Gonosomal Algebra

TL;DR

This paper introduces gonosomal algebra, extending evolution algebra of bisexual populations, to algebraically model diverse sex determination systems, including many not representable by previous models, with various algebraic constructions and properties.

Contribution

The paper defines gonosomal algebra, extends existing models, and provides new algebraic constructions and properties relevant to genetic sex determination systems.

Findings

Gonosomal algebras can represent a wide variety of sex determination systems.

Most examples cannot be represented by evolution algebra of bisexual populations.

Gonosomal algebras are not dibaric, unlike EABP.

Abstract

We introduce the gonosomal algebra. Gonosomal algebra extend the evolution algebra of the bisexual population (EABP) defined by Ladra and Rozikov. We show that gonosomal algebras can represent algebraically a wide variety of sex determination systems observed in bisexual populations. We illustrate this by about twenty genetic examples, most of these examples cannot be represented by an EABP. We give seven algebraic constructions of gonosomal algebras, each is illustrated by genetic examples. We show that unlike the EABP gonosomal algebras are not dibaric. We approach the existence of dibaric function and idempotent in gonosomal algebras.