scholarly journals Extremal Values of the Sackin Tree Balance Index

2021 ◽  
Author(s):  
Mareike Fischer
Keyword(s):  
Phylogenetic Trees ◽  
Theoretical Computer Science ◽  
Search Trees ◽  
Formal Proofs ◽  
Birth Process ◽  
Ordered Trees ◽  
Research Areas ◽  
New Findings ◽  
Mathematical Phylogenetics ◽  
Extremal Values

AbstractTree balance plays an important role in different research areas like theoretical computer science and mathematical phylogenetics. For example, it has long been known that under the Yule model, a pure birth process, imbalanced trees are more likely than balanced ones. Also, concerning ordered search trees, more balanced ones allow for more efficient data structuring than imbalanced ones. Therefore, different methods to measure the balance of trees were introduced. The Sackin index is one of the most frequently used measures for this purpose. In many contexts, statements about the minimal and maximal values of this index have been discussed, but formal proofs have only been provided for some of them, and only in the context of ordered binary (search) trees, not for general rooted trees. Moreover, while the number of trees with maximal Sackin index as well as the number of trees with minimal Sackin index when the number of leaves is a power of 2 are relatively easy to understand, the number of trees with minimal Sackin index for all other numbers of leaves has been completely unknown. In this manuscript, we extend the findings on trees with minimal and maximal Sackin indices from the literature on ordered trees and subsequently use our results to provide formulas to explicitly calculate the numbers of such trees. We also extend previous studies by analyzing the case when the underlying trees need not be binary. Finally, we use our results to contribute both to the phylogenetic as well as the computer scientific literature using the new findings on Sackin minimal and maximal trees to derive formulas to calculate the number of both minimal and maximal phylogenetic trees as well as minimal and maximal ordered trees both in the binary and non-binary settings. All our results have been implemented in the Mathematica package SackinMinimizer, which has been made publicly available.

scholarly journals Mapping diversification metrics in macroecological studies: Prospects and challenges

2018 ◽  
Author(s):  
Julián A. Velasco ◽  
Jesús N. Pinto-Ledezma
Keyword(s):  
Species Richness ◽  
Phylogenetic Trees ◽  
Evolutionary Mechanisms ◽  
Geographical Patterns ◽  
Research Areas ◽  
Evolutionary Distinctiveness ◽  
Branch Lengths ◽  
Spatial Diversification ◽  
Active Research

AbstractThe intersection of macroecology and macroevolution is one of the most active research areas today. Macroecological studies are increasingly using phylogenetic diversification metrics to explore the role of evolutionary processes in shaping present-day patterns of biodiversity. Evolutionary explanations of species richness gradients are key for our understanding of how diversity accumulated in a region. For instance, the present-day diversity in a region can be a result of in situ diversification, extinction, or colonization from other regions, or a combination of all of these processes. However, it is unknown whether these metrics capture well these diversification and dispersal processes across geography. Some metrics (e.g., mean root distance -MRD-; lineage diversification-rate -DR-; evolutionary distinctiveness -ED-) seem to provide very similar geographical patterns regardless of how they were calculated (e.g., using branch lengths or not). The lack of appropriate estimates of extinction and dispersal rates in phylogenetic trees can limit our conclusions about how species richness gradients emerged. With a review of the literature and complemented by an empirical comparison, we show that phylogenetic metrics by itself are not capturing well the speciation, extinction and dispersal processes across the geographical gradients. Furthermore, we show how new biogeographic methods can improve our inference of past events and therefore our conclusions about the evolutionary mechanisms driving regional species richness. Finally, we recommend that future studies include several approaches (e.g., spatial diversification modelling, parametric biogeographic methods) to disentangle the relative the role of speciation, extinction and dispersal in the generation and maintenance of species richness gradients.

scholarly journals Characterizing and comparing phylogenies from their Laplacian spectrum

2015 ◽  
Author(s):  
Eric Lewitus ◽  
Helene Morlon
Keyword(s):  
Population Genetics ◽  
Spectral Density ◽  
Phylogenetic Trees ◽  
Life Sciences ◽  
Laplacian Spectrum ◽  
Density Profiles ◽  
Spectral Graph ◽  
Research Areas ◽  
Graph Theoretical Approach ◽  
Comprehensive Framework

