Quantifying invasibility

Jayant Pande, Yehonatan Tsubery, Nadav M. Shnerb

Research output: Contribution to journalLetterpeer-review


Invasibility, the chance of a population to grow from rarity and become established, plays a fundamental role in population genetics, ecology, epidemiology and evolution. For many decades, the mean growth rate of a species when it is rare has been employed as an invasion criterion. Recent studies show that the mean growth rate fails as a quantitative metric for invasibility, with its magnitude sometimes even increasing while the invasibility decreases. Here we provide two novel formulae, based on the diffusion approximation and a large-deviations (Wentzel–Kramers–Brillouin) approach, for the chance of invasion given the mean growth and its variance. The first formula has the virtue of simplicity, while the second one holds over a wider parameter range. The efficacy of the formulae, including their accompanying data analysis technique, is demonstrated using synthetic time series generated from canonical models and parameterised with empirical data.

Original languageEnglish
Pages (from-to)1783-1794
Number of pages12
JournalEcology Letters
Issue number8
StatePublished - Aug 2022


  • coexistence
  • community dynamics
  • demographic stochasticity
  • environmental stochasticity
  • extinction risk
  • invasibility
  • lottery model
  • stabilising mechanisms
  • stability
  • storage effect

All Science Journal Classification (ASJC) codes

  • Ecology, Evolution, Behavior and Systematics


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