A Markov model of urban evolution: Neighbourhood change as a complex process
Bibliographic record
Abstract
This paper seeks to advance neighbourhood change research and complexity theories of cities by developing and exploring a Markov model of socio-spatial neighbourhood evolution in Toronto, Canada. First, we classify Toronto neighbourhoods into distinct groups using established geodemographic segmentation techniques, a relatively novel application in this geographic setting. Extending previous studies, we pursue a hierarchical approach to classifying neighbourhoods that situates many neighbourhood types within the city's broader structure. Our hierarchical approach is able to incorporate a richer set of types than most past research and allows us to study how neighbourhoods' positions within this hierarchy shape their trajectories of change. Second, we use Markov models to identify generative processes that produce patterns of change in the city's distribution of neighbourhood types. Moreover, we add a spatial component to the Markov process to uncover the extent to which change in one type of neighbourhood depends on the character of nearby neighbourhoods. In contrast to the few studies that have explored Markov models in this research tradition, we validate the model's predictive power. Third, we demonstrate how to use such models in theoretical scenarios considering the impact on the city's predicted evolutionary trajectory when existing probabilities of neighbourhood transitions or distributions of neighbourhood types would hypothetically change. Markov models of transition patterns prove to be highly accurate in predicting the final distribution of neighbourhood types. Counterfactual scenarios empirically demonstrate urban complexity: small initial changes reverberate throughout the system, and unfold differently depending on their initial geographic distribution. These scenarios show the value of complexity as a framework for interpreting data and guiding scenario-based planning exercises.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".