We study the connection between urban scaling, fundamental allometry (between city population and city area), and per capita vs.\ population density scaling. From simple analytical derivations we obtain the relation between the 3 involved exponents. We discuss particular cases and ranges of the exponents which we illustrate in a "phase diagram". As we show, the results are consistent with previous work.
@article{arxiv.1609.01217,
title = {Relating urban scaling, fundamental allometry, and density scaling},
author = {Diego Rybski},
journal= {arXiv preprint arXiv:1609.01217},
year = {2016}
}