Evolutionary dynamics on graphs

Evolutionary dynamics have been traditionally studied in the context of homogeneous or spatially extended populations. Here we generalize population structure by arranging individuals on a graph. Each vertex represents an individual. The weighted edges denote reproductive rates which govern how often individuals place offspring into adjacent vertices. The homogeneous population, described by the Moran process, is the special case of a fully connected graph with evenly weighted edges. Spatial structures are described by graphs where vertices are connected with their nearest neighbours. We also explore evolution on random and scale-free networks. We determine the fixation probability of mutants, and characterize those graphs for which fixation behaviour is identical to that of a homogeneous population. Furthermore, some graphs act as suppressors and others as amplifiers of selection. It is even possible to find graphs that guarantee the fixation of any advantageous mutant. We also study frequency-dependent selection and show that the outcome of evolutionary games can depend entirely on the structure of the underlying graph. Evolutionary graph theory has many fascinating applications ranging from ecology to multi-cellular organization and economics.     

Outage performance of OFDM-based selective decode-and-forward cooperative networks over Weibull fading channels

The outage performance of OFDM-based decode-and-forward cooperative networks is studied.The channels are modeled as independent Weibull distributed coefficients.A closed-form expression for the outage probability is obtained for three selective relaying schemes in the Weibull fading channels and a derived optimum power allocation method based on the closed form expressions of outage probability debases the outage probability.Monte Carlo simulations verify the analytical results.     

进化图论在知识型企业组织结构设计中的应用

 在进化图论的框架下,运用命名为“动态链接”的更新规则来计算空间结构为环路的种群中某突变个体的固定概率,并结合相关理论来分析知识型企业组织结构的合理设计。对不同类型的组织结构模式作进化图进行仿真并做了比较分析,得出的结论是具有环路性质的无边界组织结构是更合理的知识型企业组织结构。这使得进化图论的应用扩展到了经济学。     

Kin selection and eusociality

Arising from M. A. Nowak, C. E. Tarnita & E. O. Wilson 466, 1057-1062 (2010); Nowak et al. reply. Hamilton described a selective process in which individuals affect kin (kin selection), developed a novel modelling strategy for it (inclusive fitness), and derived a rule to describe it (Hamilton's rule). Nowak et al. assert that inclusive fitness is not the best modelling strategy, and also that its production has been "meagre". The former may be debated by theoreticians, but the latter is simply incorrect. There is abundant evidence to demonstrate that inclusive fitness, kin selection and Hamilton's rule have been extraordinarily productive for understanding the evolution of sociality.     

Emergence of cooperation and evolutionary stability in finite populations

To explain the evolution of cooperation by natural selection has been a major goal of biologists since Darwin. Cooperators help others at a cost to themselves, while defectors receive the benefits of altruism without providing any help in return. The standard game dynamical formulation is the 'Prisoner's Dilemma', in which two players have a choice between cooperation and defection. In the repeated game, cooperators using direct reciprocity cannot be exploited by defectors, but it is unclear how such cooperators can arise in the first place. In general, defectors are stable against invasion by cooperators. This understanding is based on traditional concepts of evolutionary stability and dynamics in infinite populations. Here we study evolutionary game dynamics in finite populations. We show that a single cooperator using a strategy like 'tit-for-tat' can invade a population of defectors with a probability that corresponds to a net selective advantage. We specify the conditions required for natural selection to favour the emergence of cooperation and define evolutionary stability in finite populations.     

Interference among deleterious mutations favours sex and recombination in finite populations

