However, biologists are sometimes interested in the other aspects of the model. 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. Phylogenetic tree topologies and other parameters 12 The no common mechanism (NCM) model and maximum parsimony.6 The mathematics of substitution models.5 Time-reversible and stationary models.4 The molecular clock and the units of time.1 Phylogenetic tree topologies and other parameters.The equation transforms the proportion of nucleotide differences between taxa 1 and 2 ( p 12 = 4/18 the four site patterns that differ between taxa 1 and 2 are indicated with asterisks) into an evolutionary distance (in this case d 12=0.2635 substitutions per site). The evolutionary distance equation ( d 12) is based on the simple model proposed by Jukes and Cantor in 1969. 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). 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). The site patterns are shown along with the number of times they occur in alignment. The data in this alignment (in this case a toy example with 18 sites) is converted to a set of site patterns. Multiple sequence alignment (in this case DNA sequences) and illustrations of the use of substitution models to make evolutionary inferences. Substitution models are also necessary to simulate sequence data for a group of organisms related by a specific tree. Substitution models are also central to phylogenetic invariants because they are necessary to predict site pattern frequencies given a tree topology. 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). Thus, substitution models are central to maximum likelihood estimation of phylogeny as well as Bayesian inference in phylogeny. Substitution models are used to calculate the likelihood of phylogenetic trees using multiple sequence alignment data. 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). In biology, a substitution model, also called models of DNA sequence evolution, are Markov models that describe changes over evolutionary time. Short description: Description of the process by which states in sequences change into each other and back