Solvable senescence model with positive mutations

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

doi:10.1103/physreve.70.021907

Cited by 5 publications

(2 citation statements)

References 13 publications

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“…These mutations are taken to be harmful so can only turn healthy sites into unhealthy ones -a mutation on an unhealthy site is ignored. This assumption is relaxed in [10] where a small rate of positive mutation is allowed: we confine ourselves here to the case of only harmful mutations.…”

Section: Introductionmentioning

confidence: 99%

Gompertz mortality law and scaling behavior of the Penna model

Coe

2005

Phys. Rev. E

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*The Penna model is a model of evolutionary ageing through mutation accumulation where traditionally time and the age of an organism are treated as discrete variables and an organism's genome by a binary bit string. We reformulate the asexual Penna model and show that a universal scale invariance emerges as we increase the number of discrete genome bits to the limit of a continuum. The continuum model, introduced by Almeida and Thomas in [Int. J. Mod. Phys. C, 11, 1209 (2000)] can be recovered from the discrete model in the limit of infinite bits coupled with a vanishing mutation rate per bit. Finally, we show that scale invariant properties may lead to the ubiquitous Gompertz Law for mortality rates for early ages, which is generally regarded as being empirical.

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Section: Introductionmentioning

confidence: 99%

Gompertz mortality law and scaling behavior of the Penna model

Coe

2005

Phys. Rev. E

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“…This was done by Coe et al in a series of papers (Coe et al 2002(Coe et al , 2004Mao 2003, 2005) where the population structure is given by the distribution function n(a, l, t). The analytical result for the self-consistent steady solution n(a, l) = n(a, l, t ?…”

Section: Introductionmentioning

confidence: 98%

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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Role of thermal fluctuations in biological copying mechanisms

Das

Kantz

2021

Phys. Rev. E

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Solvable senescence model with positive mutations

Cited by 5 publications

References 13 publications

Gompertz mortality law and scaling behavior of the Penna model

Gompertz mortality law and scaling behavior of the Penna model

Stability of the analytical solution of Penna model of biological aging

Role of thermal fluctuations in biological copying mechanisms

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