Mathematical Model for Predicting Time of a Shared Common Ancestor

Abstract

Accurate and efficient model development in the field of evolutionary biology is becoming increasingly important to study phylogenetic relationships. Studying these phylogenetic relationships can provide greater insight into areas such as drug development, analyzing disease transmission, and studying the host-pathogen evolutionary relationship. This study uses the idea of a transition matrix to predict how long ago two species shared a common ancestor. Using this concept and various linear algebraic ideas, a mathematical model that simulated amino acid mutations was developed, and it was implemented in Python to perform trials. The main result of the development of the model was a matrix containing the expected values for the number of years ago two amino acids were the same. Simulations of the model can be run in Python multiple times and the average of the values obtained gives an estimate of how many years ago two amino acids were the same. These represent the number of years ago the species shared a common ancestor. The result varies based on the species data analyzed. This model provides a foundation for development of more complex models that enhance phylogenetic tree development. As stated previously, this can have substantial impacts on biotechnology and biomedical sciences, which often rely on analyzing these evolutionary relationships.