Converging towards the optimal path to extinction

Ira B. Schwartz, Eric Forgoston, Simone Bianco, Leah B. Shaw

Research output: Contribution to journalArticlepeer-review

35 Scopus citations


Extinction appears ubiquitously in many fields, including chemical reactions, population biology, evolution and epidemiology. Even though extinction as a random process is a rare event, its occurrence is observed in large finite populations. Extinction occurs when fluctuations owing to random transitions act as an effective force that drives one or more components or species to vanish. Although there are many random paths to an extinct state, there is an optimal path that maximizes the probability to extinction. In this paper, we show that the optimal path is associated with the dynamical systems idea of having maximum sensitive dependence to initial conditions. Using the equivalence between the sensitive dependence and the path to extinction, we show that the dynamical systems picture of extinction evolves naturally towards the optimal path in several stochastic models of epidemics.

Original languageEnglish
Pages (from-to)1699-1707
Number of pages9
JournalJournal of the Royal Society Interface
Issue number65
StatePublished - 7 Dec 2011


  • Extinction
  • Finite-time Lyapunov exponents
  • Optimal path


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