempirical MO-techniques, they reproduce natural atomic orbital derived point charge (NAO-PC) and ab initio molecular potentials well. The localised orbital technique (LMO-PC) is intuitively more attractive than the hybrid orbital-point charge (HO-PC) method, although the former is more CPU-intensive.Electronic Supplementary Material available.     

Further Results in Indices for Diagnostic Screening II

This article is in continuation of a previous one on properties of diagnostic indices (Bennett, 1976). Results are presented on biases in sample estimates of the sensitivity (ξ) and specificity (η) of a diagnostic test T for a disease, as well as their asymptotic variances. The problem of combining estimates of ξ, η from various clinical centres and obtaining appropriate confidence limits is also discussed. A numerical example is also given. (Tables 1a, b). The log-linear model for ξ, η is also discussed.     

A New Algorithm for Explicit Determination of Variance Component Estimations in Mixed Models and Mixed Classifications of Balanced ANOVA

This paper deals with the balanced case of the analysis of variance. The use of a classification function leads to an easy determination of all possible sources of variation of any mixed classification. For mixed models a new method is derived, which allows to represent explicit the ANOVA-estimations of the variance components respectively the estimation of the mean sum of squares of the fixed effects for all sources of variation. Thereby the corresponding F-quotients and the approximate confidence intervals of variance components are received in a simple way.     

On Testing for Equicorrelation in Random Coefficient Models

Recently BHATTI (1993) considered an efficient estimation of random coefficient model based on survey data. The main objective of this paper is to construct one sided test for testing equicorrelation coefficient in presence of random coefficients using optimal testing procedure. The test statistic is a ratio of quadratic forms in normal variables which is most powerful and point optimal invariant.     

Understanding the Roles of FAK in Cancer: Inhibitors,Genetic Models,and New Insights

Focal adhesion kinase (FAK) is a protein tyrosine kinase that regulates cellular adhesion, motility, proliferation and survival in various types of cells. Interestingly, FAK is activated and/or overexpressed in advanced cancers, and promotes cancer progression and metastasis. For this reason, FAK became a potential therapeutic target in cancer, and small molecule FAK inhibitors have been developed and are being tested in clinical phase trials. These inhibitors have demonstrated to be effective by inducing tumor cell apoptosis in addition to reducing metastasis and angiogenesis. Furthermore, several genetic FAK mouse models have made advancements in understanding the specific role of FAK both in tumors and in the tumor environment. In this review, we discuss FAK inhibitors as well as genetic mouse models to provide mechanistic insights into FAK signaling and its potential in cancer therapy.     

A Sufficient Condition for Reducing Recursions in Hidden Markov Models

In hidden Markov models, the probability of observing a set of strings can be computed using recursion relations. We construct a sufficient condition for simplifying the recursion relations for a certain class of hidden Markov models. If the condition is satisfied, then one can construct a reduced recursion where the dependence on Markov states completely disappears. We discuss a specific example—namely, statistical multiple alignment based on the TKF-model—in which the sufficient condition is satisfied.     

SARS-CoV动物模型研究之中国现状

目的综合对比SARS-CoV感染的恒河猴、布氏田鼠及Lewis大鼠的病理学、免疫学以及病毒的复制与外排情况的变化,来探讨此三种动物在建立SARS模型上的特点。方法SARS病毒感染8只恒河猴、9只Lewis大鼠和20只布氏田鼠,在感染后不同时间安乐死动物,应用光镜对动物的各脏器进行病理观察研究;用病毒分离和RT-PCR方法检测病毒外排与复制的情况;用ELISA法检测动物产生特异性抗体情况。结果在SARS-CoV感染恒河猴、Lewis大鼠和布氏田鼠后,肺组织均出现一定的与人类SARS疾病相似的病理改变,在动物体内均可检测到活病毒或病毒核酸,并可检测到特异性IgG抗体的存在。在病死率上布氏田鼠最高;在病毒的复制与外排方面恒河猴的检出率最高,持续时间最长;在抗体产生情况上恒河猴与Lewis大鼠基本相似;在病理变化上恒河猴病变最重且最为复杂,与人类SARS疾病的病理变化最为接近。结论布氏田鼠,Lewis大鼠,特别是恒河猴动物模型可以用于SARS发病机制、疫苗和药物的研发,恒河猴动物模型是目前研究SARS疾病最理想的动物模型。     

A Monte Carlo Test for Variance Homogeneity in Linear Models

A Monte Carlo procedure is proposed for testing homogeneity of variances in linear models. The method is applicable to a variety of common experimental designs. It is valid when errors are independently normally distributed. Under nonnormality the test is expected to behave robust in a similar fashion as Levene's test. Three examples are given to demonstrate the method.     

A Consideration of Alternative Models for the Initiation of Translation in Eukaryotes

Abstract

Although recent biochemical and genetic investigations have produced some insights into the mechanism of initiation of translation in eukaryotic cells, two aspects of the initiation process remain controversial. One unsettled issue concerns a variety of functions that have been proposed for mRNA binding proteins, including some initiation factors. The need to distinguish between specific and nonspecific binding of proteins to mRNA is discussed herein. The possibility that certain initiation factors might act as RNA helicases is evaluated along with other ideas about the functions of mRNA- and ATP-binding factors. A second controversial issue concerns the universality of the scanning mechanism for initiation of translation. According to the conventional scanning model, the initial contact between eukaryotic ribosomes and mRNA occurs exclusively at the 5' terminus of the message, which is usually capped. The existence of uncapped mRNAs among a few plant and animal viruses has prompted a vigorous search for other modes of initiation. An “internal initiation” mechanism, first proposed for picornaviruses, has received considerable attention. Although a large body of evidence has been adduced in support of such a mechanism, many of the experiments appear flawed or inconclusive. Some suggestions are given for improving experiments designed to test the internal initiation hypothesis.     

Evaluation of the Kullback-Leibler Discrepancy for Model Selection in Open Population Capture-Recapture Models

The objective of this paper is to introduce the logical basis of AIC-based model selection to persons analyzing capture-recapture data and to explore the key theorettical aspect of AIC based model selection, for open-model capture-recapture, needed for AIC to perform well in this context. Almost all previous work on AIC assumes a Gaussian model; that assumption does not hold for capture-recapture models. Assuming the Cormack-Jolly-Seber model as the true model, we used numerical methods to evaluate the expectation of the log-likelihood relative to Akaike's target predictive log-likelihood. The use of this particular target criterion was motivated by the idea of using the Kullback-Leibler discrepancy for model selection, for which Akaike found the bias of the sample log-likelihood was asymptotically K, where K = the number of estimated (by MLE) parameters. In some sense, then, AIC is a bias-adjusted log-likelihood. For a set of 81 plausible cases, we evaluated this bias almost exactly. The ratio of this bias to the first order theory (bias of K) and to second order theory (K + a sample size adjustment) is essentially 1 for these 81 cases. Thus, AIC should be a suitable basis for model selection in open model capture-recapture.     

Two Models for Interaction in a 3-way Analysis of Variance With One Observation Per Cell

The paper shows that three factor interaction can be represented by two different models in a 3-way classification without replications. Each model is developed as a product of the three main effects plus the sum of the products of a main effect and a two-factor interaction. A conditional F-test for non-additivity is derived from each model. A pseudo-correlation exists between the models and as this correlation coefficient tends to unity the models are shown to converge. Extension of the procedure to four-factor interaction and higher is indicated.