1 Publication output includes only those indexed in the Scopus database. The publication output discussion uses fractional counting, which credits coauthored publications according to the collaborating institutions or regions, countries, or economies based on the proportion of their participating authors. Country assignments refer to the institutional address of authors, with partial credit given for each international coauthorship. As part of the data analysis, filters were employed on the raw Scopus S&E publication data to remove publications with questionable quality, which appear in what are sometimes called predatory journals (NSB Indicators 2018: Bibliometric Data Filters).

2 The proportion of output attributable to the large producers is consistent whether using fractional counting, as in Figure PBS-2 and Table PBS-1, or whole counting, as in Table SPBS-17. There is a slight difference between the United States and China when looking at the whole-counting total production numbers. Using whole counting for 2022, the United States had 605,633 articles, whereas China had 976,141. A whole-counting measure allocates one full count to each region, country, or economy with an author contributing to the article; in fractional counting, each region, country, or economy receives a proportion of the count based on the number of authors from that region, country, or economy. For example, if an article had four authors—two from the United States, one from China, and one from Brazil—the fractional scores would be half for the United States, a quarter for China, and a quarter for Brazil. The difference between whole and fractional counting indicates that the United States has more authors working with Chinese authors than China has working with U.S. authors.

3 The use of whole counting or fractional counting to tally the publication output of nations can change the calculated publication count based on the degree to which a region, country, or economy is involved in international collaborations. Under whole counting, a nation receives credit for any publication with an author from that nation. Under fractional counting, the nation’s credit for a publication is prorated based on the share of the publication’s coauthors who are located in that nation (Table SPBS-17 through Table SPBS-31).

4 Many publishers make their article processing charges (APCs) known publicly. For example, a list of Elsevier APCs can be found at https://www.elsevier.com/about/policies/pricing. Wiley APCs are at https://authorservices.wiley.com/author-resources/Journal-Authors/open-access/article-publication-charges.html. Springer Nature APCs are at https://www.springernature.com/gp/open-research/journals-books/journals.

5 In mathematical terms, a region, country, or economy’s HCA ratio (the share of the articles ranked in the highest 1% based on citations) is computed as follows: Sx = HCAx / Ax, where Sx is the share of output from country x in the top 1% most-cited articles, HCAx is the number of articles from country x that are among the top 1% of most-cited articles, and Ax is the total number of articles from country x with a relative citation (RC) score. HCAx and Ax are based on whole counting. The RC score is a normalized citation score assigned to a publication and is used to rank articles into the top 1%. The RC score takes into consideration the citation behavior between fields and years of publication. Based on the observation that distinct differences in the citation rates of articles appear 2 years or more after publication, the HCA ratio is calculated with a time lag of at least 2 years (meaning that in 2021, the HCA ratios were calculated based on publications issued in 2019).

6 For an analysis of the rapid growth in articles published each year by MPDI, see Petrou (2020).

7 Regions, countries, or economies contributing less than 1% of all internationally coauthored publications in 2020 were not included in the analysis.

8 The total international collaboration rate differs from the rate of co-publications of individual regions, countries, or economies. Individual scores use whole counting, in which each region, country, or economy with an institutional address on the publication receives 1 point. Therefore, the basis count for individual regions, countries, or economies will be larger than the number of publications that have authors with institutional addresses from two or more regions, countries, or economies, which is the basis for computing the total international collaboration rate.

9 RCI is a citation-based measure of scientific influence. It is calculated from a region, country, or economy’s share of all cited S&E publications divided by the other region, country, or economy’s share of all cited S&E publications; an index less than 1.00 means a lower-than-expected tendency to cite the other region, country, or economy’s publications.