Phylogenetic trees are central to many areas of biology, ranging from population genetics and epidemiology to microbiology, ecology, and macroevolution. The ability to summarize properties of trees, compare different trees, and identify distinct modes of division within trees is essential to all these research areas. But despite wide-ranging applications, there currently exists no common, comprehensive framework for such analyses. Here we present a graph-theoretical approach that provides such a framework. We show how to construct the spectral density profiles of phylogenetic trees from their Laplacian graphs. Using ultrametric simulated trees as well as non-ultrametric empirical trees, we demonstrate that the spectral density successfully identifies various properties of the trees and clusters them into meaningful groups. Finally, we illustrate how the eigengap can identify modes of division within a given tree. As phylogenetic data continue to accumulate and to be integrated into various areas of the life sciences, we expect that this spectral graph-theoretical framework to phylogenetics will have powerful and long-lasting applications.

scholarly journals A simpler linear-time algorithm for the common refinement of rooted phylogenetic trees on a common leaf set

2021 ◽  
Vol 16 (1) ◽  
Author(s):  
David Schaller ◽  
Marc Hellmuth ◽  
Peter F. Stadler
Keyword(s):  
Phylogenetic Trees ◽  
Linear Time ◽  
Time Algorithm ◽  
Input Tree ◽  
Linear Time Algorithm ◽  
Optimal Algorithms ◽  
Asymptotically Optimal ◽  
The Common ◽  
Mathematical Phylogenetics ◽  
Special Case

Abstract Background The supertree problem, i.e., the task of finding a common refinement of a set of rooted trees is an important topic in mathematical phylogenetics. The special case of a common leaf set L is known to be solvable in linear time. Existing approaches refine one input tree using information of the others and then test whether the results are isomorphic. Results An O(k|L|) algorithm, , for constructing the common refinement T of k input trees with a common leaf set L is proposed that explicitly computes the parent function of T in a bottom-up approach. Conclusion is simpler to implement than other asymptotically optimal algorithms for the problem and outperforms the alternatives in empirical comparisons. Availability An implementation of in Python is freely available at https://github.com/david-schaller/tralda.

scholarly journals Maximal Clades in Random Binary Search Trees

10.37236/4646 ◽  
2015 ◽  
Vol 22 (1) ◽  
Author(s):  
Svante Janson
Keyword(s):  
Asymptotic Normality ◽  
Phylogenetic Trees ◽  
Binary Search ◽  
Probabilistic Methods ◽  
Binary Search Trees ◽  
Search Trees

We study maximal clades in random phylogenetic trees with the Yule-Harding model or, equivalently, in binary search trees. We use probabilistic methods to reprove and extend earlier results on moment asymptotics and asymptotic normality. In particular, we give an explanation of the curious phenomenon observed by Drmota, Fuchs and Lee (2014) that asymptotic normality holds, but one should normalize using half the variance.

scholarly journals Phylogenomics with paralogs

2015 ◽  
Vol 112 (7) ◽  
pp. 2058-2063 ◽  
Author(s):  
Marc Hellmuth ◽  
Nicolas Wieseke ◽  
Marcus Lechner ◽  
Hans-Peter Lenhof ◽  
Martin Middendorf ◽  
...  
Keyword(s):  
Phylogenetic Trees ◽  
Sequence Data ◽  
Gene Families ◽  
Data Sets ◽  
Gene Trees ◽  
Species Trees ◽  
Individual Gene ◽  
Genome Wide Data ◽  
Degree Of Certainty ◽  
Mathematical Phylogenetics

Phylogenomics heavily relies on well-curated sequence data sets that comprise, for each gene, exclusively 1:1 orthologos. Paralogs are treated as a dangerous nuisance that has to be detected and removed. We show here that this severe restriction of the data sets is not necessary. Building upon recent advances in mathematical phylogenetics, we demonstrate that gene duplications convey meaningful phylogenetic information and allow the inference of plausible phylogenetic trees, provided orthologs and paralogs can be distinguished with a degree of certainty. Starting from tree-free estimates of orthology, cograph editing can sufficiently reduce the noise to find correct event-annotated gene trees. The information of gene trees can then directly be translated into constraints on the species trees. Although the resolution is very poor for individual gene families, we show that genome-wide data sets are sufficient to generate fully resolved phylogenetic trees, even in the presence of horizontal gene transfer.

