A "gene tree" is the phylogeny of alleles or haplotypes for any specified stretch of DNA. Gene trees are components of population trees or species trees; their analysis entails a shift in perspective from many of the familiar models and concepts of population genetics, which typically deal with frequencies of phylogenetically unordered alleles. Molecular surveys of haplotype diversity in mitoch...

in this paper, using generalized {polya} urn models we find the expected value of the size of a branch in recursive $k$-ary trees. we also find the expectation of the number of nodes of a given outdegree in a branch of such trees.

Gene trees are leaf-labeled trees inferred from molecular sequences. Due to duplication events arising in genome evolution, gene trees usually have multiple copies of some labels, i.e. species. Inferring a species tree from a set of multi-labeled gene trees (MUL trees) is a wellknown problem in computational biology. We propose a novel approach to tackle this problem, mainly to transform a coll...

This paper reviews P´olya urn models and their connection to random trees. Basic results are presented, together with proofs that underly the historical evolution of the accompanying thought process. Extensions and generalizations are given according to chronology: • P´olya-Eggenberger’s urn • Bernard Friedman’s urn • Generalized P´olya urns • Extended urn schemes • Invertible urn schemes ...

In this paper we consider the class of binary trees and present the results of a comprehensive experimental study on the four most representative algorithms for drawing trees, one for each of the following treedrawing approaches: Separation-Based, Path-based, Level-based, and Ringed Circular Layout. We establish a simpler, more intuitive format for storing binary trees in files and create a lar...

The advent and maturation of algorithms for estimating species trees-phylogenetic trees that allow gene tree heterogeneity and whose tips represent lineages, populations and species, as opposed to genes-represent an exciting confluence of phylogenetics, phylogeography, and population genetics, and ushers in a new generation of concepts and challenges for the molecular systematist. In this essay...

The regulation of bloom time in deciduous fruit trees is an area increasing interest due to the negative impact climate change on production. Although flower development has been well-studied model species, there are many knowledge gaps about this process perennial trees, whose floral spans four seasons and includes temperature-driven transitions. To develop solutions for minimizing crop loss, ...

The atom-bond connectivity (ABC) index is a degree-based molecular descriptor, that found chemical applications. It is well known that among all connected graphs, the graphs with minimal ABC index are trees. A complete characterization of trees with minimal ABC index is still an open problem. In this paper, we present new structural properties of trees with minimal ABC index. Our main results r...

MOTIVATION Metabolite identification from tandem mass spectrometric data is a key task in metabolomics. Various computational methods have been proposed for the identification of metabolites from tandem mass spectra. Fragmentation tree methods explore the space of possible ways in which the metabolite can fragment, and base the metabolite identification on scoring of these fragmentation trees. ...