Synchronous international scientific mobility in the space of affiliations: evidence from Russia

For the sociology of science, bibliometric data acts as a kind of ‘footprint’ recording the digital signatures of scientific processes. However, this footprint does not in itself convey sociological content (see for example Mingers and Leydesdorff 2015). Bibliometric databases such as the ‘Web of Science Core Collection—Thomson Reuters’ (hereafter—WoS CC) provide an opportunity to investigate a wide range of social scientific phenomena, but place the sociology of science within the strict limits of information technology. If the sociologist wants to avoid the bibliometric data on the screen becoming like the wall of Plato’s Cave, he must learn how to work with relatively poor, formalized information. Fortunately, modern sociology of science’s perspective on mobility is sufficiently broad to allow the use of digital traces of scientists’ movements, using fixed WoS CC affiliations.

The term ‘scientific mobility’ denotes the movement of scientists from one position in social space to another (cf. Bourdieu 1985; Shmatko and Katchanov 2016). Generally, this space is comprised of a network or structured system of socially defined positions. Social space ‘is constructed in such a way that the closer the agents, groups or institutions which are situated within this space, the more common properties they have; and the more distant, the fewer’ (Bourdieu 1989, p. 16).

The concept of scientific mobility deals with the movement of scientists from one position to another, either higher or lower in social space. Scientific mobility contributes both to the continuity and change of social space over time. In basic terms, we can say that scientific mobility analysis is the study of social shifts which have a synthetic (i.e. composite) structure. Since scientific mobility entails science-sustaining and academia-sustaining core transformations, answers to fundamental questions about social features, horizons, and opportunities of science and academia depend on the correct specification of that mobility.

In the study of scientific mobility through bibliometric methods, institutional affiliation is an important (and indeed, often the only) criterion for membership of a social position. This situation is easily explained, because the affiliation has a synthetic character, closely linked with other aspects of a scientist’s status. In classical sociological studies of social mobility profession is used as a main tool to construct social positions. In our case, affiliation plays the same role. The realm of institutional affiliations contains information about an important aspect of scientific mobility: international scientific mobility (or ISM for short). Referring to the above definition of scientific mobility, in the case of ISM we can regard social space as a kind of geopolitical space, which is demarked by national territorial boundaries.

ISM has ambiguous consequences for both receiver and donor countries. In the current structure of global science it is not always easy to assess who the winners and who the losers are Beine et al. (2008) and Docquier and Rapoport (2012). For example, the active migration of researchers to the USA affects salary levels in science and leads to the growth of temporary contracts (Stephan 2012), while the return of scientists from overseas contributes to the development of science in their home countries (Ding et al. 2010; Saxenian 2005).

We should like to remark that it is not our intention to present here a complete review of ISM. The subject is so vast that it is impossible to include every important contribution, and there are many reviews, which do this. Additional bibliographic discussions and references can be found in the books Ackers and Gill (2008), Archibugi and Filippetti (2015), Geuna (2015) and Solimano (2008).

Russian scientific migration and mobility are rather well studied. There are a significant number of studies on the impact of migration on the development and productivity of Russian science Latova and Savinkov (2012) and Shkolnikov (1994), as well as studies on the mobility of researchers in particular fields (Borjas and Doran 2012a; Boussyguine 2005; Indukaev et al. 2014) and scientific diasporas Graham and Dezhina (2008). To avoid overloading our presentation, we refer the reader to Charum and Meyer (1996), Ganguli (2015), Gerber and Yarsike Ball (2009), Ivakhnyuk (2006) and Korobkov and Zaionchkovskaia (2012) for details.

ISM refers to scientists undertaking professional activities in scientific organizations which are located in different countries. Traditionally, ISM is studied using such methods as government statistics on academic staff and data on migration (Arvizu and Bowen 2014; OECD 2013), analysis of CVs and personal web pages (Cañibano and Bozeman 2009; Sandström 2009; Woolley and Turpin 2009), questionnaires and interviews with scientists themselves (Boring et al. 2015; Flanagan 2015; Gerber and Yarsike Ball 2009), and government and administrative databases (De Filippo et al. 2009). The bibliometric approach to the study of scientific mobility is based on the information about institutional affiliation which is included in any scientific publication. We call it the ‘affiliations method’. A scientist’s place of work is like a ‘data tag’ indicating his location in the social space (country, city, organization). The websites of academic journals and databases of scientific publications serves as sources of information on institutional affiliations. The main ones are WoS CC and Scopus (Elsevier). Alongside these, such databases as Pubmed, Inspec, Mathnet and others may be used.

