The stability of the Boubaker polynomials expansion scheme (BPES)-based solution to Lotka-Volterra problem

This comment addresses critics on the claimed stability of solution to the accelerated-predator-satiety Lotka-Volterra predator-prey problem, proposed by Dubey al. (2010. A solution to the accelerated-predator-satiety Lotka-Volterra predator-prey problem using Boubaker polynomial expansion scheme. Journal of Theoretical Biology 264, 154-160). Critics are based on incompatibilities between the claimed asymptotic behavior and the presumed Malthusian growth of prey population in absence of predator.     

种间竞争的一个新的数学模型—对经典的Lotka—Vol—terra竞争方程的扩充

本文根据营养动力学理论,建立了一类种间竞争的新的数学模型:它是单种群增长的Cui-Lawson模型,在种间竞争上的推广。新的种间竞争模型克服了经典的种间竞争的Lotka-Volteira方程的局限与不足,具有更广泛和复杂的行为,并在特殊条件下以Lotka-Volterra竞争方程为其特例。因此,新的种间竞争的数学模型是更一般的解释性模型,是对经典的Lotka-Voterra竞争方程的扩充。     

A new solution for maximal clique problem based sticker model

In this paper, we use stickers to construct a solution space of DNA for the maximal clique problem (MCP). Simultaneously, we also apply the DNA operation in the sticker-based model to develop a DNA algorithm. The results of the proposed algorithm show that the MCP is resolved with biological operations in the sticker-based model for the solution space of the sticker. Moreover, this work presents clear evidence of the ability of DNA computing to solve the NP-complete problem. The potential of DNA computing for the MCP is promising given the operational time complexity of O(nxk).     

A clever solution to a vexing problem

F_ST (as well as related measures such as G_ST) has long been used both as a measure of the relative amount of genetic variation between populations and as an indicator of the amount of gene flow among populations. Unfortunately, F_ST and its clones are also sensitive to mutation, particularly when the mutation rate per locus is greater than the migration rate among populations. Relatively high mutation rates cause estimates of F_ST and G_ST to be much lower than researchers sometimes expect, when migration rates are low in the studied species. Several recent suggestions for dealing with this problem have been unsatisfactory for one reason or another, and no general solution exists (if we are not to abandon these otherwise useful measures of differentiation). In an important article in this issue, Jinliang Wang (2015) shows that it is possible to identify whether the genetic markers in a given study are likely to give estimates of F_ST that are strongly affected by mutation. The proposed test is simple and elegant, and with it, molecular ecologists can determine whether the F_ST from their makers can be depended on for further inference about their species’ genome and the demographic forces which shaped its patterns.     

A (not-so-radical) solution to the species problem

What are species? One popular answer is that species are individuals. Here I develop another approach to thinking about species, an approach based on the notion of a lineage. A lineage is a sequence of reproducing entities, individuated in terms of its components. I argue that one can conceive of species as groups of lineages, either organism lineages or population lineages. Conceiving of species as groups of lineages resolves the problems that the individual conception of species is supposed to resolve. It has added the virtue of focusing attention on the characteristic of species that is most relevant to understanding their role in evolutionary processes, namely, the lineage structure of species.     

A commentary on Ridley's cladistic solution to the species problem

The cladistic species concept proposed by Ridley (1989) rests on an undefined notion of speciation and its meaning is thus indeterminate. If the cladistic concept is made determinate through the definition of speciation, then it reduces to a form of whatever species concept is implicit in the definition of speciation and fails to be a truly alternative species concept. The cladistic formalism advocated by Ridley is designed to ensure that species are monophyletic, that they are objectively real entities, and that they are individuals. It is argued that species need not be monophyletic in order to be real entities, and that ancestor-descendant relations are not the only relations that confer individuality on entities. The species problem is recast in terms of a futile quest for a definition of that single kind of entity to which the term species should uniquely apply.     

