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.
KeywordsAllometric scaling law Subject classification code PACS MSC JEL
This work was supported by NSFC Grant 61374175, also partially by the Fundamental Research Funds for the Central Universities and Beijing Academy of Science and Technology Under Project Agreement OTP-2014-002. The authors thank the APS Physical Review for sharing the data.
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