Substitution model

In biology, a substitution model, also called models of sequence evolution, are Markov models that describe changes over evolutionary time. These models describe evolutionary changes in macromolecules, such as DNA sequences or protein sequences, that can be represented as sequence of symbols (e.g., A, C, G, and T in the case of DNA or the 20 "standard" proteinogenic amino acids in the case of proteins). 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.

Multiple sequence alignment (in this case DNA sequences) and illustrations of the use of substitution models to make evolutionary inferences. The data in this alignment (in this case a toy example with 18 sites) is converted to a set of site patterns. The site patterns are shown along with the number of times they occur in alignment. These site patterns are used to calculate the likelihood given the substitution model and a phylogenetic tree (in this case an unrooted four-taxon tree). It is also necessary to assume a substitution model to estimate evolutionary distances for pairs of sequences (distances are the number of substitutions that have occurred since sequences had a common ancestor). The evolutionary distance equation (d12) is based on the simple model proposed by Jukes and Cantor in 1969. The equation transforms the proportion of nucleotide differences between taxa 1 and 2 (p12 = 4/18; the four site patterns that differ between taxa 1 and 2 are indicated with asterisks) into an evolutionary distance (in this case d12=0.2635 substitutions per site).