In biology, a substitution model, also called models of DNA sequence evolution, are Markov models that describe changes over evolutionary time. These models describe evolutionary changes in macromolecules (e.g., DNA sequences) represented as sequence of symbols (A, C, G, and T in the case of DNA). Substitution models are used to calculate the likelihood of phylogenetic trees using multiple sequence alignment data. Thus, substitution models are central to maximum likelihood estimation of phylogeny as well as Bayesian inference in phylogeny. Estimates of evolutionary distances (numbers of substitutions that have occurred since a pair of sequences diverged from a common ancestor) are typically calculated using substitution models (evolutionary distances are used input for distance methods such as neighbor joining). Substitution models are also central to phylogenetic invariants because they are necessary to predict site pattern frequencies given a tree topology. Substitution models are also necessary to simulate sequence data for a group of organisms related by a specific tree. Phylogenetic tree topologies and other parameters Phylogenetic tree topologies are often the parameter of interest; thus, branch lengths and any other parameters describing the substitution process are often viewed as nuisance parameters. However, biologists are sometimes interested in the other aspects of the model. For example, branch lengths, especially when those branch lengths are combined with information from the fossil record and a model to estimate the timeframe for evolution. Other model parameters have been used to gain insights into various aspects of the process of evolution. The Ka/Ks ratio (also called ω in codon substitution models) is a parameter of interest in many studies. The Ka/Ks ratio can be used to examine the action of natural selection on protein-coding regions, it provides information about the relative rates of nucleotide substitutions that change amino acids (non-synonymous substitutions) to those that do not change the encoded amino acid (synonymous substitutions). Application to sequence data Most of the work on substitution models has focused on DNA/RNA and protein sequence evolution. Models of DNA sequence evolution, where the alphabet corresponds to the four nucleotides (A, C, G, and T), are probably the easiest models to understand. DNA models can also be used to examine RNA virus evolution; this reflects the fact that RNA also has a four nucleotide alphabet (A, C, G, and U). However, substitution models can be used for alphabets of any size; the alphabet is the 20 proteinogenic amino acids for proteins