Abstract
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 language | English |
|---|---|
| Pages (from-to) | 1699-1707 |
| Number of pages | 9 |
| Journal | Journal of the Royal Society Interface |
| Volume | 8 |
| Issue number | 65 |
| DOIs | |
| State | Published - 7 Dec 2011 |
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Keywords
- Extinction
- Finite-time Lyapunov exponents
- Optimal path
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Converging towards the optimal path to extinction. / Schwartz, Ira B.; Forgoston, Eric; Bianco, Simone; Shaw, Leah B.
In: Journal of the Royal Society Interface, Vol. 8, No. 65, 07.12.2011, p. 1699-1707.Research output: Contribution to journal › Article › Research › peer-review
TY - JOUR
T1 - Converging towards the optimal path to extinction
AU - Schwartz, Ira B.
AU - Forgoston, Eric
AU - Bianco, Simone
AU - Shaw, Leah B.
PY - 2011/12/7
Y1 - 2011/12/7
N2 - 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.
AB - 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.
KW - Extinction
KW - Finite-time Lyapunov exponents
KW - Optimal path
UR - http://www.scopus.com/inward/record.url?scp=82655178492&partnerID=8YFLogxK
U2 - 10.1098/rsif.2011.0159
DO - 10.1098/rsif.2011.0159
M3 - Article
VL - 8
SP - 1699
EP - 1707
JO - Journal of the Royal Society Interface
JF - Journal of the Royal Society Interface
SN - 1742-5689
IS - 65
ER -