Individual-based models (IBMs), unlike the mean-field ones, are commonly not described by equations, but instead by well-defined rules, which are meant to be ran in a computer. Although widely used in many biological fields, it is not easy to achieve general results, once they can bear many tunable parameters whose interplay can be very complex. In this talk, I aim to introduce three interesting models in which a mathematical description can be formulated and some analytical results can be found.
Considering binary strings as a proxy for individuals’ genetic sequence, it is possible to analyze their evolution under different scenarios. The so-called Derrida-Higgs model, which is an IBM of this type, mimics the species formation process in a sympatric community; from this, a model of coevolution between mitochondrial and nuclear DNA has been proposed by Príncepe and de Aguiar (2020), which will also be covered during the talk.
Moreover, binary strings have also been used to model RNA viruses going on epidemic, and together with network theory they can provide a powerful framework for the study of viral evolution.