# Allometric Scaling in Scientific Fields

## TL;DR

This study uncovers stable allometric scaling laws in scientific fields, linking outputs like publications and citations to the number of authors, and shows deviations can effectively rank subfields.

## Contribution

It is the first comprehensive analysis revealing allometric scaling laws in scientific disciplines and their stability over time, providing a new metric for subfield ranking.

## Key findings

- Scaling laws relate outputs and inputs to field size across disciplines.
- Exponents of scaling laws are stable over years.
- Deviations from scaling laws can rank subfields independently of size.

## 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.