Uncertainty of the second order

Quasispecies model with inverse Bayesian inference
  • Taichi HarunaEmail author
Original Article


We study the stochastic dynamics of the quasispecies model with inverse Bayesian inference under environmental uncertainty. Inverse Bayesian inference is introduced through the correspondence between Bayesian inference and the replicator equation. We consider environmental uncertainty that is not modeled as the stochastic fitness called uncertainty of the second order. This is in contrast to uncertainty of the first order that can be subsumed by the stochastic fitness. The difference between these two kinds of uncertainty is discussed in the framework of categorical Bayesian probability theory. We analytically show that if the time scale of inverse Bayesian inference is sufficiently larger than that of Bayesian inference, then the quasispecies model exhibits a noise-induced transition. The theoretical result is verified by a numerical simulation.


Bayesian inference Replicator equation Quasispecies model Category theory Fokker–Planck equation Noise-induced transition 



The author is grateful to the anonymous reviewers for their helpful suggestions. The author was partially supported by JSPS KAKENHI Grant Number 18K03423.


  1. 1.
    Arecchi FT (2011) Phenomenology of consciousness: from apprehension to judgement. Nonlinear Dyn Psychol Life Sci 15:359–375Google Scholar
  2. 2.
    Culbertson J, Sturtz K (2014) A categorical foundation for Bayesian probability. Appl Categorical Struct 22:647–662MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Eigen M (1971) Selforganization of matter and the evolution of biological macromolecules. Naturwissenshaften 58:465–523CrossRefGoogle Scholar
  4. 4.
    Friston K (2010) The free-energy principle: a unified brain theory? Nat Rev Neurosci 11:127–138CrossRefGoogle Scholar
  5. 5.
    Gardiner CW (2004) Handbook of stochastic methods, 3rd edn. Springer, BerlinCrossRefzbMATHGoogle Scholar
  6. 6.
    Gunji YP, Shinohara S, Haruna T, Basios V (2017) Inverse Bayesian inference as a key of consciousness featuring a macroscopic quantum logical structure. Biosystems 152:44–65CrossRefGoogle Scholar
  7. 7.
    Gunji YP, Sonoda K, Basios V (2016) Quantum cognition based on an ambiguous representation derived from a rough set approximation. Biosystems 141:55–66CrossRefGoogle Scholar
  8. 8.
    Harper M (2009) The replicator equation as an inference dynamic. arXiv:0911.1763v3
  9. 9.
    Horsthemke W, Lefever R (1984) Noise-induced transitions. Springer, BerlinzbMATHGoogle Scholar
  10. 10.
    Knill DC, Pouget A (2004) The Bayesian brain: the role of uncertainty in neural coding and computation. Trends Neurosci 27:712–719CrossRefGoogle Scholar
  11. 11.
    Kobayashi TJ (2011) Connection between noise-induced symmetry breaking and an information-decoding function for intracellular networks. Phys Rev Lett 106:228101CrossRefGoogle Scholar
  12. 12.
    Nowak M (2006) Evolution dynamics: exploring equation of life. Belknap Press, HarvardGoogle Scholar
  13. 13.
    Pöppel E (2004) Lost in time: a historical frame, elementary processing units and the 3-second window. Acta Neurobiol Exp 64:295–301Google Scholar
  14. 14.
    Pöppel E (2009) Pre-semantically defined temporal windows for cognitive processing. Phil Trans R Soc B 364:1887–1896CrossRefGoogle Scholar
  15. 15.
    Shalizi CR (2009) Dynamics of Bayesian updating with dependent data and misspecified models. Electr J Stat 3:1039–1074MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© International Society of Artificial Life and Robotics (ISAROB) 2019

Authors and Affiliations

  1. 1.Department of Information and SciencesTokyo Woman’s Christian UniversityTokyoJapan

Personalised recommendations