However, all of these studies consider diachronic ISM, i.e. the movement of scientists from one country to another, and disregard synchronous ISM—simultaneously holding scientific positions in organizations located in different countries. For instance, in their study of the contribution of different countries to the production of publications in the field of high energy physics, Kraus, Mele and Lindqvist categorize authors with multiple affiliations as belonging to just one country (Krause et al. 2007). We find similar approach in OECD studies and some others (OECD 2013; Quayle and Greer 2014). Yet, such synchronous mobility is quite common. The bibliometric method records this form of mobility as multiple affiliations. Synchronous international mobility of individual scientists serves as a marker of the extent to which national scientific labor markets overlap, and the strength of international relations between countries.

ISM is one of the paradigms in the sociology of science and scientometrics. New approaches in scientometrics often arise not from discarding current paradigms, but rather by expanding them to provide more substantial information. In this article we have expanded the paradigm of ISM by studying the synchronous international scientific mobility of Russian researchers. Since ISM is a global structure, its components should be investigated in their synchronous relationships. Needless to say, the evolution of ISM means that new synchronous relationships are continually being generated. However, the core patterns of the ISM system can only be identified by means of synchronous analysis. Analysis of synchronous international scientific mobility (SISM for short) as the aggregate of permanent statistical relationships between affiliations reveals the structure of ISM. This structure is presented in our paper as the space of affiliations.

In the present paper, we focus our study on SISM in the framework of multiple affiliations. We aim to characterize SISM through study of the statistical relationships between separate institutional and geographical movements of Russian authors. Our purpose is to understand which factors determine the space of affiliation.

The empirical object of our analysis is a sample of papers by Russian authors published between 2008 and 2013 and indexed in the database WoS CC (access date: June 2014). Six years is a sufficient publication window to obtain an adequate sample of papers that is resistant to stochastic fluctuations.

We classified a publication as ‘Russian’ if at least one of the authors had a Russian institutional affiliation, i.e. their place of work was listed as an organization located in Russia. Russian authors published a total of 199,965 articles and other types of document during the period under analysis. On average, the WoS CC database indexed 33–34 thousand publications by Russian authors annually.

In the Russian case AA had an average of 36 % FA, and their number gradually increased (from 35 to 39 %). On the one hand this is hardly surprising, in view of the increasing number of publications with a large number of co-authors, especially in the field of physics, which accounts for a significant share of Russian publications. On the other hand, it suggests that the Russian publication activity of AA depends essentially on collaboration with scientists from other countries. For comparison, Conchi and Michels found that the share of FA in Germany and Austria is 10, 7 % in France, and 12 % in Great Britain (Conchi and Michels 2014).

In our sample MA accounts for around 15 %, and RA 85 % for the entire period of study. MA totals 6249 authors. This statistical group serves as the empirical basis for our further analysis of SISM.

The emergence of one or more foreign affiliations corresponds to researcher’s mobility in geographical spaces. Hence, synchronous international scientific mobility (SISM) can be defined as the emergence and loss of foreign affiliations. The SISM model considers that the researcher participates in each of the institutes with which she/he is affiliated not as a unified whole but only as a part; the latter we call ‘parton’. A parton has a virtual bibliometric identity that appears in processes of international division and cooperation of research if these processes are de jure formed via multiple simultaneous affiliations. As noted above, our sample counts 6249 MA, which constitute 10,826 partons. According to the SISM model, a mobile researcher behaves as a combination of partons. The multiple affiliations in the framework of bibliometrics are to a some extent uncertainty in the sense that one cannot predict exactly where the scientist will be, but only the probability that she/he is in a country corresponding to one of several partons of this author. Therefore, it is necessary to include probability when describing SISM. Analogous to quantum mechanics, we only can estimate the probability that a researcher with multiple affiliations is located in a given country.