New species and new findings of phoma-like fungi (Didymellaceae) associated with some Asteraceae in Russia

Nova Hedwigia ◽  
2020 ◽  
Vol 111 (1) ◽  
pp. 131-149
Author(s):  
Maria Gomzhina ◽  
Elena Gasich ◽  
Lyudmila Khlopunova ◽  
Philipp Gannibal
Keyword(s):  
New Species ◽  
Phylogenetic Trees ◽  
Phylogenetic Analyses ◽  
Wild Plants ◽  
Morphological Identification ◽  
New Findings ◽  
The Family ◽  
Poor Understanding ◽  
Sonchus Arvensis ◽  
A New Species

The notable difficulties in the morphological identification of phoma-like fungi have resulted in a poor understanding of the generic and species boundaries in this group of organisms. In most available mycofloristic and phytopathological studies, there is no reliable information on the distribution of certain nonspecialized phomoid species on cultivated crops or wild plants. Both the revision of existing data on the biodiversity and geographical distribution of phoma-like fungi associated with Asteraceae in Russia and the acquisition of new knowledge according to modern concepts of these fungi are therefore of great significance. The aim of this study was to identify phoma-like strains from Asteraceae based primarily on phylogenetic analyses of the sequences of four loci (ITS, LSU, TUB, RPB2) as well as on traditional morphological approaches. The resulting phylogenetic trees revealed six well-supported monophyletic clads corresponding to six genera in the family Didymellaceae: Ascochyta, Boeremia, Didymella, Neoascochyta, Nothophoma, and Stagonosporopsis. The isolates were identified as As. kamchatica, B. exigua, B. exigua var. forsythiae, B. exigua var. linicola, D. americana, D. glomerata, D. macrophylla, D. pinodella , D. pomorum, D. rosea, Ne. desmazieri, Ne. paspali, No. quercina, St. dennisii, and St. inoxydabilis. Ascochyta kamchatica sp. nov. was described as a new species. Three Didymella species ( D. pinodella from Cirsium arvense, D. rosea from Sonchus arvensis, and D. macrophylla from Taraxacum officinale), two Neoascochyta species (Ne. desmazieri from T. officinale and Ne. paspali from Achillea millefolium) and St. dennisii from T. officinale were the first records of these phoma-like fungi in Russia.

scholarly journals DNA Barcoding of Marine Mollusks Associated with Corallina officinalis Turfs in Southern Istria (Adriatic Sea)

Diversity ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 196
Author(s):  
Moira Buršić ◽  
Ljiljana Iveša ◽  
Andrej Jaklin ◽  
Milvana Arko Pijevac ◽  
Mladen Kučinić ◽  
...  
Keyword(s):  
Dna Barcoding ◽  
Adriatic Sea ◽  
Gastropod Species ◽  
Invertebrate Species ◽  
Research Areas ◽  
New Findings ◽  
Corallina Officinalis ◽  
Coi Sequences ◽  
Mollusk Species ◽  
Mollusk Assemblages

Presence of mollusk assemblages was studied within red coralligenous algae Corallina officinalis L. along the southern Istrian coast. C. officinalis turfs can be considered a biodiversity reservoir, as they shelter numerous invertebrate species. The aim of this study was to identify mollusk species within these settlements using DNA barcoding as a method for detailed identification of mollusks. Nine locations and 18 localities with algal coverage range above 90% were chosen at four research areas. From 54 collected samples of C. officinalis turfs, a total of 46 mollusk species were identified. Molecular methods helped identify 16 gastropod, 14 bivalve and one polyplacophoran species. COI sequences for two bivalve species (Musculus cf. costulatus (Risso, 1826) and Gregariella semigranata (Reeve, 1858)) and seven gastropod species (Megastomia winfriedi Peñas & Rolán, 1999, Eatonina sp. Thiele, 1912, Eatonina cossurae (Calcara, 1841), Crisilla cf. maculata (Monterosato, 1869), Alvania cf. carinata (da Costa, 1778), Vitreolina antiflexa (Monterosato, 1884) and Odostomia plicata (Montagu, 1803)) represent new BINs in BOLD database. This study contributes to new findings related to the high biodiversity of mollusks associated with widespread C. officinalis settlements along the southern coastal area of Istria.

scholarly journals Analysis of some statistics for increasing tree families

2004 ◽  
Vol Vol. 6 no. 2 ◽  
Author(s):  
Alois Panholzer ◽  
Helmut Prodinger
Keyword(s):  
Computer Science ◽  
Normal Distribution ◽  
Probabilistic Models ◽  
Binary Search ◽  
Rooted Trees ◽  
Binary Search Trees ◽  
Search Trees ◽  
Ordered Trees ◽  
International Audience

