Allometric scaling in scientific fields

Abstract

Allometric scaling can reflect underlying mechanisms, dynamics and structures in complex systems; examples include typical scaling laws in biology, ecology and urban development. In this work, we study allometric scaling in scientific fields. By performing an analysis of the outputs/inputs of various scientific fields, including the numbers of publications, citations, and references, with respect to the number of authors, we find that in all fields that we have studied thus far, including physics, mathematics and economics, there are allometric scaling laws relating the outputs/inputs and the sizes of scientific fields. Furthermore, the exponents of the scaling relations have remained quite stable over the years. We also find that the deviations of individual subfields from the overall scaling laws are good indicators for ranking subfields independently of their sizes.Key Words: Allometric scaling law, Subject classification code, PACS, MSC, JEL, Some scientific fields might have many scientists and generate many publications while some might have small amount of researchers but with disproportionably larger publications. Have you wonder ever what is the relationship between the number of scientists and the number of papers (also number of references and received citations etc.) in scientific fields, and furthermore, whether and how such a relation can be used to indicate developmental stages of scientific fields? This question attracted considerable attention [1][2][3][4]. In general, scaling laws are helpful to answer the above questions. For example, it is found that scaling laws are common phenomenon in scientific fields, including power law correlations between number of papers and of received citations [1][2][3] as well as between economic indicators and bibliometric measures [4]. In addition, a scale-independent indicator has been presented to evaluate the research performance [2]. These studies help us to understand the performance of research units in terms of universities, cities and countries etc. In this study, we present a scaling analysis between size, which is measured by the number of authors, and input/output, where the former is represented by the number of references and the latter refers to number of papers and of received citations, of subfields at various levels. In a sense, we treat subfields as the universities, cities and countries in previous studies [1][2][3][4].The formation, flourishing and decline of scientific fields, like the formation, rise and fall of cities, countries and industrial sectors [5,6], certainly comprise a question worth studying, although of a more abstract nature since the boundaries between scientific fields are less well defined than those of, e.g., cities. Several researchers have begun to study the dynamic evolution of scientific fields [7,8] or to evaluate the scientific performances of universities [9, 10], research groups [11][12][13] and metropolitan areas [14].We note that in studies of cities, countries and many other systems, analyses of the scaling bet...

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