Table 1.
Variables used in the analysis.
Fig 1.
Overall workflow.
Fig 2.
Dendrogram of clustering results.
This figure shows the dendrogram generated by the hierarchical k-means clustering process described in the methodology section. The regions of the figure marked by dashed rectangles and colours show the thirteen clusters selected for deeper analysis in this study. In other words, each coloured area of the dendrogram includes the set of census tracts associated with the thirteen neighbourhood types listed in Table 2.
Table 2.
Hierarchical typology of Toronto neighbourhoods.
Table 3.
Evaluating the error of the model.
Fig 3.
Network representation of neighbourhood transition probabilities.
This figure summarizes the transition probabilities across neighbourhood types as a simplified network. To increase legibility, the figure excludes transitions with a probability less than or equal to .02 and only labels probabilities greater than or equal to .05 on edges. Edge widths are proportional to transition probabilities (excluding self-loops), and nodes are coloured to correspond to the higher-order structures of which each neighbourhood is a member. Node sizes are proportional to the number of census tracts of that type.
Fig 4.
Map of neighbourhood reproduction rates.
This figure maps the reproduction rates of neighbourhoods across the city“Reproduction rates” refer to the probability that a given neighbourhood type will recur, that is, the diagonal value in the transition matrix. In this map, each census tract is assigned its neighbourhood type’s diagonal value, according to the thirteen neighbourhood types listed in Table 2. Pink areas are more volatile, and yellow areas are more stable. Tract borders are coloured to indicate each tract’s position in the higher-order typology depicted in Table 2.
Fig 5.
Spatial markov model results regarding differences on reproduction rates.
This figure represents an increase (blue) or decrease (red) of at least 5% on the reproduction rate (diagonal value) on the spatial case compared to the non-spatial case. Numbers on top and right are the total counts of colored cells for each column and line, respectively.
Fig 6.
Predicted changes in neighbourhood distribution according to multiple scenarios.
This figure summarizes predicted changes in the overall distribution of neighbourhood types in 50 time steps for multiple models, compared to the distribution at t5. 0 represents no change to current transition probabilities (darkest green dots) and shows the non-counterfactual scenario in which the city continues to evolve according to its current pattern. Dots positioned further to the right or left in Fig 6 indicate divergence from the distribution at t5, which is represented by the vertical dashed line. Lighter shaded dots represent increasingly larger changes to transitional probabilities, as outlined in the methodology section. As a robustness check, we explored fewer and more time steps, and the same pattern was observed, just less/more extreme.
Fig 7.
Results of counterfactual scenarios for the spatial case.
This figure summarizes the spatial counterfactual scenarios’ results (Scenarios 1 and 2), showing where there is a difference of at least 1% in relation to the non-counterfactual case when predicting the distribution of neighbourhood types: blue (at least 1% increase) and red (at least 1% decrease). Labels on the y-axis left indicate the conditioned neighbourhood type on the spatial Markov over all other ones (x-axis bottom). Numbers on top and right are the total counts of coloured cells for each column and line, respectively. As a robustness check, we explored fewer and more time steps, and the same pattern was observed, just less/more extreme.