Evolutionary Rate Change and the Transformation from Additive to Ultrametric: Modal Similarity of Orthologs in Fish and Flower Phylogenomics

  • Daniella Santos Muñoz
  • Eric Lam
  • David SankoffEmail author
Part of the Computational Biology book series (COBO, volume 29)


Branch lengths in a phylogeny may be in units of elapsed time, so that the nodes have dates associated with them, or in units of evolutionary change, such as the number of mutations that have accrued between the two endpoints of a branch. Methods to account for the mutational change in terms of an additive tree are generally incompatible with the ultrametric requirement of time-based tree representations because of changes in mutation rate. There are some principled ways of converting additive trees to ultrametric form, and these suggest which branches have seen increased or decreased rates. We spell these methods out and apply them to the ray-finned fishes and the plant families Solanaceae and Malvaceae. The methods based on nonparametric rate smoothing prove to be more revealing than the Farris transform methods.


Tree metrics Peaks tree Fish phylogeny Solanaceae Malvaceae 



This work was supported in part by a Discovery grant from the Natural Sciences and Engineering Research Council of Canada. DS holds the Canada Research Chair in Mathematical Genomics.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Daniella Santos Muñoz
    • 1
  • Eric Lam
    • 1
  • David Sankoff
    • 1
    Email author
  1. 1.University of OttawaOttawaCanada

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