# Who invented dN/dS?

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

• I would suggest that you write the full names of the variables (dN, dS) it might help to better understand the context of the question and get more answers Aug 31, 2019 at 16:09

In the paper you cite, we see KA and KS 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, KA, and those leading to synonymous changes, KS, 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 kS' 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 KA and KS metrics was simultaneous, if not collaborative.