Rare events in stochastic populations under bursty reproduction

Be'er, Shay; Assaf, Michael

doi:10.1088/1742-5468/2016/11/113501

Cited by 20 publications

(52 citation statements)

References 66 publications

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“…In addition to the MTE, the quasi-stationary distribution can also be found once the SSD is explicitly specified, see SM. An important quantity that represents the overall noise magnitude (both demographic and nondemographic) and strongly affects the MTE is the observed variance of the quasi-stationary distribution, σ obs [28,29], which can be found for any SSD…”

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confidence: 99%

Reducing the extinction risk of stochastic populations via nondemographic noise

Be'er

Assaf

2018

Phys. Rev. E

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We consider nondemographic noise in the form of uncertainty in the reaction step size and reveal a dramatic effect this noise may have on the stability of self-regulating populations. Employing the reaction scheme mA→kA but allowing, e.g., the product number k to be a priori unknown and sampled from a given distribution, we show that such nondemographic noise can greatly reduce the population's extinction risk compared to the fixed k case. Our analysis is tested against numerical simulations, and by using empirical data of different species, we argue that certain distributions may be more evolutionary beneficial than others.

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confidence: 99%

Reducing the extinction risk of stochastic populations via nondemographic noise

Be'er

Assaf

2018

Phys. Rev. E

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“…Here D (k) denotes the burst size distribution (BSD) [30][31][32] -the probability distribution for k virions to be released upon the death of the cell. Multiplying Eq.…”

Section: B Stochastic Approach: 2d Modelmentioning

confidence: 99%

Time distribution for persistent viral infection

Sagi¹,

Assaf²

2019

J. Stat. Mech.

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We study the early stages of viral infection, and the distribution of times to obtain a persistent infection. The virus population proliferates by entering and reproducing inside a target cell until a sufficient number of new virus particles are released via a burst, with a given burst size distribution, which results in the death of the infected cell. Starting with a 2D model describing the joint dynamics of the virus and infected cell populations, we analyze the corresponding master equation using the probability generating function formalism. Exploiting time-scale separation between the virus and infected cell dynamics, the 2D model can be cast into an effective 1D model. To this end, we solve the 1D model analytically for a particular choice of burst size distribution. In the general case, we solve the model numerically by performing extensive Monte-Carlo simulations, and demonstrate the equivalence between the 2D and 1D models by measuring the Kullback-Leibler divergence between the corresponding distributions. Importantly, we find that the distribution of infection times is highly skewed with a "fat" exponential right tail. This indicates that there is non-negligible portion of individuals with an infection time, significantly longer than the mean, which may have implications on when HIV tests should be performed.

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“…In this approximation the MTE is equal to 1/r ex . The mean extinction rate under bursty reproduction and constant reaction rates has been calculated by Be'er et al [33], including pre-exponential corrections. Following the steps outlined in the Appendix of Ref.…”

Section: Adiabatic Approximationmentioning

confidence: 99%

“…Following the steps outlined in the Appendix of Ref. [33], the time-instantaneous extinction rate in our case is given by…”

Section: Adiabatic Approximationmentioning

confidence: 99%

Population extinction under bursty reproduction in a time-modulated environment

Vilk

Assaf

2018

Phys. Rev. E

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In recent years nondemographic variability has been shown to greatly affect dynamics of stochastic populations. For example, nondemographic noise in the form of a bursty reproduction process with an a priori unknown burst size, or environmental variability in the form of time-varying reaction rates, have been separately found to dramatically impact the extinction risk of isolated populations. In this work we investigate the extinction risk of an isolated population under the combined influence of these two types of nondemographic variation. Using the so-called momentum-space Wentzel-Kramers-Brillouin (WKB) approach and accounting for the explicit time dependence in the reaction rates, we arrive at a set of time-dependent Hamilton equations. To this end, we evaluate the population's extinction risk by finding the instanton of the time-perturbed Hamiltonian numerically, whereas analytical expressions are presented in particular limits using various perturbation techniques. We focus on two classes of time-varying environments: periodically varying rates corresponding to seasonal effects and a sudden decrease in the birth rate corresponding to a catastrophe. All our theoretical results are tested against numerical Monte Carlo simulations with time-dependent rates and also against a numerical solution of the corresponding time-dependent Hamilton equations.

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Rare events in stochastic populations under bursty reproduction

Cited by 20 publications

References 66 publications

Reducing the extinction risk of stochastic populations via nondemographic noise

Reducing the extinction risk of stochastic populations via nondemographic noise

Time distribution for persistent viral infection

Population extinction under bursty reproduction in a time-modulated environment

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