Travel bans and scientific mobility: utility of asymmetry and affinity indexes to inform science policy

Methods are necessary to understand more comprehensively the relationship between countries, particularly those that tend to be obscured from analyses focused on elite countries. This is motivated, in part, by the rise of nationalistic policies which threaten the exchange of scholars at the global level. This proof-of-concept study attempts to move from anecdote to empiricism by looking affinities and association strength rather than raw co-authorship or mobility numbers with the justification that, even if there are only a few publications or researchers in mobility, these could be proportionally important partnerships from the perspective of the non-elite country. This analysis focuses on four dimensions of partnership strength for each of the ten countries for which visas were temporarily suspended as well as the United States: (a) asymmetry of collaboration, (b) asymmetry of mobility, (c) association strength for collaboration, and (d) association strength for mobility. The first two dimensions allow us to identify the main partners for a country considering their asymmetrical relationships, and the latter two reveal what the stronger and preferred partners are considering all the potential countries. We provide collaboration and mobility in parallel to highlight the different insights that can be gained by examining these indicators in concert, rather than independently.

By using affiliation data from scientific publications, it is possible to track the trajectory of individual scientists and analyze collaboration and mobility patterns at meso and macro levels (Moed and Halevi 2014; Sugimoto et al. 2017; Wagner et al. 2018). A bibliometric approach allows us to conduct a comparative study of number of mobile researchers and the amount of internationally co-authored papers countries have. In this study, we use co-authorship as a measure to examine international collaboration and the number of affiliations of scholars with different countries as a proxy of international mobility (Sugimoto et al. 2017) in a sample composed of ten countries involved in the US immigration ban—Chad, Iran, Iraq, Libya, North Korea, Somalia, Sudan, Syria, Venezuela, and Yemen—and the United States. We define a researcher as mobile as those who are affiliated, at any point of their research trajectory, to more than one country. Further details on the methodology followed to track international mobility is provided by Robinson-Garcia et al. (2018).

This study uses the in-house version of the Web of Science (WoS) maintained at CWTS of Leiden University. Nation-to-nation links were collected from 13,699,176 distinct publications (UT codes) retrieved from WoS for the 2008–2015 period, yielding connections among 216 countries. Unique authors were identified using a large-scale author disambiguation algorithm applied to the in-house CWTS version of the Web of Science (Caron and van Eck 2014). This algorithm clusters publications that belong to a single author based on a set of similar publication patterns (co-authorship network, address data, etc.). This resulted in a total of 15,931,847 authors, 595,891 of which were affiliated with more than one country (3.7%). For collaboration linkages, we included all authors and all document types: this yielded 2718,556 publications (20% of the total) with international coauthoring. Reprint affiliations were included for both collaboration and mobility data.

Country names were cleaned and standardized (e.g., merging Timor-Leste and East Timor, Congo and Republic of Congo as well as Zaire and the Democratic Republic of Congo). The cleaning resulted in 212 countries. We then enriched this data by adding additional several country-level classifications. Income level category, as defined by the World Bank (2016) was used as a proxy for economic capacity. The Scientific Technological and Capacity Index (Wagner et al. 2001) was used as an indicator of scientific capacity. This index categorizes countries into four groups of unequal sizes: advanced (n = 22), proficient (n = 24), developing (n = 22), and lagging (n = 80). In the present study, an additional group (“other”) is added to account for the 66 countries that were not placed in the Wagner et al. (2001) classification. Every country was assigned to one of seven geographical regions defined by the World Bank (2016): East Asia and Pacific, Europe and Central Asia, Latin America and Caribbean, Middle East and North Africa, South Asia and, Sub-Saharan Africa.

To measure the asymmetry in collaboration and mobility patterns, we use a pair of inclusion indexes \(: AFI\left( {i,j} \right)\), and counterpart, \(AFI\left( {j,i} \right)\), with one-way normalization (Zitt et al. 2000). AFI is a measure of the links between a given country (i) with another country (j), compared to the total links country (j) with the entire world during the same period. \(AFI\left( {j,i} \right)\) is calculated as:

\(AFI\left( {i,j} \right) = \frac{{n\left( {i,j} \right)}}{n\left( i \right)}\), where n(i, j) is the volume of links between countries i and j, and n(i) = ∑ _j n(i, j), total coauthorship linkage of i. This index is size-dependent given that the preference for partner j in \(AFI\left( {i,j} \right)\) is influenced by the global size of j (conversely, preference is dependent upon the size of i for \(AFI\left( {j,i} \right)\). This index highlights the important partners in terms of quantity and demonstrates asymmetry in parternships.

To normalize by the size of both countries, we employ the Probabilistic Affinity Index (PAI), used in science policy to demonstrate the degree to which proximity (both material and immaterial) contributes to scientific relationships among the countries. It indicates the intensity of scientific exchanges between two countries, according to coauthored articles measured and collaborations/mobility theoretically expected. An index above 0 reflects higher collaboration/mobility strength between two countries than their respective weight and propensity to collaborate would indicate. The index is capable of demonstrating strong relationships with small countries and presents the strength of relationships in their global context. For PAI, we refer to Zitt et al. (2000)’s algorithm and apply it to calculate the relationships between countries for both collaboration and mobility:

\(PAI\left( {i,j} \right) = \frac{{\left[ {n\left( \ldots \right)n\left( {i,j} \right)/n\left( i \right)n\left( j \right)} \right]^{2} - 1}}{{\left[ {n\left( \ldots \right)n\left( {i,j} \right)/n\left( i \right)n\left( j \right)} \right]^{2} + 1}}\), where \(n\left( i \right) = \sum\nolimits_{j} {n\left( {i,j} \right)}\) and \(n\left( \ldots \right) = \sum\nolimits_{i \ne j} {n\left( {i,j} \right)}\). In this way, PAI is normalized into [− 1, 1].

Each indicator yields a different lens on the international portfolio of a given country. The affinity index reveals asymmetries, demonstrating that collaborations with country i might constitute a large portion of the total collaborations of country i, but a small proportion of the collaborations of country j. It simultaneously provides an indicator of the main collaborators in the global network. PAI, on the other hand, highlights the strengths of countries that might not have high output, but have disproportionately strong connections in the global environment. We present, for both collaboration and mobility, the 50 main and preferred partners for the countries in our sample, according to the AFI and PAI.