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Hasegawa–Kishino–Yano (1985) distance (HKY85)

Source: R/HKY85_distance.R
HKY85_distance.Rd

Computes the HKY85 nucleotide substitution distance between two sequences, using only the A/C/G/T block of a pairwise count matrix. Base frequencies are estimated as the average of row and column marginals, and transitions are pooled into a single class (A↔G and C↔T).

Usage

HKY85_distance(m)

Arguments

m

A numeric matrix of pair counts with row/column names including A,C,G,T. If m is a list, the field $probability_matrix is used (for compatibility with your other helpers).

Value

A single numeric: the HKY85 distance (substitutions/site).

Details

Let \(P\) be the total fraction of transition differences (A↔G plus C↔T) among A/C/G/T pairs, and \(Q\) the fraction of transversion differences (all other A↔{C,T}, G↔{C,T} pairs). Let \(\pi_A,\pi_C,\pi_G,\pi_T\) be the average base frequencies across the two sequences (row and column marginals averaged), \(\pi_R = \pi_A + \pi_G\), and \(\pi_Y = \pi_C + \pi_T\).

The HKY85 distance (special case of TN93 with a single transition rate) is: $$ d_{\mathrm{HKY85}} = -\,2(\pi_A \pi_G + \pi_C \pi_T)\; \ln\!\left(1 - \frac{P}{2(\pi_A \pi_G + \pi_C \pi_T)}\right) -\,2\,\pi_R \pi_Y\; \ln\!\left(1 - \frac{Q}{2\,\pi_R \pi_Y}\right). $$

Implementation notes:

  • Rows/columns outside A,C,G,T are dropped.

  • \(P\) and \(Q\) are computed from the normalized 4×4 table.

  • \(\pi_\bullet\) are estimated as the average of row and column marginals.

  • Returns Inf if any log argument is non‑positive or a denominator is zero.

References

Hasegawa, M., Kishino, H., and Yano, T. (1985). Dating of the human–ape splitting by a molecular clock of mitochondrial DNA. J. Mol. Evol. 22:160–174.

RevBayes tutorial (overview of HKY, parameters \(\kappa,\pi\)): https://revbayes.github.io/tutorials/ctmc/

IQ‑TREE model manual (relationships among HKY, K80, TN93): https://iqtree.github.io/doc/Substitution-Models

See also

Other Alignment statistics: F81_distance(), GCequilibrium(), GCpressure(), GCproportion(), JC69_distance(), K80_distance(), P_distance(), T92_distance(), TN93_distance(), exampleSubstitutionMatrix, gapProportion(), logDet_distance()

Other Similarity indexes: F81_distance(), GOC(), JC69_distance(), K80_distance(), P_distance(), T92_distance(), TN93_distance(), correlation_index(), karyotype_index(), logDet_distance(), slidingWindow(), strand_randomisation_index(), synteny_index(), tau_index()

Author

Entirely written by Copilot and not proofchecked yet

Examples

HKY85_distance(exampleSubstitutionMatrix)
#> [1] 0.288648