Stability of the analytical solution of Penna model of biological aging

Magdon-Maksymowicz, Maria Stanislawa

doi:10.1007/s12064-008-0051-y

Cited by 3 publications

(2 citation statements)

References 9 publications

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“…The Penna model of bad-mutations accumulation, however, lacks an analytical solution -apart from a very limited case of a single mutation threshold that kills. The Coe ([8]) et al analytical results of the Penna model were also obtained in our earlier simulations [9]. Competition within the Penna model in a restricted habitat was studied in [10,11].…”

Section: Introductionmentioning

confidence: 94%

On Evolution of Migrating Population with Two Competing Species

Magdon-Maksymowicz¹,

Maksymowicz²

2013

csci

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A computer experiment study of population evolution and its dynamics is presented for two competing species (A and B) which share two habitats (1 and 2) of a limited environmental capacity. The Penna model of biological aging, based on the concept of defective mutation accumulation, was adopted for migrating population. In this paper, we assume and concentrate on the case when only one species (A) is mobile. For isolated habitats and for any initial population, we get at equilibrium spatial population distribution (A, B) in which A occupies location '1' only, while B-species is the ultimate winner in '2'. This is achieved by suitable choice of model parameters so habitat '1' is more attractive for species 'A' while location '2' is more advantageous to 'B'. However, population distribution begins to differ when migration between habitats is allowed. Initially stable distribution (A, B), becomes (A, A&B) with a mixed stationary population in location '2'. For a higher migration rate, initial (A, B) distribution goes to (A, A) distribution, in which A species is dominant also in a less friendly habitat '2'. However, a further increase in migration rate brings sequence (A, B) → (B, B). In short, for sufficiently high mobility of A-species, they eliminate themselves. Other scenarios not discussed here were also studied. They offer a rich variety of different sequences of population distribution regarding their size as well as other characteristics.

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Section: Introductionmentioning

confidence: 94%

On Evolution of Migrating Population with Two Competing Species

Magdon-Maksymowicz¹,

Maksymowicz²

2013

csci

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“…Let us mention some examples of the many possible variations of the Penna model. Fluctuations in T, which come from mutations already activated at birth time (Maksymowicz 1999); a learning process which gives an advantage in the life game for more intelligent individuals (He and Pan 2005;He et al 2006); tracing back history to prove divergent evolution paths of different species, which may lead in the evolution process to severe reduction of number of the species (Sitarz and Maksymowicz 2005), birth rate B controlled by already active deleterious mutations (Magdoń-Maksymowicz 2008), and mutation rate M varying with parent's age a (Magdoń- Maksymowicz and Maksymowicz 2009)-they all are based on the Penna model. Also, simple classifications of mutations as deleterious or beneficial may not be so simple as the role and significance of mutations may change with age, showing antagonistic pleiotropy (Westendorp and Kirkwood 1998;Gavrilov and Gavrilova 1999).…”

Section: Introductionmentioning

confidence: 99%

Epigenetic contribution to age distribution of mortality within the Penna model

Magdon-Maksymowicz¹,

Maksymowicz²

2015

Theory Biosci.

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Some modifications of the simple asexual Penna model, enriched by epigenetic contributions, are presented. The standard bit-string Penna model of biological aging and population evolution is based on an inherited DNA structure which defines the future life of a newly born individuals, when genes are activated by the biological clock, and the predefined genetic death is fully controlled by the number of defected genes. Epigenomes allow to introduce additional mechanism of gene activation or silencing without affecting the DNA genome itself. It may be either inherited or may reflect external, environmental factors. In the presented model, information read from the introduced epigenome may alter gene expression that may be stopped or re-activated. We concentrate on the influence of epigenetics on the age a distribution of genetic mortality m(a). Changes in m(a) are strong for the case of inherited epigenetic contribution with nearly perfect inheritance and 'positive' epigenome that partly ignores the 'bad' mutations. We conclude that the epigenetic contribution may influence population structure m(a) and could be, at least partly, responsible for deviation of m(a) distribution from the Gompertz law. In short, we claim that proposed epigenetic contribution may be seen as a candidate for possible explanation of observed deviation from the Gompertz law, also among senior members of society. A very simple model was used in this paper and many crucial mechanisms of biological aging were omitted. Therefore, further work based on a more realistic models is necessary.

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Numerical solution of the Penna model of biological aging with age-modified mutation rate

Magdon-Maksymowicz

Maksymowicz

2009

Phys. Rev. E

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In this paper we present results of numerical calculation of the Penna bit-string model of biological aging, modified for the case of a -dependent mutation rate m(a), where a is the parent's age. The mutation rate m(a) is the probability per bit of an extra bad mutation introduced in offspring inherited genome. We assume that m(a) increases with age a. As compared with the reference case of the standard Penna model based on a constant mutation rate m , the dynamics of the population growth shows distinct changes in age distribution of the population. Here we concentrate on mortality q(a), a fraction of items eliminated from the population when we go from age (a) to (a+1) in simulated transition from time (t) to next time (t+1). The experimentally observed q(a) dependence essentially follows the Gompertz exponential law for a above the minimum reproduction age. Deviation from the Gompertz law is however observed for the very old items, close to the maximal age. This effect may also result from an increase in mutation rate m with age a discussed in this paper. The numerical calculations are based on analytical solution of the Penna model, presented in a series of papers by Coe et al. [J. B. Coe, Y. Mao, and M. E. Cates, Phys. Rev. Lett. 89, 288103 (2002)]. Results of the numerical calculations are supported by the data obtained from computer simulation based on the solution by Coe et al.

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Stability of the analytical solution of Penna model of biological aging

Cited by 3 publications

References 9 publications

On Evolution of Migrating Population with Two Competing Species

On Evolution of Migrating Population with Two Competing Species

Epigenetic contribution to age distribution of mortality within the Penna model

Numerical solution of the Penna model of biological aging with age-modified mutation rate

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