  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.
