Ordering uniform supertrees by their spectral radii

A supertree is a connected and acyclic hypergraph. For a hypergraph H, the maximal modulus of the eigenvalues of its adjacency tensor is called the spectral radius of H. By applying the operation of moving edges on hypergraphs and the weighted incidence matrix method, we determine the ninth and the tenth k-uniform supertrees with the largest spectral radii among all k-uniform supertrees on n vertices, which extends the known result.

Largest signless Laplacian spectral radius of uniform supertrees with diameter and pendent edges(vertices)

Let S(m,d,k)be the set of k-uniform supertrees with m edges and diameter d,and S1(m,d,k)be the k-uniform supertree obtained from a loose path u_(1),e_(1),u_(2),e_(2),...,u_(d),e_(d),u_(d+1),with length d by attaching m-d edges at vertex u_[d/2]+1.In this paper,we mainly determine S1(m,d,k)with the largest signless Laplacian spectral radius in S(m,d,k)for 3≤d≤m-1.We also determine the supertree with the second largest signless Laplacian spectral radius in S(m,3,k).Furthermore,we determine the unique/c-uniform supertree with the largest signless Laplacian spectral radius among all fc-uniform supertrees with n vertices and pendent edges(vertices).

Uniform supertrees with extremal spectral radii

A supertree is a connected and acyclic hypergraph.We investigate the supertrees with the extremal spectral radii among several kinds of r-uniform supertrees.First,by using the matching polynomials of supertrees,a new and useful grafting operation is proposed for comparing the spectral radii of supertrees,and its applications are shown to obtain the supertrees with the extremal spectral radi among some kinds of r-uniform supertrees.Second,the supertree with the third smallest spectral radius among the r-uniform supertrees is deduced.Third,among the r-uniform supertrees with a given maximum degree,the supertree with the smallest spectral radius is derived.At last,among the r-uniform starlike supert rees,the supertrees with the smallest and the largest spectral radii are characterized.

整合系统发育信息：概念、方法与挑战

DNA序列、形态和其他同源性状可以用于推断物种的起源和历史。整合所有可利用的系统发育信息可以大大拓展所覆盖类群的范围,推进我们对现存生物的认识,而且使得生物学家提出和验证的假说尺度更广,更有统计说服力。文章综述了整合系统发育信息的概念及其与传统分析的异同,重点讨论了整合系统发育信息中应用最广的超级树(Supertree)和超级矩阵(Supermatrix)方法;在比较分析了这两个方法的优缺点之后,介绍了近些年提出的新的方法。文章详细分析了整合系统发育信息的发展所面临的来自数据和理论方面的挑战,认为尽管整合分析的发展困难较多,它仍然是到目前为止构建完整生命之树(网)的唯一方法;它的完善必将拓展我们对于生物进化过程的认识,并对进化生物学相关学科产生积极影响。

Fifty years of character compatibility concepts at work

In the mid 19th century, systematic biologists realized that observable similarities and differences among a group of related species could be the basis for hypotheses about the evolutionary relationships among the species and their ancestors. Such hypotheses can be expressed as characters. A character is comprised of two or more character states of species considered to be similar with respect to a basis for comparison. The states of a character may also be arranged into a character state tree to hypothesize speciation events associated with changes from one character state to another. In the mid 20th century, some systematists realized that sometimes pairs of characters （or character state trees） could be incompatible as hypotheses, i.e., they could not both be true. Through the 1950s, ＇60s and ＇70s, tests for, and ways to resolve, incompatibilities were used to estimate an ancestor rela-tion based on mutually compatible characters. An estimate was often shown as a diagram connecting ancestors to their immediate descendants （not quite correctly） called a phylogenetic tree. More recently, other applications of compatibility concepts have been developed, including： identify characters that appear to be random in the context of their data set; combine estimates of ancestor relations for subsets of taxa in a larger collection into a single estimate （a so-called supertree） for the whole collection; and interpret geographic patterns in an evolutionary context.

An updated megaphylogeny of plants,a tool for generating plant phylogenies and an analysis of phylogenetic community structure

Aims The aim of this article is 3-fold.First,we present an updated version of a published megaphylogeny of vascular plants that can be used in studies of plant ecology and biogeography.second,we develop a tool that can be used by botanists and plant ecologists to generate phylogenetic hypotheses in three scenarios.Third,we use a set of regional assemblages of angiosperm trees in North america as a model system to evaluate the effect of differences in phylogenies generated using the three scenarios on the quantification of phylogenetic properties and the relationship between measures of phylogenetic properties and environment.Methods The taxonomy and nomenclature of plant species in the megaphy-logeny were standardized according to The Plant list(version 1.1).a tool for generating phylogenies was created using the r language.The robustness of derived phylogenies was evaluated using correlation and regression analyses.Important Findingsan updated megaphylogeny of vascular plants(PhytoPhylo)and a tool for reconstructing phylogenies of seed plants(s.Phylomaker)were generated.our study shows that phylogenies generated by s.Phylomaker using the PhytoPhylo megaphylogeny as a backbone are nearly as good as phylogeny resolved at the species level when using derived phylogenies to quantify phylogenetic properties(e.g.phylogenetic diversity and phylogenetic relatedness)of biological assemblages,and that s.Phylomaker-generated phylogenies are robust for studies of community ecology and biogeography,par-ticularly those seeking for patterns of phylogenetic properties along environmental gradients.