skbio.sequence.transition.f81#

skbio.sequence.transition.f81(d, freqs, seqtype='DNA')[source]#

Calculate the F81 transition probability matrix for a given distance.

Added in version 0.7.4.

The Felsenstein 1981 (F81) model assumes equal substitution rates among nucleotide pairs but allows unequal equilibrium base frequencies \(\pi\).

The transition probability between nucleotide states for sequences separated by evolutionary distance \(d\) is given by:

\[\begin{split}P_{ij} = \begin{cases} \pi_i + (1 - \pi_i) e^{-\frac{d}{b}} & i = j \\ \pi_j (1 - e^{-\frac{d}{b}}) & i \neq j \end{cases}\end{split}\]

Where \(i,j \in \{A, C, G, T/U\}\), \(i\) is ancestral nucleotide, \(j\) is descendant nucleotide. The normalization constant \(b\) is defined as:

\[b = 1 - \pi_A^2 - \pi_C^2 - \pi_G^2 - \pi_T^2\]

Parameters:

dfloat: distance or distances between sequences.
freqsarray_like of float of shape (4,): Relative frequencies of nucleobases A, C, G, and T/U, respectively. Should sum to 1.
seqtypestr: String that holds type of the sequence. “DNA” (default) and “RNA” are valid options. Needed to assign proper nucleotide letters to SubstitutionMatrix dimensions.

Returns:

SubstitutionMatrix: Transition probability matrix. Rows are ancestral nucleotides, columns are descendant nucleotides.