Switching between phenotypes and population extinction

Lohmar, Ingo; Meerson, Baruch

doi:10.1103/physreve.84.051901

Cited by 25 publications

(46 citation statements)

References 31 publications

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“…However, the probability distribution remains peaked around m ∼ 100 and shows no sign of leakage to m = 0, up to 10 6 min ( Fig. 13, red line), 7 The authors thank an anonymous referee for providing the parameters. 8 The ID number of BioNumber Database [84].…”

Section: Shift Of the Fixed Points By Stochastic Noisementioning

confidence: 94%

Quantitative analysis of a transient dynamics of a gene regulatory network

Lee

2018

Phys. Rev. E

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In a stochastic process, noise often modifies the picture offered by the mean field dynamics.In particular, when there is an absorbing state, the noise erases a stable fixed point of the mean field equation from the stationary distribution, and turns it into a transient peak. We make a quantitative analysis of this effect for a simple genetic regulatory network with positive feedback, where the proteins become extinct in the presence of stochastic noise, contrary to the prediction of the deterministic rate equation that the protein number converges to a non-zero value. We show that the transient peak appears near the stable fixed point of the rate equation, and the extinction time diverges exponentially as the stochastic noise approaches zero. We also show how the baseline production from the inactive gene ameliorates the effect of the stochastic noise, and interpret the opposite effects of the noise and the baseline production in terms of the position shift of the unstable fixed point. The order of magnitude estimates using biological parameters suggest that for a real gene regulatory network, the stochastic noise is sufficiently small so that not only is the extinction time much larger than biologically relevant time-scales, but also the effect of the baseline production dominates over that of the stochastic noise, leading to the protection from the catastrophic rare event of protein extinction. * jul@ssu.ac.kr 1 This is also called the transcriptional leakage, but we will refrain from using this terminology because we will be using the word leakage in quite the opposite sense. 2 The concentration is defined as x ≡ m/m, where m is the number of proteins andm is a large number chosen to be of the order of average number of proteins [31]. The ratesr,k 1 , andã of the rate equation, and the corresponding quantities r, k, and a in the master equation, are related byr = r/m,k 1 = k 1 /m, andã = a/m. See appendix E for details.

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Section: Shift Of the Fixed Points By Stochastic Noisementioning

confidence: 94%

Quantitative analysis of a transient dynamics of a gene regulatory network

Lee

2018

Phys. Rev. E

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“…The two other fixed points, F 1 and F 2 , are fluctuational fixed points describing a fox-free state at a non-zero number of rabbits (F 2 ) and an empty system (F 1 ). Fluctuational fixed points have a non-zero p x or p y component and appear in a broad class of stochastic population models exhibiting extinction in the absence of an Allee effect [2,10,11,14,17,18,20,22,24,27,38]. They play an important role in the calculations of the quasistationary distributions and the mean time to extinction.…”

Section: Generalmentioning

confidence: 99%

Multiple extinction routes in stochastic population models

Gottesman

Meerson

2012

Phys. Rev. E

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Isolated populations ultimately go extinct because of the intrinsic noise of elementary processes. In multi-population systems extinction of a population may occur via more than one route. We investigate this generic situation in a simple predator-prey (or infected-susceptible) model. The predator and prey populations may coexist for a long time but ultimately both go extinct. In the first extinction route the predators go extinct first, whereas the prey thrive for a long time and then also go extinct. In the second route the prey go extinct first causing a rapid extinction of the predators. Assuming large sub-population sizes in the coexistence state, we compare the probabilities of each of the two extinction routes and predict the most likely path of the sub-populations to extinction. We also suggest an effective three-state master equation for the probabilities to observe the coexistence state, the predator-free state and the empty state.

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“…Phase Diagram: Comparing Eqs. (5) and (20), one sees that there is a sizable region in the α-g parameter space where one species has a smaller quasi-stationary population and yet an (exponentially) smaller probability to first become extinct. As an illustration, Fig.…”

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confidence: 99%

Survival of the scarcer

2013

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We investigate extinction dynamics in the paradigmatic model of two competing species A and B that reproduce (A→2A, B→2B), self-regulate by annihilation (2A→0, 2B→0), and compete (A+B→A, A+B→B). For a finite system that is in the well-mixed limit, a quasistationary state arises which describes coexistence of the two species. Because of discrete noise, both species eventually become extinct in time that is exponentially long in the quasistationary population size. For a sizable range of asymmetries in the growth and competition rates, the paradoxical situation arises in which the numerically disadvantaged species according to the deterministic rate equations survives much longer.

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Switching between phenotypes and population extinction

Cited by 25 publications

References 31 publications

Quantitative analysis of a transient dynamics of a gene regulatory network

Quantitative analysis of a transient dynamics of a gene regulatory network

Multiple extinction routes in stochastic population models

Survival of the scarcer

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