Using Generating Functions to Prove Additivity of Gene-Neighborhood Based Phylogenetics - Extended Abstract

Guy Katriel, Udi Mahanaymi, Christoph Koutschan, Doron Zeilberger, Mike Steel, Sagi Snir

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


Prokaryotic evolution is often described as the Spaghetti of Life due to massive genome dynamics (GD) events of gene gain and loss, resulting in different evolutionary histories for the set of genes comprising the organism. These different histories, dubbed as gene trees provide confounding signals, hampering the attempt to reconstruct the species tree describing the main trend of evolution of the species under study. The synteny index (SI) between a pair of genomes combines gene order and gene content information, allowing comparison of unequal gene content genomes, together with order considerations of their common genes. Recently, GD has been modelled as a continuous-time Markov process. Under this formulation, the distance between genes along the chromosome was shown to follow a birth-death-immigration process. Using classical results from birth-death theory, we recently showed that the SI measure is consistent under that formulation. In this work, we provide an alternative, stand alone combinatorial proof of the same result. By using generating function techniques we derive explicit expressions of the system’s probabilistic dynamics in the form of rational functions of the model parameters. This, in turn, allows us to infer analytically the expected distances between organisms based on a transformation of their SI. Although the expressions obtained are rather complex, we establish additivity of this estimated evolutionary distance (a desirable property yielding phylogenetic consistency). This approach relies on holonomic functions and the Zeilberger Algorithm in order to establish additivity of the transformation of SI.

Original languageEnglish
Title of host publicationBioinformatics Research and Applications - 19th International Symposium, ISBRA 2023, Proceedings
EditorsXuan Guo, Serghei Mangul, Murray Patterson, Alexander Zelikovsky
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages16
ISBN (Print)9789819970735
StatePublished - 2023
Event19th International Symposium on Bioinformatics Research and Applications, ISBRA 2023 - Wroclaw, Poland
Duration: 9 Oct 202312 Oct 2023

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume14248 LNBI
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference19th International Symposium on Bioinformatics Research and Applications, ISBRA 2023

Bibliographical note

Publisher Copyright:
© 2023, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.


  • Generating Functions
  • Genome Dynamics
  • Holonomic Functions
  • Markovian Processes
  • Phylogenetics

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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