Author(s): Cassidy R. Sugimoto (corresponding author) ; Nicolas Robinson-Garcia ; Dakota S. Murray ; Alfredo Yegros-Yegros ; Rodrigo Costas ; Vincent Larivière 
Recent political upheavals portend an era of increased isolationism in science, with a chilling effect on collaboration and mobility. Last month, US President Donald Trump issued his third travel ban in a year, suspending entry of individuals from several countries into the United States, and placing restrictions on many more for visa renewals. These orders have stranded scholars abroad and prevented those who were in the country from engaging in international work. In March, UK Prime Minister Theresa May began the process of formally severing ties with the European Union. As a result, British institutions face a potential exodus of non-resident EU researchers and will have to overcome barriers to participating in and receiving funding for European collaborative projects. The list of countries engaging in these isolationist actions, and the list of actions themselves, grows longer.
To assess the impacts of such political actions, we need better ways to measure researcher mobility. Although the size and composition of the scientific workforce is fairly well established through national surveys and registries , less is known about how often researchers move, where they go, what networks they form, and how important their movement is to the scientific impact of their work .
We present here a new analysis based on the records of 14 million papers from nearly 16 million unique individuals who published between 2008 and 2015. In our study, some 96% of researchers had only one country of affiliation; we classed these as non-mobile. About 4% (more than 595,000 researchers) were mobile - meaning that they had more than one affiliation during that period. Our analysis revealed surprising trends.
Over the study period, Europe and Asia saw a dramatic net loss of researchers, whereas North America saw large gains. Many commentators have anguished about 'brain drain' or 'brain gain', assuming that receiving countries get the lion's share of scientific capital at the expense of the nations from which researchers originate. The reality is more complicated (see 'Brain circulation').
We found that the majority of scientists didn't cut ties with their country of origin but instead built a chain of affiliations that linked nations together. Many researchers returned to their home country. Brain circulation may be a more apt term for the movement of contemporary scholars .
Different nations have different roles in the circulation of elite scholars (for which our proxy is highly cited researchers). But wherever they are, wherever they stop off and wherever they come from, mobile scholars have about 40% higher citation rates, on average, than non-mobile ones (see Supplementary Information; Table S7). Closing borders takes these elite scholars out of circulation.
Our study looks at the country stated in a researcher's affiliation when they published their first paper, and uses this as their country of scientific origin (this should not be confused with where they were born). We then...