Stationary distribution of population size inTribolium

Peters, Craig S.; Mangel, Marc; Costantino, R. F.

doi:10.1007/bf02459970

Cited by 7 publications

(3 citation statements)

References 21 publications

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“…Further increasing ε "locks" persisters ever stronger to the dynamics of normals, see Eqs. (13) and (28). For very large ε, P Y ≃ P X and Y ≃ ΓX with only small deviations.…”

Section: Why Are Switching Rates Small In Nature?mentioning

confidence: 92%

“…III B. Time-scale separation is still effective: X and P X show fast dynamics on the time scale T ∼ 1, or even T ∼ δ , see Eq. (28). They drive the slow Y and P Y , which change on a time scale T ′ = εT .…”

Section: Analytic Theory With Catastrophementioning

confidence: 99%

“…When N is sufficiently large, one can approximately solve Eq. ( 4) by a Wentzel-Kramers-Brillouin (WKB) eikonal ansatz [16,[26][27][28] π n,m = exp −NS(x, y) ,…”

Section: B Wkb Approximationmentioning

confidence: 99%

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Switching between phenotypes and population extinction

Lohmar

Meerson

2011

Phys. Rev. E

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Many types of bacteria can survive under stress by switching stochastically between two different phenotypes: the "normals" who multiply fast, but are vulnerable to stress, and the "persisters" who hardly multiply, but are resilient to stress. Previous theoretical studies of such bacterial populations have focused on the fitness: the asymptotic rate of unbounded growth of the population. Yet for an isolated population of established (and not very large) size, a more relevant measure may be the population extinction risk due to the interplay of adverse extrinsic variations and intrinsic noise of birth, death and switching processes. Applying a WKB approximation to the pertinent master equation of such a two-population system, we quantify the extinction risk, and find the most likely path to extinction under both favorable and adverse conditions. Analytical results are obtained both in the biologically relevant regime when the switching is rare compared with the birth and death processes, and in the opposite regime of frequent switching. We show that rare switches are most beneficial in reducing the extinction risk.

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“…Further increasing ε "locks" persisters ever stronger to the dynamics of normals, see Eqs. (13) and (28). For very large ε, P Y ≃ P X and Y ≃ ΓX with only small deviations.…”

Section: Why Are Switching Rates Small In Nature?mentioning

confidence: 92%

Section: Analytic Theory With Catastrophementioning

confidence: 99%

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Switching between phenotypes and population extinction

Lohmar

Meerson

2011

Phys. Rev. E

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Stochastic models of population extinction

Ovaskainen

Meerson

2010

Trends in Ecology & Evolution

384

432

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Theoretical ecologists have long sought to understand how the persistence of populations depends on biotic and abiotic factors. Classical work showed that demographic stochasticity causes the mean time to extinction to increase exponentially with population size, whereas variation in environmental conditions can lead to a power-law scaling. Recent work has focused especially on the influence of the autocorrelation structure ('color') of environmental noise. In theoretical physics, there is a burst of research activity in analyzing large fluctuations in stochastic population dynamics. This research provides powerful tools for determining extinction times and characterizing the pathway to extinction. It yields, therefore, sharp insights into extinction processes and has great potential for further applications in theoretical biology.

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