Phylodynamic theory of persistence, extinction and speciation of rapidly adapting pathogens

  1. Le Yan  Is a corresponding author
  2. Richard A Neher  Is a corresponding author
  3. Boris I Shraiman  Is a corresponding author
  1. University of California, Santa Barbara, United States
  2. University of Basel, Switzerland


Rapidly evolving pathogens like influenza viruses can persist by changing their antigenic properties fast enough to evade the adaptive immunity, yet they rarely split into diverging lineages. By mapping the multi-strain Susceptible-Infected-Recovered model onto the traveling wave model of adapting populations, we demonstrate that persistence of a rapidly evolving, Red-Queen-like state of the pathogen population requires long-ranged cross-immunity and sufficiently large population sizes. This state is unstable and the population goes extinct or 'speciates' into two pathogen strains with antigenic divergence beyond the range of cross-inhibition. However, in a certain range of evolutionary parameters, a single cross-inhibiting population can exist for times long compared to the time to the most recent common ancestor (TMRCA) and gives rise to phylogenetic patterns typical of influenza virus. We demonstrate that the rate of speciation is related to fluctuations of TMRCA and construct a 'phase diagram' identifying different phylodynamic regimes as a function of evolutionary parameters.

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Computer programs used for numerical simulations and analysis have been made publicly available at

Article and author information

Author details

  1. Le Yan

    Kavli Institute for Theoretical Physics, University of California, Santa Barbara, Santa Barbara, United States
    For correspondence
    Competing interests
    No competing interests declared.
  2. Richard A Neher

    Biozentrum, University of Basel, Basel, Switzerland
    For correspondence
    Competing interests
    Richard A Neher, Reviewing editor, eLife.
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0003-2525-1407
  3. Boris I Shraiman

    Kavli Institute for Theoretical Physics, University of California, Santa Barbara, Santa Barbara, United States
    For correspondence
    Competing interests
    No competing interests declared.
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0003-0886-8990


Simons Foundation (326844)

  • Boris I Shraiman

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

Reviewing Editor

  1. Katia Koelle, Emory University, United States

Publication history

  1. Received: December 7, 2018
  2. Accepted: September 14, 2019
  3. Accepted Manuscript published: September 18, 2019 (version 1)
  4. Version of Record published: October 23, 2019 (version 2)


© 2019, Yan et al.

This article is distributed under the terms of the Creative Commons Attribution License permitting unrestricted use and redistribution provided that the original author and source are credited.


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  1. Le Yan
  2. Richard A Neher
  3. Boris I Shraiman
Phylodynamic theory of persistence, extinction and speciation of rapidly adapting pathogens
eLife 8:e44205.

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