If we are talking about multiple affiliations, then the author is ‘delocalized’: his/her characteristics are distributed in both the geographic space and in the space of research institutes. Moreover, any co-authored paper is a result of a process often involving a significant number of researchers, each of whom may have multiple affiliations. That yields that the local description of every research paper is effaced. The concept of SISM provides us with a deep insight into spatially distributed information interactions, because bibliometrics does not give us sufficient information to be able to uniquely determine the location of an author. In conventional ISM the scientists are ‘mathematical points’ in space and time, whereas in SISM the fundamental objects are consistent sets of partons, and the ‘intensity’ of the parton in a country gives probability of finding the scientist in this country. The main idea of SISM is that instead of an accurate tracking of geographic location and institutional affiliation depending on time, we can evaluate the probability that a researcher is located in a given state. This probability can be used to calculate statistical indicators of SISM.

Figure 1 shows the probability of a parton ‘to be affiliated with a given country’. For our sample the probability of having an affiliation in Russia is 0.36, for the USA—0.10, for Germany—0.09, for France—0.05, for Great Britain—0.04, for Italy and Japan—0.03. As for Canada, Spain, Sweden, Switzerland and Ukraine the probability is 0.02 for each country. For the other countries in our sample, it is 0.01 or less.

The initial concept in the SISM approach is an event of affiliation. The events of affiliations form, in bibliometrics, the mass phenomena comprising the subject of SISM. By event of affiliation, we understand any fact of affiliation, which in certain circumstances can occur or not. As a bibliometric concept, an event of affiliation in the framework of SISM is only defined in terms of whether it occurred or not, but not by its concrete social nature. Bibliometrically, an event of affiliation is seen as a state of the corresponding researcher.

To bibliometrically describe SISM, we first need the notion of the space of affiliations corresponding to the data set under consideration. The space of affiliations is an aggregate of events of affiliation. The concept of an affiliation set of partons is the basis for the practical definitions of the space of affiliations. We say that a homogenous collection of partons is an affiliation set, if it contains all events of a given affiliation. In this case, a space of affiliations is a family of affiliation sets (constructed statistically) on condition that there are objective relations within this family similar to the usual spatial relations. Such a system of statistical positions can be likened to a chessboard: all the significance arises from differences between the positions.

If we take country affiliation as a characteristic affiliation, then we are able to describe the family of affiliation sets in terms of political geography. In bibliometrics, the space of affiliations plays a role of a space of existence and development of forms of scientific communication. As a prerequisite, the space of affiliations manifests itself in international scientific cooperation.

Of 6249 MA, 89.7 % maintain professional scientific ties with countries in which the HDI is higher than in Russia. These are Russia’s main scientific partners: USA, Germany, France, Japan and Italy, together with three other countries: Norway, Australia and Switzerland.

We now turn to indicators which allow us to assess the level and scale of the development of science in the country (GERD, RDP, and NP). The relationship between the three indicators and PA is analogous to its relationship with GDP: PA displays a significant positive correlation with the three indicators (Table 2). We can say the same about PA, NC and NTP. There is a strong positive correlation between PA and the two indicators of a country’s scientific impact. From this we can conclude that PA focus on countries where science is better funded and where there are more opportunities for carrying out large-scale and long-term studies. In turn, the development of scientific production creates a labor market that acts as an attractor for PA.

The correlation between NC, NTP and PA suggests a similar trend: the higher the level of scientific impact of the national science, the higher PA it attracts. In turn, the level of citations of MA is significantly higher than for RA (Table 3). Our results accord with the OECD’s data for other countries: the “impact factor” of mobile authors is higher than that of non-mobile authors OECD (2013). In addition, according to the citations indicator, the citation rate for mobile authors’ publications is approaching that for authors of the receiver country. There is a strong positive correlation between PC and the level of citations, NC (\(r = 0{.}834\)). In terms of publication activity and citations, the relationships between MA and RA on the one hand, and FA and Russian authors (as a whole) on the other hand, are isomorphic. That is to say, MA have higher publication activity (and more citations) than RA, just as authors from the leading scientific nations have higher publication activity (and more citations) than all Russian authors, including MA.

A significant statistical relationship between countries’ socio-economic and scientific indicators and PA points out that SISM acts as a means of virtually ‘drawing in’ partons to the scientific systems of more developed countries. (In contrast to the analysis of co-authorship, which often does not establish direct links between countries, the study of SISM allows us to show the direction of close scientific cooperation and the place of a country in the international division of scientific work.) The higher the economic and scientific indicators of a country, the more partons the country can integrate into its scientific system. In the leading scientific countries partons usually operate as temporary, part-time and remote workers. They are the most flexible part of the scientific labor force. In turn, partons have an impact on the scientific labor market of their host country, expanding the zone of social uncertainty, insecurity and flexible employment.

