Under-smoothed kernel confidence intervals for the hazard ratio based on censored data

In cancer clinical trials, it is often of interest in estimating the ratios of hazard rates at some specific time points during the study from two independent populations. In this paper, we consider nonparametric confidence interval procedures for the hazard ratio based on kernel estimates for the hazard rates with under-smoothing bandwidths. Two methods are used to derive the confidence intervals: one based on the asymptotic normality of the ratio of the kernel estimates for the hazard rates in two populations and another through Fieller's Theorem. The performances of the proposed confidence intervals are evaluated through Monte-Carlo simulations and applied to the analysis of data from a clinical trial on early breast cancer.     

一个具有扩散和时滞的捕食模型的持久性与周期解的存在性

对一类在斑块环境下具有Beddington型功能性反应和时滞现象的非自治捕食系统进行了研究,证明系统在适当的条件下是永久持续生存的;利用重合度理论,得到了一组保证该系统存在正周期解的充分条件．     

Independence and interdependence in the nest-site choice by honeybee swarms: Agent-based models, analytical approaches and pattern formation

In a recent paper List, Elsholtz and Seeley (List et al., 2009) have devised an agent-based model of the nest-choice dynamics in swarms of honeybees, and have concluded that both interdependence and independence are needed for the bees to reach a consensus on the best nest site. We here present a simplified version of the model which can be treated analytically with the tools of statistical physics and which largely has the same features as the original dynamics. Based on our analytical approaches it is possible to characterize the co-ordination outcome exactly on the deterministic level, and to a good approximation if stochastic effects are taken into account, reducing the need for computer simulations on the agent-based level. In the second part of the paper we present a spatial extension, and show that transient non-trivial patterns emerge, before consensus is reached. Approaches in terms of Langevin equations for continuous field variables are discussed.     

The prediction of adaptive evolution: empirical application of the secondary theorem of selection and comparison to the breeder's equation

Adaptive evolution occurs when fitness covaries with genetic merit for a trait (or traits). The breeder's equation (BE), in both its univariate and multivariate forms, allows us to predict this process by combining estimates of selection on phenotype with estimates of genetic (co)variation. However, predictions are only valid if all factors causal for trait-fitness covariance are measured. Although this requirement will rarely (if ever) be met in practice, it can be avoided by applying Robertson's secondary theorem of selection (STS). The STS predicts evolution by directly estimating the genetic basis of trait-fitness covariation without any explicit model of selection. Here we apply the BE and STS to four morphological traits measured in Soay sheep (Ovis aries) from St. Kilda. Despite apparently positive selection on heritable size traits, sheep are not getting larger. However, although the BE predicts increasing size, the STS does not, which is a discrepancy that suggests unmeasured factors are upwardly biasing our estimates of selection on phenotype. We suggest this is likely to be a general issue, and that wider application of the STS could offer at least a partial resolution to the common discrepancy between naive expectations and observed trait dynamics in natural populations.     

Natural selection. IV. The Price equation

The Price equation partitions total evolutionary change into two components. The first component provides an abstract expression of natural selection. The second component subsumes all other evolutionary processes, including changes during transmission. The natural selection component is often used in applications. Those applications attract widespread interest for their simplicity of expression and ease of interpretation. Those same applications attract widespread criticism by dropping the second component of evolutionary change and by leaving unspecified the detailed assumptions needed for a complete study of dynamics. Controversies over approximation and dynamics have nothing to do with the Price equation itself, which is simply a mathematical equivalence relation for total evolutionary change expressed in an alternative form. Disagreements about approach have to do with the tension between the relative valuation of abstract versus concrete analyses. The Price equation's greatest value has been on the abstract side, particularly the invariance relations that illuminate the understanding of natural selection. Those abstract insights lay the foundation for applications in terms of kin selection, information theory interpretations of natural selection and partitions of causes by path analysis. I discuss recent critiques of the Price equation by Nowak and van Veelen.     