A solution to the problem of monotone likelihood in Cox regression

The phenomenon of monotone likelihood is observed in the fitting process of a Cox model if the likelihood converges to a finite value while at least one parameter estimate diverges to +/- infinity. Monotone likelihood primarily occurs in small samples with substantial censoring of survival times and several highly predictive covariates. Previous options to deal with monotone likelihood have been unsatisfactory. The solution we suggest is an adaptation of a procedure by Firth (1993, Biometrika 80, 27-38) originally developed to reduce the bias of maximum likelihood estimates. This procedure produces finite parameter estimates by means of penalized maximum likelihood estimation. Corresponding Wald-type tests and confidence intervals are available, but it is shown that penalized likelihood ratio tests and profile penalized likelihood confidence intervals are often preferable. An empirical study of the suggested procedures confirms satisfactory performance of both estimation and inference. The advantage of the procedure over previous options of analysis is finally exemplified in the analysis of a breast cancer study.     

UPGMA树的不惟一性问题及其解决方法

对于一组给定的DNA或蛋白质序列,UPGMA算法构建的二叉进化树可能是不惟一的,其具体拓扑结构与序列输入顺序相关,这一现象通常被称为"tied trees"。提出了UPGMA的一种改进算法——不加权算术平均组群方法(UMGMA),用以解决UPGMA树的不惟一问题。在UPGMA树惟一时,该方法产生的进化树与UPGMA树相同;而在UPGMA树不惟一时,该方法可以产生一棵惟一的、与序列输入顺序无关的多叉进化树,而且该算法还具有一个可调的容差参数,来控制生成进化树的主要分枝结构,这对于突出大规模进化树的总体脉络具有重要意义。     

The cladistic solution to the species problem

The correct explanation of why species, in evolutionary theory, are individuals and not classes is the cladistic species concept. The cladistic species concept defines species as the group of organisms between two speciation events, or between one speciation event and one extinction event, or (for living species) that are descended from a speciation event. It is a theoretical concept, and therefore has the virtue of distinguishing clearly the theoretical nature of species from the practical criteria by which species may be recognized at any one time. Ecological or biological (reproductive) criteria may help in the practical recognition of species. Ecological and biological species concepts are also needed to explain why cladistic species exist as distinct lineages, and to explain what exactly takes place during a speciation event. The ecological and biological species concepts work only as sub-theories of the cladistic species concept and if taken by themselves independently of cladism they are liable to blunder. The biological species concept neither provides a better explanation of species indivudualism than the ecological species concept, nor, taken by itself, can the biological species concept even be reconciled with species individualism. Taking the individuality of species seriously requires subordinating the biological, to the cladistic, species concept.     

A problem with using derivatives to explain the matching law

Herrnstein (1979) recently claimed that the matching law could be derived from an ordinary differential equation. He failed, however, to analyze the dynamic properties of his proposed equation. I show that it implies behavior cannot stabilize in accordance with the matching law. Consequently, Herrnstein's equation cannot explain why matching behavior has been widely observed.     

Convergence to equilibrium states for a reaction-diffusion system modelling the spatial spread of a class of bacterial and viral diseases

A reaction-diffusion system which describes the spatial spread of bacterial diseases is studied. It consists of two nonlinear parabolic equations which concern the evolution of the bacteria population and of the human infective population in an urban community, respectively. Different boundary conditions of the third type are considered, for the two variables. This model is suitable to study oro-faecal transmitted diseases in the European Mediterranean regions. A threshold parameter is introduced such that for suitable values of it the epidemic eventually tends to extinction, otherwise a globally asymptotically stable spatially inhomogeneous stationary endemic state appears. The case in which the bacteria diffuse but the human population does not, has also been considered.Work performed under the auspices of the G.N.A.F.A. [L. M.] and the G.N.F.M. [V. C.] C.N.R. in the context of the Program of Preventive Medicine (Project MPP1), C.N.R., Italy