Sex and recombination are widespread, but explaining these phenomena has been one of the most difficult problems in evolutionary biology. Recombination is advantageous when different individuals in a population carry different advantageous alleles. By bringing together advantageous alleles onto the same chromosome, recombination speeds up the process of adaptation and opposes the fixation of harmful mutations by means of Muller's ratchet. Nevertheless, adaptive substitutions favour sex and recombination only if the rate of adaptive mutation is high, and Muller's ratchet operates only in small or asexual populations. Here, by tracking the fate of modifier alleles that alter the frequency of sex and recombination, we show that background selection against deleterious mutant alleles provides a stochastic advantage to sex and recombination that increases with population size. The advantage arises because, with low levels of recombination, selection at other loci severely reduces the effective population size and genetic variance in fitness at a focal locus (the Hill-Robertson effect), making a population less able to respond to selection and to rid itself of deleterious mutations. Sex and recombination reveal the hidden genetic variance in fitness by combining chromosomes of intermediate fitness to create chromosomes that are relatively free of (or are loaded with) deleterious mutations. This increase in genetic variance within finite populations improves the response to selection and generates a substantial advantage to sex and recombination that is fairly insensitive to the form of epistatic interactions between deleterious alleles. The mechanism supported by our results offers a robust and broadly applicable explanation for the evolutionary advantage of recombination and can explain the spread of costly sex.     

哈拉里图的可靠性分析

在图的顶点相互独立地以常数据 概率失效的情况下，图的可靠度定义为删除失效顶点及顶关联的边所得到的图连通的概率。对一类具有最佳连通性的图－哈拉里图，得到可靠度的界，并分析了可靠度的渐近性质。     

预测型关联规则演化学习的适应值函数

为了提高基于遗传算法的分类预测准确度,探讨了评价规则质量的适应值函数,提出了基于置信度和支持度加权和的适应值函数,以取代传统的基于灵敏性和选择性的适应值函数．理论分析和实验结果都表明,文中提出的新适应值函数对于预测型关联规则演化搜索的引导作用明显地优于传统的适应值函数．新的适应值函数有利于改进基于遗传算法的机器学习．     

大学课程贝叶斯网络模型研究

提出一种大学课程关系的贝叶斯网络构造方法,以学生课程考试成绩作为数据样本,以基于信息论的结构学习算法构造无向图,最后以课程开设的先后顺序给边定向,得到课程依赖关系的贝叶斯网络,并以数理统计的方法学习其条件概率表。该模型直观的反映了课程间的依赖联系,而条件概率表则量化了联系的紧密程度,对大学课程的设置和编排具有指导作用,对学生成绩具有预测能力。     

具有适应度的无标度网络

提出了一个具有适应度的无标度网络模型。每个时间间隔,网络以概率p增加一个新点,并以适应度择优选择m个旧点与新点连接,产生m条新边;以概率1-p按度数择优的规则在旧点之间生成m条新边。对于一些特定的节点适应度的概率密度函数ρ（x）和率函数f（x,y）,该网络的度分布具有幂律尾部,且幂律指数2〈γ〈＋∞。     

相对于锥的合作或竞争系统的一个证明

利用图论知识结合归纳法,给出了一个系统在区域D中相对于某个锥Km是合作的还是竞争的等价于图G中的闭回路的“-”号边的个数为偶数还是奇数的证明。     

Inclusive fitness in evolution

Arising from M. A. Nowak, C. E. Tarnita & E. O. Wilson 466, 1057-1062 (2010); Nowak et al. reply. For over fifty years, the evolution of social behaviour has been guided by the concept of inclusive fitness as a measure of evolutionary success. Nowak et al. argue that inclusive fitness should be abandoned. In so doing, however, they misrepresent the role that inclusive fitness has played in the theory of social evolution by which understanding social behaviour in a variety of disciplines has developed and flourished. By discarding inclusive fitness on the basis of its limitations, they create a conceptual tension which, we argue, is unnecessary, and potentially dangerous for evolutionary biology.     

Genetic segregation and the maintenance of sexual reproduction

Sexual reproduction confronts evolutionary biology with a paradox: other things being equal, an asexual (all-female) population will have twice the reproductive potential of a competing sexual population and therefore should rapidly drive the sexual population to extinction. Thus, the persistence of sexual reproduction in most life forms implies a compensatory advantage to sexual reproduction. Work on this problem has emphasized the evolutionary advantages produced by the genetic recombination that accompanies sexual reproduction. Here we show that genetic segregation produces an advantage to sexual reproduction even in the absence of an advantage from recombination. Segregation in a diploid sexual population allows selection to carry a single advantageous mutation to a homozygous state, whereas two separate mutations are required in a parthenogenetic population. The complete fixation of advantageous mutations is thus delayed in a heterozygous state in asexual populations. Calculation of the selective load incurred suggests that it may offset the intrinsic twofold reproductive advantage of asexual reproduction and maintain sexual reproduction in diploid populations.     