International audience This paper deals with statistics concerning distances between randomly chosen nodes in varieties of increasing trees. Increasing trees are labelled rooted trees where labels along any branch from the root go in increasing order. Many mportant tree families that have applications in computer science or are used as probabilistic models in various applications, like \emphrecursive trees, heap-ordered trees or \emphbinary increasing trees (isomorphic to binary search trees) are members of this variety of trees. We consider the parameters \textitdepth of a randomly chosen node, \textitdistance between two randomly chosen nodes, and the generalisations where \textitp nodes are randomly chosen Under the restriction that the node-degrees are bounded, we can prove that all these parameters converge in law to the Normal distribution. This extends results obtained earlier for binary search trees and heap-ordered trees to a much larger class of structures.

scholarly journals Complex Evolutionary Patterns of tRNAUAALeu Group I Introns in Cyanobacterial Radiation

1999 ◽  
Vol 181 (11) ◽  
pp. 3445-3451 ◽  
Author(s):  
Knut Rudi ◽  
Kjetill S. Jakobsen
Keyword(s):  
16S Rdna ◽  
Phylogenetic Trees ◽  
Lateral Transfer ◽  
Trna Genes ◽  
Group I Introns ◽  
Evolutionary Patterns ◽  
Group I ◽  
New Findings ◽  
Different Strains ◽  
Rdna Analysis

ABSTRACT Based on the findings that plastids and cyanobacteria have similar group I introns inserted into tRNAUAA Leu genes, these introns have been suggested to be immobile and of ancient origin. In contrast, recent evidence suggests lateral transfer of cyanobacterial group I introns located in tRNAUAA Leu genes. In light of these new findings, we have readdressed the evolution and lateral transfer of tRNAUAA Leu group I introns in cyanobacteral radiation. We determined the presence of introns in 38 different strains, representing the major cyanobacterial lineages, and characterized the introns in 22 of the strains. Notably, two of these strains have two tRNAUAA Leu genes, with each of these genes interrupted by introns, while three of the strains have both interrupted and uninterrupted genes. Two evolutionary distinct clusters of tRNA genes, with the genes interrupted by introns belonging to two distinct intron clusters, were identified. We also compared 16S rDNA and intron evolution for both closely and distantly related strains. The distribution of the introns in the clustered groups, as defined from 16S rDNA analysis, indicates relatively recent gain and/or loss of the introns in some of these lineages. The comparative analysis also suggests differences in the phylogenetic trees for 16S rDNA and the tRNAUAA Leu group I introns. Taken together, our results show that the evolution of the intron is considerably more complex than previous studies found to be the case. We discuss, based on our results, evolutionary models involving lateral intron transfer and models involving differential loss of the intron.

Further studies on the ultrastructure of the cochlea

1990 ◽  
Vol 48 (3) ◽  
pp. 440-441
Author(s):  
Zhixian Wang ◽  
Pinjin Zhu ◽  
Jianhe Sun ◽  
Xuezheng Song
Keyword(s):  
Hair Cells ◽  
Military Medicine ◽  
Outer Hair Cells ◽  
Apical Surface ◽  
Epithelial Surface ◽  
Hearing Research ◽  
New Findings ◽  
Fine Structures ◽  
Temporal Bones ◽  
Accurate Observation

Hearing research is important not only for clinical, professional and military medicine, but also for toxicology, gerontology and genetics. Ultrastructure of the cochlea attracts much attention of electron microscopists, (1―3) but the research lags far behind that of the other parts of the organnism. On the basis of careful microdissection, technical improvment and accurate observation, we have got some new findings which have not been reported in the literature.We collected four cochleas from human corpses. Temporal bones dissected 1 h after death and cochleas perfused with fixatives 4 h after death were good enough in terms of preservation of fine structures. SEM:The apical surface of OHCs (Outer hair cells) and DTs (Deiters cells) is narrower than that of IPs (Inner pillar cells). The mosaic configuration of the reticular membrane is not typical. The stereocilia of IHCs (Inner hair cells) are not uniform and some kinocilia could be seen on the OHCs in adults. The epithelial surface of RM (Reissner’s membrane) is not smooth and no mesh could be seen on the mesothelial surface of RM. TEM.

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