skbio.sequence.transition.hky85#

skbio.sequence.transition.hky85(d, freqs, kappa, seqtype='DNA')[source]#

Calculate the HKY85 transition probability matrix for a given distance.

Added in version 0.7.4.

The Hasegawa, Kishino, and Yano 1985 (HKY85) allows differential base frequencies (\(\pi\)) and assumes fixed ratio \(\kappa\) between rates of transitions (substitutions between two purines or between two pyrimidines) and transversions (substitutions between a purine and a pyrimidine). Transition probability for a nucleotide for sequences with a distance \(d\) between them can be calculated like:

\[P_{ij} = e^{\frac{-(\kappa + 1)d}{2b}}\delta_{ij} + e^{-\frac{d}{b}}\left (1 - e^{\frac{-(\kappa - 1)d}{2b}}\right ) \frac{\pi_j\epsilon_{ij}}{\sum_k \epsilon_{jk}\pi_k} + \left (1 - e^{-\frac{d}{b}}\right )\pi_j\]

Where \(i,j \in \{A, C, G, T/U\}\), \(i\) is ancestral nucleotide, \(j\) is descendant nucleotide, \(\delta_{ij}\) is Kronecker delta function and is 1 if \(i=j\) and 0 otherwise, epsilon_{ij} is purine/pyrimidine indicator function and is 1 if \(i\) and \(j\) in the same nucloetide class and is 0 otherwise. 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.
kappa: Transition/transversion rate ratio. Should be \(0 < \kappa \leq 1\).
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.