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Marginal distributions of genetic coalgebras

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Abstract

We consider the backward evolution of a particular type of Mendelian genetic system whose transition probabilities give place to the so-called coalgebras with genetic realization and describe the equilibrium states of such mathematical objects and therefore those of the genetic system. We exploit the relationship between the genetic coalgebras modeling the transference of the genetic inheritance and cubic stochastic matrices of type (1, 2) studying first the ergodicity of these matrices in terms of the stationary probability distributions of the bivariate Markov chains defined by their accompanying matrices. Then we apply the obtained results to describe the equilibrium states of coalgebras with genetic realization.

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Authors and Affiliations

  1. Department of Statistics and Operative Research, Public University of Navarre, 31006 , Pamplona, Spain

    Irene Paniello

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  1. Irene Paniello
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Correspondence to Irene Paniello.

Additional information

Partially supported by the Spanish Ministerio de Ciencia y Tecnología and FEDER (MTM2010-18370-C04-02).

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Paniello, I. Marginal distributions of genetic coalgebras. J. Math. Biol. 68, 1071–1087 (2014). https://doi.org/10.1007/s00285-013-0663-9

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  • DOI: https://doi.org/10.1007/s00285-013-0663-9

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