Elsevier

Journal of Symbolic Computation

Volume 79, Part 2, March–April 2017, Pages 342-355
Journal of Symbolic Computation

Polynomial dynamics of human blood genotypes frequencies

https://doi.org/10.1016/j.jsc.2016.02.012Get rights and content
Under an Elsevier user license
open archive

Abstract

The frequencies of human blood genotypes in the ABO and Rh systems differ between populations. Moreover, in a given population, these frequencies typically evolve over time. The possible reasons for the existing and expected differences in these frequencies (such as disease, random genetic drift, founder effects, differences in fitness between the various blood groups etc.) are the focus of intensive research. To understand the effects of historical and evolutionary influences on the blood genotypes frequencies, it is important to know how these frequencies behave if no influences at all are present. Under this assumption the dynamics of the blood genotypes frequencies is described by a polynomial dynamical system defined by a family of quadratic forms on the 17-dimensional projective space. To describe the dynamics of such a polynomial map is a task of substantial computational complexity.

We give a complete analytic description of the evolutionary trajectory of an arbitrary distribution of human blood variations frequencies with respect to the clinically most important ABO and RhD antigens. We also show that the attracting algebraic manifold of the polynomial dynamical system in question is defined by a binomial ideal.

MSC

37N25
37F10
74H05

Keywords

Polynomial dynamical systems
Binomial ideals
Projective space
Human blood genotypes frequencies
ABO and Rh blood systems
Evolutionary trajectories

Cited by (0)

Funding for this research was provided by the grant of the Russian Federation Government to support scientific research under the supervision of leading scientist at Siberian Federal University, No. 14.Y26.31.0006. The author was also supported by the grants of the Russian Foundation for Basic Research Nos. 13-01-12417-ofi-m2, 14-01-00544-a, and 15-31-20008-mol-a-ved.