RNA oligonucleotide association coefficient ($S_{AB}=2N_{AB}/(N_A+N_B)$)

The RNA oligonucleotide association coefficient measures the overlap of two catalogs produced through ribosomal RNA oligonucleotide cataloguing, weighting the retained shared fragments by their nucleotide content. In the 1977 comparison, catalogued sequences had at least six residues, andwhere $N_A,N_B$ count nucleotide residues represented in the two eligible catalogs and $N_{AB}$ counts those represented in their shared portion. It is a catalog-overlap statistic, not the percentage identity of a complete sequence alignment.^[ref]

An original example uses distinct fragment labels with specified lengths. CatalogA contains $a_6,b_8,c_{10}$; catalogB contains $a_6,b_8,d_6$. The subscripts denote nucleotide counts, and differently named fragments are different sequences. ThusCounting only matched labels would instead give two shared labels out of three per catalog, producing $2/3$. The difference exposes the effect of weighting: a shared eight-residue fragment contributes more than a shared six-residue fragment.

For a nonzero denominator, $0\le N_{AB}\le \min (N_A,N_B)$ gives $0\le S_{AB}\le 1$. A useful equivalent form isThe numerator in the subtracted fraction represents the catalog material outside the overlap under this counting model. If both catalogs are empty, the original formula has denominator zero; assigning a value would require an extra convention.

The coefficient is also sensitive to catalog coverage. Add the same new six-residue fragment to both example catalogs: the totals become30 and26, with20 shared, so the coefficient rises to $40/56=5/7$. Add it only toA instead, and the coefficient is $28/50=0.56$. These constructed changes alter the statistic without specifying any new evolutionary history.

The original ribosomal RNA oligonucleotide cataloguing experiments used comparisons of this kind as evidence for phylogenetics. Turning a similarity into a particular phylogenetic tree or a divergence date needs additional assumptions and evidence. The statistic itself records the specified molecular overlap.^[ref]