To construct metrics quantifying the service provision equity, we calculated eight socio-demographic variables: the percentages of Females, Indigenous people, White people, Chinese people, Black people, Latino people, people with household total income below $40,000, and people with household total income above $100,000 in 2020 for each census dissemination area in the City of Toronto. We used the areal package in R (Prener & Revord, 2019) to reshape the census data into the non-overlapping coverage areas, using the areal weighted interpolation method.

Areal weighted interpolation involves four steps:

1. Intersecting the non-overlapping coverage areas with the census dissemination areas.
2. Calculating an areal weight for each intersected feature, using W_i=\frac{A_i}{\sum_i A_{ik}}.
3. Estimating the share of the population value that occupies the intersected feature, using E_i=V_j\times W_i.
4. Summarizing the data based on the target identification number, using G_k=\sum_i E_{ik}.

Then, the Toronto Bike Share system-wide socio-demographics were calculated as a weighted average based on ridership at each station, \overline{x}=\frac{\sum n\times x}{n}.

We applied the Multivariate Clustering Geoprocessing tool (K-means Clustering) in ArcGIS Pro to the eight socio-demographic variables of the bike share stations in order to group them into five clusters based on their attribute similarities. From these five clusters, we identified existing catchment areas that are relatively more equitable compared to others.

We used Hotspot Analysis or Getis-Ord Gi^* (Getis & Ord, 1992) to identify the census dissemination areas that have high or low values of the socio-demographic variables, compared to the surrounding areas. We employed a spatial weight matrix constructed using the 40-nearest neighbours method, along with the row standardized Bisquare Kernel Function, w_{ij}=[1-(\frac{d_{ij}}{\alpha_i})^2]^2 and \sum_j w_{ij}=1.

We identified socio-demographic hotspots with a confidence level exceeding 90% and converted them into raster format, with cell values equal to the original socio-demographic variables. We created an approximate 1-kilometre buffer zone raster around the equitable catchment areas identified by the cluster analysis. We computed a weighted sum of these layers to ascertain the most suitable areas for the expansion of the Bike Share Toronto system. The weights for the socio-demographic hotspot layers were set as the inverse of their respective means, w_i=\frac{1}{\mu_i}. The buffer layer was assigned a weight of 1.2 to balance the importance of proximity to existing stations against the need to serve underserved populations. For more details, you can access the maps for each raster layer and their corresponding weights through this link.