A survey of the modified Moran process and evolutionary graph theory

Abstract Historically, the field of evolutionary dynamics has been a relevant tool in modeling the evolution of processes in areas as biology, sociology and others. In this work we first present a survey of the field from the XVIII century to mid XX century, until the genetic models of Wright–Fisher and Moran. In the second part we survey recent mathematical and algorithmic results on the adaptation of the Moran process due to Lieberman et al. (2005). We survey the results related to the absorption probability and the absorption time.