A Markov model of urban evolution: Neighbourhood change as a complex process

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 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.

A manifesto for computational sociology: The Canadian perspective

“…Computational methods include a gamut of different techniques including machine learning (e.g., deep learning, statistical learning, reinforcement learning), social network analysis, text and data mining (e.g., sentiment analysis, topic modelling, named‐entity recognition), agent‐based modelling, more flexible regression/estimation models (e.g., regression shrinkage and selection, Bayesian statistics, spatial regression models), advances in survey methods (e.g., survey experiments, optimum design, respondent‐driven sampling), and so on. Some sociologists in Canada have contributed directly to the development of particular methods (Alexander & Alkema, 2021; Andersen, 2008; Bignami‐Van Assche et al., forthcoming; Fosse & Winship, 2019; Fox, 2015; Fox & Andersen, 2006; Fu et al., 2020, 2021; Hayduk, 1996; Li et al., forthcoming; Miles, 2016; Nelson, 2020; Stecklov et al., 2018; Wellman et al., 2003, 2020), but more often sociologists have embraced and adapted methods developed by computer scientists, statisticians, and econometricians (Abul‐Fottouh et al., 2020; Boase, 2016; Das, 2022; Gallupe et al., 2019; Gruzd & Mai, 2020; Gu et al., 2021; Hogan & Berry, 2011; Howe et al., forthcoming; Kudla & Parnaby, 2018; Letarte et al., 2021; Li & Luo, 2020; McLevey, 2022; McMahan & McFarland, 2021; Quan‐Haase et al., 2021; Richardson et al., 2021; Roth et al., forthcoming; Shor & Miltsov, 2020; Shor et al., 2013; Silver & Silva, 2021; Smith, 2020; Sytsma et al., 2021; Veenstra & Vanzella‐Yang, 2022; Yuan et al., 2022).…”