Affiliation with leading countries contributes to greater scientific productivity and heightened reputation for MA. In comparison with RA, MA receive more scientific recognition (as measured by citations) and more opportunities to carry out projects, which in turn contributes to their high rate of publication activity. In this respect, MA become like their foreign colleagues. Therefore, in terms of productivity and level of recognition, the gap between MA and non-mobile authors is similar to that between authors in the leading receiver countries and MA. This means that the bibliometric characteristics of MA are isomorphic to those of receiver country authors. This supports our thesis that SISM acts as a form of social mobility for Russian scientists.

For MA, international virtualization has mixed consequences. On the one hand, it extends the MA’s professional opportunities, as it allows heterogeneous scientific resources to be combined and compensates for the shortcomings of Russian science. Moreover, such involvement does not require the MA to relocate in geographic space; in many cases, partons are associated with a foreign research institution remotely, only pro forma, as part of a bureaucratic reporting etc. On the other hand, the existence of partons is associated with the uncertainty of social and professional status, the temporary and non-guaranteed nature of institutional positions.

In essence, SISM is a modern, virtual form of the international division of labor in science, to some extent supplanting real migration. Researchers seek work where it exists, even when it is in a partial and/or virtual form, and where there are greater opportunities to receive scientific recognition in the form of citations.

To determine the one-dimensional configuration of our \(56\) countries in the space of social-economic indicators, we used the ALSCAL procedure (Takane et al. 1977), found in IBM SPSS Statistics 20. In this paper, we interpret this configuration (see Fig. 2) in a broader sense as the variable that indicates the level of development of countries and the determinants of upward/downward SISM.

In the present paper, Russia serves as a reference point for the assessment of vertical SISM. Affiliations in countries that are located to the right of Russia on Fig. 2 provide upward SISM, while affiliations in countries to the left of Russia provide neutral or downward SISM. Countries located ‘above’ Russia are Canada, India, Great Britain, France, South Korea, Germany, China, Japan and the United States. These are either countries with developed science or those where it has been developing dynamically in recent years (India, South Korea and China). In other words, upward SISM is enabled by institutional links either with those countries that are the traditional leaders in science or those where scientific production is actively expanding.

Further to the left of Russia in Fig. 2 are the countries of the former Soviet Union (with the exception of Ukraine and Belarus), and former member states of the Council for Mutual Economic Assistance (except Poland). In these countries science is either stagnating, or contracting. Figure 3 shows PA in each country.

As a result of the information gathered from the WoS CC database, to each author we can assign a numerical code \(\xi\), and \(\eta\) is a numerical code that corresponds to each paper. Thus, \(\xi\) is a unique identifier of an author, and \(\eta\) is a unique identifier (or ID) of a paper, respectively.

The first object encountered in the SISM model is the space of elementary outcomes, or partons. Generally, it is a non-empty set \(\Omega\), whose elements \(\omega \in \Omega\) are partons, or sample points. Obviously, the specification characterizing a parton \(\omega\) can, e.g., be: ‘the paper ID \(\eta _{i}\), the author ID \(\xi _{j}\), with Russian and German affiliation’. Roughly speaking, the value of \(\omega\) attached to a paper is what we call the parton, the description of one of the authors of this paper at the adopted level.

We consider the subspace \(D_{e}\) of the Skorokhod space [see details in Jacod and Shiryaev 2003] containing all bounded empirical distribution functions. We can to provide the space \(D_{e}\) with the Kolmogorov metric Rachev et al. (2013)

$$\begin{aligned} \varrho \left( \hat{F}_{n}^{(i)}(x), \hat{F}_{m}^{(j)}(x)\right) = \sup _{x}\left| \hat{F}_{n}^{(i)}(x) - \hat{F}_{m}^{(j)}(x) \right| . \end{aligned}$$

(1)

Furthermore, consider the matrix \(R\) of pairwise distances Eq. (1), in the space \(D_{e}\), between the \(55\) countries

$$\begin{aligned} R = \left( \varrho _{ij} \right) _{i,j = 1}^{i,j = 55}, \end{aligned}$$

(2)

where the distance between two countries reflects their bibliometric differences. We use multidimensional scaling techniques (namely, the ALSCAL procedure) to derive country position in a space of affiliations that fit Kolmogorov distances Eq. (2). The space of affiliations is a spatial configuration of the \(55\) countries, represented as points in a Euclidean space of two dimension. As a matter of fact, the structure of the space of affiliations reflects both the publication activity of MA, and the level of involvement of MA in the scientific systems of other countries.

