Tag: tools

  • On distributions of scientific activity and productivity

    Uncategorized | Douglas Kell

    The availability of many records in digital format opens up many possibilities, not least in bibliometrics, a subject that I anticipate will be a regular feature of these blogs. For this blog we are going to look briefly at the distribution of scientific activity between individuals, as encapsulated by the question ‘if n individuals have published 1 scientific paper in a particular time period, how many individuals have published 2 papers or 10 papers or 100 papers?’

    Now one might wonder whether one should expect there to be any regularities in such a (quantised) distribution, but there are. The question was posed and answered most pertinently by Alfred Lotka in 1926, and the relationship is known as Lotka’s Law. Lotka observed, from a study of papers listed in Chemical Abstracts and in Auerbach’s Geschichtstafeln der Physik, that the number of persons making n contributions is  given by 1/na of those making a single contribution, with a equalling approximately 2. Thus for every 100 people who have published 1 paper, 25 have published 2 papers and 1 person has published 10 papers. In other words, the distribution of scientific productivity is best described by an inverse square law (a specific version of a negative exponential more generally referred to as a Zipf distribution). Although this is not universally true, it is a reasonable approximation and has some interesting mechanistic bases. The consequences, as recognised in Lotka’s original survey, included the fact that 60% of contributions were made by authors who contributed only one paper (and note that all joint papers were taken to have been written by the ‘senior’ author only). Nowadays this would be seen as a long-tail phenomenon, as popularised in Chris Anderson’s excellent book. [...]