Who invented dN/dS?

Question

I am writing a paper, and I want to refer to the original paper that coined the term dN/dS (or Ka/Ks for that matter). I have found early works on dN and dS (like Miyata and Yasunaga 1980), but cannot find the first paper that used the ratio dN/dS. Does anyone know which paper is the best to cite dN/dS?

Edit: dN is the rate of non-synonymous substitutions per non-synonymous sites; dS is the rate of synonymous substitutions per synonymous sites. dN/dS is simply the ratio between dN and dS.

Reference: Miyata, T., & Yasunaga, T. (1980). Molecular evolution of mRNA: A method for estimating evolutionary rates of synonymous and amino acid substitutions from homologous nucleotide sequences and its application. Journal of Molecular Evolution, 16(1), 23–36. https://doi.org/10.1007/BF01732067

Answer 1

In the paper you cite, we see K_A and K_S defined by the authors.

The direct comparison between a pair of known nucleotide sequences in coding regions permits us to evaluate both the nucleotide differences per site caused by nucleotide substitutions leading to amino acid changes, K_A, and those leading to synonymous changes, K_S, simultaneously.

The same year, Motoo Kimura published A Simple Method for Estimating Evolutionary Rates of Base Substitutions Through Comparative Studies of Nucleotide Sequences, in which he derives similar terms k'_(nuc)S and k_(nuc)A.

Writing k'_(nuc)S rather than k_S' to emphasize that this refers to the rate per nucleotide site, we get, using Eq. 14, the following formula.

$k'_{(nuc)S} = -\frac{1}{4T} log_e (1 - 2P - Q)$

The corresponding formula for amino acid-altering substitutions may be obtained by

$k_{(nuc)A} = \frac{K"}{2T}$

The reason why neither paper cites the other is because they appeared in the same edition of Journal of Molecular Evolution. Based on the extensive cross-citation between these authors, as well as some co-authorships, it's likely that the development of the K_A and K_S metrics was simultaneous, if not collaborative.