Evolution algebra of a bisexual population
By Manuel Ladra, Utkir A. Rozikov. 2010
53 citations recorded by the source corpus.
We introduce an (evolution) algebra identifying the coefficients of inheritance of a bisexual population as the structure constants of the algebra. The basic properties of the algebra are studied. We prove that this algebra is commutative (and hence flexible), not associative and not necessarily power associative. We show that the evolution algebra of the bisexual population is not a baric algebra, but a dibaric algebra and hence its square is baric. Moreover, we show that the algebra is a Banach algebra. The set of all derivations of the evolution algebra is described. We find necessary conditions for a state of the population to be a fixed point or a zero point of the evolution operator which corresponds to the evolution algebra. We also establish upper estimate of the limit points set for trajectories of the evolution operator. Using the necessary conditions we give a detailed analysis of a special case of the evolution algebra (bisexual population of which has a preference on type "1" of females and males). For such a special case we describe the full set of idempotent elements and the full set of absolute nilpotent elements.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/2a951e5501e415ffdee88d83127925fed6c125f6
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In Algebra and Number Theory
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Evolution algebras of arbitrary dimension and their decompositions (2016, methodology): “In [14], the evolution algebras have been used to describe the inheritance of a bisexual population and, in this setting, the existence of non-trivial homomorphisms onto the sex differentiation algebra have been studied in [15].”