Genetic algebras and associated evolution operators

Abstract

The study of populations and the mechanisms that regulate them is essential for understanding ecosystems. In particular, analysing how a population evolves over time has long been regarded as a central mathematical challenge. Among the many existing mathematical frameworks for modelling population dynamics, this dissertation adopts an algebraic viewpoint, examining the role of certain nonassociative algebras, collectively known as genetic algebras, that provide a powerful tool for describing inheritance patterns in genetics. Although several classes of genetic algebras have been introduced in the literature, this thesis addresses two of them, each treated in a separate part: evolution algebras and gonosomal algebras.