Substitution model

In biology, a substitution model describes the process from which a sequence of symbols changes into another set of traits. For example, in cladistics, each position in the sequence might correspond to a property of a species which can either be present or absent. The alphabet could then consist of "0" for absence and "1" for presence. Then the sequence 00110 could mean, for example, that a species does not have feathers or lay eggs, does have fur, is warm-blooded, and cannot breathe underwater. Another sequence 11010 would mean that a species has feathers, lays eggs, does not have fur, is warm-blooded, and cannot breathe underwater. In phylogenetics, sequences are often obtained by firstly obtaining a nucleotide or protein sequence alignment, and then taking the bases or amino acids at corresponding positions in the alignment as the characters. Sequences achieved by this might look like AGCGGAGCTTA and GCCGTAGACGC.

Substitution models are used for a number of things:

Most substitution models used to date are neutral, independent, finite sites models.

Typically, a branch length of a phylogenetic tree is expressed as the expected number of substitutions per site; if the evolutionary model indicates that each site within an ancestral sequence will typically experience x substitutions by the time it evolves to a particular descendant's sequence then the ancestor and descendant are considered to be separated by branch length x.

Sometimes a branch length is measured in terms of geological years. For example, a fossil record may make it possible to determine the number of years between an ancestral species and a descendant species. Because some species evolve at faster rates than others, these two measures of branch length are not always in direct proportion. The expected number of substitutions per site per year is often indicated with the Greek letter mu (μ).

A model is said to have a strict molecular clock if the expected number of substitutions per year μ is constant regardless of which species' evolution is being examined. An important implication of a strict molecular clock is that the number of expected substitutions between an ancestral species and any of its present-day descendants must be independent of which descendant species is examined.

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