Time-reversible and Stationary Models
Many useful substitution models are time-reversible; in terms of the mathematics, the model does not care which sequence is the ancestor and which is the descendant so long as all other parameters (such as the number of substitutions per site that is expected between the two sequences) are held constant.
When an analysis of real biological data is performed, there is generally no access to the sequences of ancestral species, only to the present-day species. However, when a model is time-reversible, which species was the ancestral species is irrelevant. Instead, the phylogenetic tree can be rooted using any of the species, re-rooted later based on new knowledge, or left unrooted. This is because there is no 'special' species, all species will eventually derive from one another with the same probability.
A model is time reversible if and only if it satisfies the property
or, equivalently, the detailed balance property,
for every i, j, and t. The notation is explained below.
Time-reversibility should not be confused with stationarity. A model is stationary if Q does not change with time. The analysis below assumes a stationary model.
Read more about this topic: Substitution Model
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