In Fig. 4 several clusters of countries can be clearly observed. On the right of the ‘East-West’ axis is a group of seven countries (Switzerland, Canada, Italy, Great Britain, France, Germany, and the USA). Almost all of them (with the exception of Switzerland) are members of the G7. In our terminology these are countries with upward SISM; in Fig. 4 they form a ‘Western’ pole. The Western pole accounts for \(57{.}8\,\%\) of PA.

In the upper left hand area of the space of affiliations (see Fig. 4) are China and Japan, with South Korea, India, and Brazil lying just below them. These are predominantly countries with rapidly growing science, with the exception of Japan, which is one of the traditional scientific leaders. These five countries form an ‘Eastern’ pole in the space of affiliations, and account for \(9{.}3\,\%\) of PA.

In the lower left hand corner of the space of affiliations is a large cluster of countries with low or relatively low levels of performance and citation impact. MA have less intensive scientific connections with these \(43\) countries (\(32{.}8\,\%\) of PA).

In the space of affiliations the bibliometric characteristics of MA are isomorphic with countries’ scientific characteristics: the higher and further right the MA is located, the higher on average their productivity and level of citations. Migration in the space of affiliations is possible only in accordance with the regularities of the citation system. In other words, to move from the bottom left to the upper right hand corner, an author needs to produce a large amount of scientific work, dramatically increasing their bibliometric indicators.

The advantage of the proposed model is that it accurately describes the relatively complex phenomenon of SISM, and also that Eq. (4) allows for direct interpretation.

The SISM model does not pretend to represent all the institutional and social circumstances of scientific production. However, it helps to cancel the variety of notions used to describe ISM. Instead of studying separately ‘brain drain’, ‘brain circulation’ or ‘brain gain’, the approach of SISM enables to construct the integral model to describe authors’ localization in the space of affiliation, which is a social space at the same time.

The concept of an affiliation event puts into a precise mathematical form the initially rather vague representation of multiple affiliations. The elements of an exhaustive description of the individual author (and its development in time) are not contained within the conceptual scheme of the SISM model. The idea of the SISM model is that partons are the elementary ingredients of multiple affiliations, and the authors are just bundles of partons. This is not to say that partons are more fundamental than authors. In this paper, we focus on partons, not because they are necessarily more fundamental, but because what we know about partons is more certain. The SISM approach, including the concept of partons, represents an attempt to express the current composition of the scientific labor market using bibliometric methods. In particular, this encompasses the predominance of various forms of part-time, temporary and remote employment of scientists.

Countries with developed science gain the labor of scientists from less advanced countries in the form of temporary, part-time and remote work, which takes the form of SISM. This blurs the national affiliation of successful scientists and generates a virtual international market of scientific labor. Analysis of the Russian case in the space of affiliations clearly outlines the country’s position in the system of global science: between East and West, between developed and newly-developing sciences. The distribution of partons in the space of affiliations is acutely sloped: G7 countries and Switzerland attract a disproportionate number of partons compared to Japan, China, South Korea, Brazil and India. The configuration in the space of affiliations that has formed historically can serve as a predictor of the subsequent development of science in Russia.

Study of SISM enables us to establish the specifics of a country’s involvement in the international division of scientific labor and to determine its position in it. Constructing spaces of affiliations for each country opens up new possibilities for studying the virtual international market of scientific labor. Each country can be represented in the form of a subspace of affiliations, which also represents the country’s position in the global scientific space. Our proposed model of SISM gives a quantitative interpretation of the distribution of partons between countries. It turns out that the number of partons in each country can be explained by the difference between the ‘potential’ of the host country and the donor country (i.e. Russia). If the potential of the ‘attraction’ (the country’s share in total NC) is more than the potential of the ‘push’ (Russia’s share in total NC), then this increases the flow of partons, and vice versa. Moreover, the number of partons associated with a given country strongly depends on the bibliometric distance between Russia and that country. Thus, the strength of the flow of partons is determined not by the absolute values of the host country’s bibliometric indicators, but by its differences from Russia as a donor country.