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Gompertz mortality law and scaling behavior of the Penna model

J. B. Coe1,* and Y. Mao2

  • 1Biomathematics & Statistics Scotland, James Clerk Maxwell Building, The King’s Building, Edinburgh EH9 3JZ Scotland
  • 2School of Physics and Astronomy, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom

  • *J.B.C. is also affiliated to the Institute of Evolutionary Biology, University of Edinburgh and Department of Physics and Astronomy, University of Edinburgh.
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Phys. Rev. E 72, 051925 – Published 28 November, 2005

DOI: https://doi.org/10.1103/PhysRevE.72.051925

Abstract

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 is represented 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 [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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Outline

Information

Phys. Rev. E 72, 051925– Published 28 November, 2005
  • Received 10 May 2005

© 2005 American Physical Society

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