群体博弈合作均衡的存在性和适定性研究

针对许多经济问题面临着大规模大群体之间的策略互动, 且策略互动时,参与主体之间为寻求更高利益可 能达成合作的行为, 研究群体博弈合作均衡的存在性,为这些情况提供统一分析框架。 首先, 介绍群体博弈模型 及群体博弈合作均衡的定义;其次,在群体状态函数为伪连续的条件下, 构造辅助偏好映射, 借助伪连续的性质, 得到群体博弈问题合作均衡的存在性结果, 并举例说明该存在性定理的优越性。 针对求解群体博弈合作均衡时, 原始数据收集可能会出现偏差, 模型数据可能受到干扰, 求解的近似解序列可能不可行的情形, 研究群体博弈合 作均衡的适定性,为数值计算提供理论依据。 首先, 分别引入该类群体博弈问题合作均衡的 Hadamard 适定性和 Levitin-Polyak 适定性概念;然后, 借助合作均衡映射的半连续性和紧性结果, 建立 Hadamard 适定性成立的充分性 条件;最后, 借助群体状态函数的伪连续性, 建立 Levitin-Polyak 适定性成立的充分性条件。     

关于三类图的伴随唯一性

讨论了ｎ个顶点ｎ＋２条边的连通图中三类图的伴随多项式的性质，得到了这些图是伴随唯一的一个充分条件，并利用它来讨论其色唯一性，得到一个色唯一图，同时提出一个未解决问题。     

认知无线网络中双中继协作策略及其差错性能分析

在认知无线网络中同时存在着主用户和次用户,次用户的通信必须在保证主用户不受干扰的条件下进行,次用户在检测到主用户未占用授权频段时机会地占用信道进行数据传输.为了保证次用户传输的连续性及QoS,研究人员在认知无线网络中引入了协作通信技术,研究发现认知无线电中的协作传输能够显著改善网络的传输性能.提出一种次用户双中继协作次用户的协作传输策略,并给出了该策略下平均误比特率和中断率的解析表达式,为了进行比较同时给出了单中继协作策略下次用户平均误比特率及中断率的表达式.理论分析和仿真结果表明,双中继协作次用户策略较单中继协作次用户策略有效地提高了次用户的差错性能.     

南京市居民参与体育活动的现状分析

对南京市1681名居民参与体育活动的情况进行了调查分析。结果表明,南京市居民具有较强的健身意识,但实际参与体育锻炼的人数较少;体育人口偏低;体育消费观念有待进一步改善;农村健身活动的开展需要进一步加强,农村健身活动开展的好坏将直接影响江苏省全民健身计划第二期目标的完成。     

关于一类(g,f)-2-覆盖图的研究

一个图G称为(g,f)-2-覆盖图,如果G的任何两条边都属于它的一个(g,f)-因子,得到了如下结论:(1)当g≤f时,一个二部图是(g,f)-2-覆盖图的一个充分必要条件;(2)当f(X)=f(Y)时,一个二部图是f-2-覆盖图的一个充分必要条件及其简单判别准则.     

有向非循环图的可反向边集合的结构与判定

讨论了有向非循环图(dag)G的可反向边集合R_G的结构,给出了判断R_G的充分必要条件。这一结果将有助于设计算法搜索G中的等价类,在用得分等价原则学习贝叶斯网络结构时,可以进行局部得分,从而减少所需的数据量,提高效率。     

完全k部图和一些特殊图的CORDIAL性

给出了完全ｋ部图是Ｃｏｒｄｉａｌ图的充要条件，并给出此类Ｃｏｒｄｉａｌ图的Ｃｏｒｄｉａｌ标号，给出ｎ阶Ｃｏｒｄｉａｌ图的最大边数，并构造了相应的极图；给出正则图是Ｃｏｒｄｉａｌ图的必要条件；解决了轮的Ｃｏｒｄｉａｌ问题。