Transition probability models (skbio.sequence.tpm)

This module provides functions for calculating transition probability matrices (TPMs) under several substitution models for a specified evolutionary distance (branch length).

A TPM gives the probability that each ancestral state (rows) is observed as each descendant state (columns) after the specified evolutionary distance. For continuous-time Markov models, the TPM is obtained from the instantaneous rate matrix, \(Q\), as \(P(t) = e^{Qt}\). Each row of the matrix sums to one.

Different models differ in the assumptions they make about instantaneous substitution rates and equilibrium state frequencies, resulting in different sets of model parameters. TPMs are also known as substitution probability matrices.

Transition probability matrices

jc69	Calculate the JC69 transition probability matrix for a given distance.
k2p	Calculate the K2P transition probability matrix for a given distance.
f81	Calculate the F81 transition probability matrix for a given distance.
hky85	Calculate the HKY85 transition probability matrix for a given distance.
tn93	Calculate the TN93 transition probability matrix for a given distance.