Algebraic representation and modeling of evolutionary innovation and adaptation in biological systems

Abstract

Living systems are equipped with the coding system which enables them to autonomously determine set of agents for performing all functional tasks. Since scope of their functioning for given environment is entirely dependant on internally given structure of the coding system they are able to evolve both new traits (evolutionary innovation) and optimize existent ones (evolutionary adaptation) by means of mutations and different mechanisms of genetic rearrangements. In this paper we give a generalized mathematical framework for presenting evolution in living systems in terms of category theory, comprising both innovation and adaptation. On that basis we construct a simple computational model, where as an example we performed evolution of randomly generated coding sequences and analyze appearance of interaction networks and their evolution, as well as evolution of the coding sequence itself. We also demonstrate that evolved networks have some properties of metabolism-like systems.