On the minimum value of the Colless index and the bifurcating trees that achieve it

DOI10.1007/s00285-020-01488-9zbMath1443.92126arXiv1907.05064OpenAlexW3014141567WikidataQ91715343 ScholiaQ91715343MaRDI QIDQ2184640

Mareike Fischer, Tomás M. Coronado, Lina Herbst, Kristina Wicke, Francesc Rosselló

Publication date: 29 May 2020

Published in: Journal of Mathematical Biology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1907.05064

zbMATH Keywords

phylogenetic treeSackin indexTakagi curvetree balanceColless indexBlancmange curve

Mathematics Subject Classification ID

Trees (05C05) Problems related to evolution (92D15) Applications of graph theory (05C90)

Related Items (9)

Squaring within the Colless index yields a better balance index ⋮ On the Colijn-Plazzotta numbering scheme for unlabeled binary rooted trees ⋮ Hardness of \textsc{Balanced Mobiles} ⋮ Unnamed Item ⋮ Revisiting Shao and Sokal's \(B_2\) index of phylogenetic balance ⋮ Extremal values of the Sackin tree balance index ⋮ Measuring tree balance using symmetry nodes -- a new balance index and its extremal properties ⋮ A simple derivation of the mean of the Sackin index of tree balance under the uniform model on rooted binary labeled trees ⋮ On the Balance of Unrooted Trees

Uses Software

• OEIS
• TreeBASE
• apTreeshape
• SackinMinimizer

Cites Work

• Unnamed Item
• Unnamed Item
• A new balance index for phylogenetic trees
• On joint subtree distributions under two evolutionary models
• The Takagi function: a survey
• Topological properties of phylogenetic trees in evolutionary models
• The mean, variance and limiting distribution of two statistics sensitive to phylogenetic tree balance
• The coalescent
• Stochastic models and descriptive statistics for phylogenetic trees, from Yule to today.
• Distributions of cherries for two models of trees
• A balance index for phylogenetic trees based on rooted quartets
• Exact formulas for the variance of several balance indices under the Yule model
• On statistical tests of phylogenetic tree imbalance: The Sackin and other indices revisited
• Phylogeny
• On the Balance of Unrooted Trees

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