Next-generation tools for evolutionary invasion analyses

Amy Hurford*, Daniel Cownden, Troy Day

*Corresponding author for this work

Research output: Contribution to journalReview articlepeer-review

63 Citations (Scopus)

Abstract

Evolutionary invasion analysis is a powerful technique for modelling in evolutionary biology. The general approach is to derive an expression for the growth rate of a mutant allele encoding some novel phenotype, and then to use this expression to predict long-term evolutionary outcomes. Mathematically, such 'invasion fitness' expressions are most often derived using standard linear stability analyses from dynamical systems theory. Interestingly, there is a mathematically equivalent approach to such stability analyses that is often employed in mathematical epidemiology, and that is based on so-called 'next-generation' matrices. Although this next-generation matrix approach has sometimes also been used in evolutionary invasion analyses, it is not yet common in this area despite the fact that it can sometimes greatly simplify calculations. The aim of this article is to bring the approach to a wider evolutionary audience in two ways. First, we review the next-generation matrix approach and provide a novel, and easily intuited, interpretation of how this approach relates to more standard techniques. Second, we illustrate next-generation methods in evolutionary invasion analysis through a series of informative examples. Although focusing primarily on evolutionary invasion analysis, we provide several insights that apply to biological modelling in general.

Original languageEnglish
Pages (from-to)561-571
Number of pages11
JournalJournal of the Royal Society Interface
Volume7
Issue number45
DOIs
Publication statusPublished - 6 Apr 2010

Keywords

  • basic reproduction number
  • invasion fitness
  • evolutionarily stable strategy
  • next-generation operator
  • adaptive dynamics
  • game theory
  • DISEASE-TRANSMISSION
  • MODELS
  • COEVOLUTION
  • VIRULENCE
  • FITNESS
  • STRATEGIES
  • STABILITY
  • SELECTION
  • TRAITS
  • RATIO

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