A gentle Introduction to Probabilistic Evolutionary Models

A large body of research is dedicated to model sequence evolutionary dynamics. The evolutionary process may vary within groups of genes, among sites within a gene, between populations and among diverged species. Evolutionary models aiming to describe these dynamics must account for base pair substitutions as well as insertion and deletion (indel) events. Here, we explain the fundamental of continuous time Markov models used to describe sequence evolution. We begin by describing discrete Markov models, and slowly progress towards more realistic and more computationally complicated continuous time Markov models. Among other topics, we discuss nucleotide, amino acid, and codon models, among site rate variation, model reversibility, stationary distributions, rate matrix normalization, mixture models, indel models, and models of gene family evolution. Understanding the concepts presented here is vital for various phylogenom-ics analyses such as the inference of positive selection, alignment and phylogeny reconstruction, ancestral sequence reconstruction, and molecular dating.