Canadian Gas Stations

In Geoffrey West's Scale, he shows that a bunch of things in cities (e.g. number of gas stations, length of roads and pipes) scale sub-linearly.  For example, he suggests that for each doubling in population size, the number of gas stations should increase by 80% (i.e. a power law with exponent 0.85).

I decided to investigate this for Canadian cities and gas stations.  I used OpenStreetMap data to get the location of all Canadian gas stations (there are about 11,800, which agrees well with the 2018 estimate of 11,929 from the Canadian Fuels Association).  I then calculated the number of gas stations per capita in each census subdivision (i.e. municipality).  The results, with a lighter shade indicating fewer gas stations per capita, are shown in the map below (click here for an interactive map).

Visually, there is some clear sub-linear scaling going on; Toronto and suburbs have fewer gas stations then expected for their population based on linear scaling, while rural areas have more.  The results of graphing the relation (for municipalities with population greater than 100,000) are shown below.

The equation at the bottom suggests power law scaling with an exponent of 0.76, which is reasonably close to the expected exponent of 0.85, so the sub-linear scaling that West found is true in Canada as well.

The exceptions are interesting as well.  Saguenay seems to have more gas stations than expected, while Guelph has fewer.  The map below shows the % error between the predicted and actual number of gas stations for all municipalities.