Solvable Senescence Model Showing a Mortality Plateau

Coe, J. B.; Y, Mao; Cates, Michael

doi:10.1103/physrevlett.89.288103

Cited by 24 publications

(37 citation statements)

References 29 publications

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“…Here we develop an analytical solution to a Penna model with a small rate of positive mutation. Our analysis builds upon previous work where a solution to a generalized class of stochastic Penna models was presented [7]. All populations are considered in the thermodynamic limit of a large population where statistical fluctuations and effects of discretization can be ignored.…”

Section: Introductionmentioning

confidence: 99%

Solvable senescence model with positive mutations

Coe

Cates

2004

Phys. Rev. E

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We build upon our previous analytical results for the Penna model of senescence to include positive mutations. We investigate whether a small but non-zero positive mutation rate gives qualitatively different results to the traditional Penna model in which no positive mutations are considered. We find that the high-lifespan tail of the distribution is radically changed in structure, but that there is not much effect on the bulk of the population. The mortality plateau that we found previously for a stochastic generalization of the Penna model is stable to a small positive mutation rate.

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Section: Introductionmentioning

confidence: 99%

Solvable senescence model with positive mutations

Coe

Cates

2004

Phys. Rev. E

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“…For simplicity we present our dynamics analysis within this simple Penna model, since it is straightforward to generalise to the case of T > 1 [8]. The steadystate solution [7] to the simple Penna model is given in brief below:…”

Section: The Simple Penna Modelmentioning

confidence: 99%

“…For any population there is a maximum sustainable string-length l max , the stability analysis of which [7,8] leads the stationary-state interdependence of b and β:…”

Section: The Simple Penna Modelmentioning

confidence: 99%

“…The Penna model, essentially a mutation accumulation model, has been so successful that it has rapidly established itself as a major model for population simulations [4]. Recently, analytical solutions have been presented for the steady states of the Penna model [7,8], shedding insights into the inter-relationships between various Penna parameters of the simulation model. Here, we build upon this analytical framework to study populations undergoing steady growth or decline and to study the transient behaviour of the model when the system is away from its steady states.…”

Section: Introductionmentioning

confidence: 99%

“…Here, we build upon this analytical framework to study populations undergoing steady growth or decline and to study the transient behaviour of the model when the system is away from its steady states. Previous attempts [9] to analyse the population dynamics did not have the advantage of the full analytic steady state solution [7,8], and consequently could not fully explore the dynamics of the model. We find that the fluctuations in a population away from steady state can be decomposed into a collection of modes each of which decays exponentially with its respective time constant.…”

Section: Introductionmentioning

confidence: 99%

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Population dynamics in the Penna model

2004

Phys. Rev. E

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We build upon the recent steady-state Penna model solution, Phys. Rev. Lett. 89, 288103 (2002), to study the population dynamics within the Penna model. We show, that any perturbation to the population can be broken into a collection of modes each of which decay exponentially with its respective time constant. The long time behaviour of population is therefore likely to be dominated by the modes with the largest time constants. We confirm our analytical approach with simulation data.

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Stability of the analytical solution of Penna model of biological aging

Magdon-Maksymowicz

2008

Theory Biosci.

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There are some analytical solutions of the Penna model of biological aging; here, we discuss the approach by Coe et al. (Phys. Rev. Lett. 89, 288103, 2002), based on the concept of self-consistent solution of a master equation representing the Penna model. The equation describes transition of the population distribution at time t to next time step (t + 1). For the steady state, the population n(a, l, t) at age a and for given genome length l becomes time-independent. In this paper we discuss the stability of the analytical solution at various ranges of the model parameters--the birth rate b or mutation rate m. The map for the transition from n(a, l, t) to the next time step population distribution n(a + 1, l, t + 1) is constructed. Then the fix point (the steady state solution) brings recovery of Coe et al. results. From the analysis of the stability matrix, the Lyapunov coefficients, indicative of the stability of the solutions, are extracted. The results lead to phase diagram of the stable solutions in the space of model parameters (b, m, h), where h is the hunt rate. With increasing birth rate b, we observe critical b (0) below which population is extinct, followed by non-zero stable single solution. Further increase in b leads to typical series of bifurcations with the cycle doubling until the chaos is reached at some b (c). Limiting cases such as those leading to the logistic model are also discussed.

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Solvable Senescence Model Showing a Mortality Plateau

Cited by 24 publications

References 29 publications

Solvable senescence model with positive mutations

Solvable senescence model with positive mutations

Population dynamics in the Penna model

Stability of the analytical solution of Penna model of biological aging

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