The assessment, covering nearly 300,000 faculty at 368 PhD-granting institutions over the most recent decade, also showed widespread gains in gender equity at US research universities – but found that improvement was largely the result of male retirement rather than female hiring.

“Our analyses”, researchers from the University of Colorado Boulder write in the journal Nature, “show universal inequalities in which a small minority of universities supply a large majority of faculty across fields, exacerbated by patterns of attrition and reflecting steep hierarchies of privilege.”

The basic pattern has been suspected across academia, even if not proven as rigorously as the Colorado team has now done. A 2018 study by Tolga Yuret at Istanbul Technical University, covering 12,500 full professors at 48 top US universities, found that more than a third of them gained their doctorate at just five elite US institutions.

For their far-larger review, the Colorado team used data from 2011 to 2020 on 295,000 US faculty from Academic Analytics, a private consulting firm that universities have been using – sometimes controversially – to help make productivity-related decisions on tenure and promotion.

To define prestige, the Colorado team – led by Daniel Larremore, an assistant professor of computer science, and Hunter Wapman, a doctoral student in computer science – used a metric based on the rate at which each university has its doctoral graduates hired by other universities.

By field, the share of US faculty working at a university rated more prestigious than the one at which they earned their doctorate ranged from only 5 per cent to 23 per cent.

Just five US universities trained a full eighth of the nation’s entire tenure-track faculty, and 80 per cent of tenure-track faculty earned their doctorates at just 20 per cent of US universities, the authors found.

The five institutions producing the most US professors, they said, are the University of California, Berkeley, Harvard University, the University of Michigan, Stanford University and the University of Wisconsin-Madison.

The 2018 study by Dr Yuret in the journal Scientometrics – using only a fraction of the Colorado sample size – had a somewhat different top five, adding the Massachusetts Institute of Technology and Princeton University to Berkeley, Stanford and Harvard.

The Colorado team’s employment-based definition of prestigious, Dr Larremore explained, was designed to get past the unreliability of opinion-based rankings by treating a hiring decision as a clear-cut demonstration of respect.

That perspective also helps point out, he said, the “fascinating” socially constructed nature of prestige in higher education.

“It’s the same kind of socially constructed feedback loops that lead us to give deference to some journals and institutions and so on more than others,” Dr Larremore said. “It just characterises so much about academia.”

The Colorado numbers showed that women faculty over the past decade gained in their overall representation in 75 per cent of 107 fields covered by the analysis. But that was due, the authors found, to men retiring, with no increase in female hiring from a decade earlier. Because of that, Mr Wapman said, US universities will struggle to see meaningful gains in gender parity without making substantial changes in their hiring practices.