Concentrating research funding on a small number of large universities is not the best way to maximise research quality, a paper suggests.

Ralph Kenna, from the Applied Mathematics Research Centre at Coventry University, and Bertrand Berche, from the Statistical Physics Group at Nancy-Universit¨¦ in France, studied the quality assessments taken from the UK's 2008 research assessment exercise and its French equivalent.

Their paper, "The extensive nature of group quality", published online by the physics journal EPL last week, plots the quality scores against the number of researchers entered.

It shows that with respect to the size of research groups in a particular discipline, there is an upper threshold or critical mass above which quality does not improve significantly.

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The researchers explain the results using a mathematical model that posits interaction between researchers as the key driver of quality. They interpret the upper threshold as the maximum number of colleagues with whom a researcher can communicate meaningfully.

"The collaborative effect is an order of magnitude stronger than that of individual calibre. This means the strength of the community is greater than the sum of its parts," Dr Kenna told Times ÖйúAƬ.

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The model also predicts a lower threshold, below which groups are unstable and their research tends to be of lower quality. The lower critical masses range from 15 researchers for law and geography to three for foreign languages and about two for pure mathematics.

Dr Kenna said the study indicated that the best way to maximise research quality in a particular discipline would be to allocate extra researchers to medium-sized teams in order to help them reach the upper critical mass. Universities should also try to maximise interactions between researchers and discourage distance working, he said.

He added that the research explained the results of a report published in March by the ÖйúAƬ Policy Institute, which showed, based on citation counts, that the research of the 1994 Group of smaller research-intensive universities was mostly on a par with that of the Russell Group of large research-intensive universities despite a smaller average size of research teams. This was because team sizes in both groups tend to be above the upper threshold, he said.

Wendy Piatt, director general of the Russell Group, said critical mass was not just about the direct effect of numbers of researchers on quality. "What is crucial at team level and across institutions is the critical mass of excellence across the board and the role it plays in developing world-class capability," she said.

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Les Ebdon, chair of the Million+ group of post-1992 universities, said critical mass and concentration of funding were "neither necessary nor sufficient" to produce world-leading research.

He said 62 per cent of recent UK research funding had been concentrated in just 15 institutions, with limited success.

paul.jump@tsleducation.com