Statistics of canonical RNA pseudoknot structures

In this paper we study canonical RNA pseudoknot structures. We prove central limit theorems for the distributions of the arc-numbers of k-noncrossing RNA structures with given minimum stack-size τ over n nucleotides. Furthermore we compare the space of all canonical structures with canonical minimum free energy pseudoknot structures. Our results generalize the analysis of Schuster et al. obtained for RNA secondary structures [Hofacker, I.L., Schuster, P., Stadler, P.F., 1998. Combinatorics of RNA secondary structures. Discrete Appl. Math. 88, 207–237; Jin, E.Y., Reidys, C.M., 2007b. Central and local limit theorems for RNA structures. J. Theor. Biol. 250 (2008), 547–559; 2007a. Asymptotic enumeration of RNA structures with pseudoknots. Bull. Math. Biol., 70 (4), 951–970] to k-noncrossing RNA structures. Here k2 and τ are arbitrary natural numbers. We compare canonical pseudoknot structures to arbitrary structures and show that canonical pseudoknot structures exhibit significantly smaller exponential growth rates. We then compute the asymptotic distribution of their arc-numbers. Finally, we analyze how the minimum stack-size and crossing number factor into the distributions.     

Does Dormancy Increase Fitness of Bacterial Populations in Time-Varying Environments?

A simple family of models of a bacterial population in a time varying environment in which cells can transit between dormant and active states is constructed. It consists of a linear system of ordinary differential equations for active and dormant cells with time-dependent coefficients reflecting an environment which may be periodic or random, with alternate periods of low and high resource levels. The focus is on computing/estimating the dominant Lyapunov exponent, the fitness, and determining its dependence on various parameters and the two strategies—responsive and stochastic—by which organisms switch between dormant and active states. A responsive switcher responds to good and bad times by making timely and appropriate transitions while a stochastic switcher switches continuously without regard to the environmental state. The fitness of a responsive switcher is examined and compared with fitness of a stochastic switcher, and with the fitness of a dormancy-incapable organism. Analytical methods show that both switching strategists have higher fitness than a dormancy-incapable organism when good times are rare and that responsive switcher has higher fitness than stochastic switcher when good times are either rare or common. Numerical calculations show that stochastic switcher can be most fit when good times are neither too rare or too common. This research was supported by NSF Grant DMS 0414270, Department of Mathematics, Arizona State University, Tempe, AZ.     

Knowing your habitat: linking patch-encounter rate and patch exploitation in parasitoids

According to optimal foraging theory, animals should decidewhether or not to leave a resource patch by comparing the currentprofitability of the patch with the expected profitability ofsearching elsewhere in the habitat. Although there is abundantevidence in the literature that foragers in general are wellable to estimate the value of a single resource patch, theirdecision making has rarely been investigated with respect tohabitat quality. This is especially true for invertebrates.We have conducted experiments to test whether parasitic waspsadjust patch residence time and exploitation in relation tothe abundance of patches within the environment. We used thebraconid Asobara tabida, a parasitoid of Drosophila larvae,as our model species. Our experiments show that these waspsreduce both the residence time and the degree of patch exploitationwhen patches become abundant in their environment, as predictedby optimal foraging models. Based upon a detailed analysis ofwasp foraging behavior, we discuss proximate mechanisms thatmight lead to the observed response. We suggest that parasitoidsuse a mechanism of sensitization and desensitization to chemicalsassociated with hosts and patches, in order to respond adaptivelyto the abundance of patches within their environment.     

遗传密码格式的组合编码数分析

用N个密码子对m个编码对象进行编码的编码格式是m元N维空间中的一个顶点。64个密码子对20种氨基酸和终止密码子进行编码格式的组合编码数是一个十分巨大的数字。对多元高维编码空间的拓扑特性进行了分析和研究 ,并由此推导出m -N空间的特性三角的排列方式以及给出特性三角公式的数学证明。指出 ,目前的遗传密码的编码格式是21元64维编码空间的一个顶点。应用组合数学分析的方法 ,计算了遗传密码格式的最大组合编码数CM =4.19×1084 ,基因组遗传密码的组合编码数CG =1.13×1080 以及线粒体遗传密码的组合编码数CT =1.38×1079 等。分析结果表明 ,遗传密码的指定是一个小概率事件 ,可能来源于λ简并后的偶数三联密码配对的组合编码的对称破缺     

The distribution of rare alleles

Population geneticists have long been interested in the behavior of rare variants. The definition of a rare variant has been the subject of some debate, centered mainly on whether alleles with small relative frequency should be considered rare, or whether alleles with small numbers should be. We study the behavior of the counts of rare alleles in samples taken from a population genetics model that allows for selection and infinitely-many-alleles mutation structure. We show that in large samples the counts of rare alleles — those represented once, twice, ... — are approximately distributed as a Poisson process, with a parameter that depends on the total mutation rate, but not on the selection parameters. This result is applied to the problem of estimating the fraction of neutral mutations.