Over Viewing The Substitution Models

Over Viewing The Substitution Models

Continuing from the previous post, here is a run-down of the commonly used models, their abbreviations, alternative names and abbreviations, and parameters. They are sorted from most parameter-rich to simplest.

General Time-Reversible (GTR)

Base frequencies variable.

All six substitution rates variable.

Number of free parameters: 8

Transversional (TVM)

Base frequencies variable.

All four transversion rates variable, transitions equal.

Number of free parameters: 7

Transitional (TIM)

Base frequencies variable.

Two different transversion rates, transitions equal.

Number of free parameters: 6

Symmetrical (SYM)

Base frequencies equal.

All six substitution rates variable.

Number of free parameters: 5

Kimura 3-parameters (K81, K3P, TPM1)

Base frequencies variable.

Two different transversion rates, transition rates equal.

Number of free parameters: 5

Tamura-Nei (TN93, TrN)

Base frequencies variable.

Transversion rates equal, transition rates variable.

Number of free parameters: 5

Hasegawa-Kishino-Yano (HKY)

Base frequencies variable.

Transversion rates equal, transition rates equal.

Number of free parameters: 4

Differs from F84 in how the transversion rate and transition rate parameters are derived.

Felsenstein 84 (F84)

Base frequencies variable.

Transversion rates equal, transition rates equal.

Number of free parameters: 4

Differs from HKY in how the transversion rate and transition rate parameters are derived.

Felsenstein 81 (F81, TN84)

Base frequencies variable.

All substitution rates equal.

Number of free parameters: 3

Kimura 2-parameters (K80, K2P)

Base frequencies equal.

Transversion rates equal, transition rates equal.

Number of free parameters: 1

Jukes-Cantor (JC, JC69)

Base frequencies equal.

All substitution rates equal.

Number of free parameters: 0

And below an overview of the same information in graphical form. The numbers in brackets are the numbers of free parameters that the relevant axis is contributing.

Apparently at least some people fill the empty fields on the left in by using the name of the relevant model to the right and adding "ef" to it. So TVMef would, for example, be a model with all transversion rates variable, transition rates equal, and equal base frequencies. But there is probably a reason why those missing models don't have any well known names; they seem to be rarely used, if ever.