skbio.sequence.transition.hky85#

skbio.sequence.transition.hky85(d, freqs, kappa, seqtype='DNA', dtype='float32')[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: Evolutionary distance between sequences.
freqsarray_like of float of shape (4,): Relative frequencies of nucleobases A, C, G, and T/U, respectively. Should sum to 1.
kappafloat: Ratio between transition and transversion rates. Should be between 0 and 1.
seqtype{‘DNA’, ‘RNA’}, optional: Sequence type. Used to label matrix states as nucleotides (A, C, G, T/U). Default is “DNA”.
dtypestr or dtype, optional: Floating-point data type of the transition probability matrix. Options are “float32” (default) and “float64”.

Returns:

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