Fig 1 - uploaded by Timoteo Carletti
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Visualisations of the metapopulation framework. On the left panel, agents' positions inside each cell are showed. On the right panel, the aggregated representation of all the possible states is presented: blue represents cells where only blue agents are present, red represents cells containing only red agents, cyan denotes cells where there is a majority of blue agents with respect to red one, similarly orange represents cells where more red than blue agents are present, grey represents cells with an equal number of red and blue agents, finally white represents empty cells.
Source publication
The Schelling model describes the formation of spatially segregated clusters starting from individual preferences based on tolerance. To adapt this framework to an urban scenario, characterized by several individuals sharing very close physical spaces, we propose a metapopulation version of the Schelling model defined on the top of a regular lattic...
Contexts in source publication
Context 1
... feature of the metapopulation version of the Schelling model analysed in this paper is the fact that the dynamics takes place on a two-dimensional lattice, composed by N = D 2 cells, with periodic boundary conditions where each cell can be occupied by at most L agents (carrying capacity) at any given time (for a pictorial representation, see Fig. ...
Context 2
... the metapopulation case two different segregation levels should be considered. We call cell-level segregation once all the agents inside a cell are of the same kind (see Fig. 1). This kind of segregation will be analysed in section 4.1. In the L = 1 case the cells can have only three states: occupied by an agent of kind A, occupied by an agent of kind B and to be empty. In the metapopulation framework we can observe six different states (see Fig1, right panel): cell-level segregation of kind A (or B), empty ...
Citations
... Recently, the use of different tolerance levels for the agents was proposed in [7], in a system with no vacancies, where agents could only exchange locations with agents of a different type. On the other hand, in [8] each cell of the system is considered a building containing many agents, and segregation was considered both at a microscopic and a macroscopic level, giving rise to a complex phase diagram. Some of the mentioned works take into account the importance of the initial conditions [2,7], and some others also consider migratory movements [7,9]. ...
Residential segregation is analyzed via the Schelling model, in which two types of agents attempt to optimize their situation according to certain preferences and tolerance levels. Several variants of this work are focused on urban or social aspects. Whereas these models consider fixed values for wealth or tolerance, here we consider how sudden changes in the tolerance level affect the urban structure in the closed city model. In this framework, when tolerance decreases continuously, the change rate is a key parameter for the final state reached by the system. On the other hand, sudden drops in tolerance tend to group agents into clusters whose boundary can be characterized using tools from kinetic roughening. This frontier can be categorized into the Edward-Wilkinson (EW) universality class. Likewise, the understanding of these processes and how society adapts to tolerance variations are of the utmost importance in a world where migratory movements and pro-segregational attitudes are commonplace.
... Recently, the use of different tolerance levels for the agents was proposed in [7], in a system with no vacancies, where agents could only exchange locations with agents of a different type. On the other hand, in [8] each cell of the system is considered a building containing many agents, and segregation was considered both at a microscopic and a macroscopic level, giving rise to a complex phase diagram. Some of the mentioned works take into account the importance of the initial conditions [2,7], and some others also consider migratory movements [7,9]. ...
Residential segregation is analyzed via the Schelling model, in which two types of agents attempt to optimize their situation according to certain preferences and tolerance levels. Several variants of this work are focused on urban or social aspects. Whereas these models consider fixed values for wealth or tolerance, here we consider how sudden changes in the tolerance level affect the urban structure in the closed city model. In this framework, when tolerance decreases continuously, the change rate is a key parameter for the final state reached by the system. On the other hand, sudden drops in tolerance tend to group agents into clusters whose boundary can be characterized using tools from kinetic roughening. This frontier can be categorized into the Edward-Wilkinson (EW) universality class. Likewise, the understanding of these processes and how society adapts to tolerance variations are of the utmost importance in a world where migratory movements and pro-segregational attitudes are commonplace.
... The regular grid might be a reasonable approximation of the real world for many purposes, but human settlement shows much greater variation in local population density than can be modeled in a grid with only one resident per patch. Multiple residents per patch might be a fruitful route to more realistically model this variation [17]. ...
How individuals’ residential moves in space—derived from their varied preferences and constraints—translate into the overall segregation patterns that we observe, remains a key challenge in neighborhood ethnic segregation research. In this paper we use agent-based modeling to explore this concern, focusing on the interactive role of ethnic and socio-economic homophily preferences and housing constraints as determinants of residential choice. Specifically, we extend the notorious Schelling’s model to a random utility discrete choice approach to simulate the relocation decision of people (micro level) and how they translate into spatial segregation outcomes (macro level). We model different weights for preferences of ethnic and socioeconomic similarity in neighborhood composition over random relocations, in addition to housing constraints. We formalize how different combinations of these variables could replicate real segregation scenarios in Bradford, a substantially segregated local authority in the UK. We initialize our model with geo-referenced data from the 2011 Census and use Dissimilarity and the Average Local Simpson Indices as measures of segregation. As in the original Schelling model, the simulation shows that even mild preferences to reside close to co-ethnics can lead to high segregation levels. Nevertheless, ethnic over-segregation decreases, and results come close to real data, when preferences for socioeconomic similarity are slightly above preferences for ethnic similarity, and even more so when housing constraints are considered in relocation moves of agents. We discuss the theoretical and policy contributions of our work.
... Recently, the use of different tolerance levels for the agents was proposed in [10], in a system with no vacancies, where agents could only exchange locations with agents of a different type. On the other hand, in [11] each cell of the system is considered a building containing many agents, and segregation was considered both at a microscopic and a macroscopic level, giving rise to a complex phase diagram. Some of the mentioned works take into account the importance of the initial conditions [2,10], and some others also consider migratory movements [9,10]. ...
... N d = 2. Straight segments of vacancies are completed, but contacts along diagonals between distinct clusters are allowed (I-type border [11]), as in Fig. 5 (c). ...
... N d = 1. Diagonal contacts between clusters are not allowed any more (II-type border [11]), see Fig. 5 (d). ...
Residential segregation is analyzed via the Schelling model, in which two types of agents attempt to optimize their situation according to certain preferences and tolerance levels. Several variants of this work are focused on urban or social aspects. Whereas these models consider fixed values for wealth or tolerance, here we consider how sudden changes in the economic environment or the tolerance level affect the urban structure both in the closed city and open city frameworks, i.e. depending on whether migration processes are relevant or not. In the closed city framework, agents tend to group into clusters, whose boundary can be characterized using tools from kinetic roughening. On the other hand, in the open city approximation agents of a certain type may enter or leave the city in series of avalanches, whose statistical properties are discussed.
... We also measure the extent of segregation between residents and migrants that emerges at the end of each iteration using the Cell Segregation Indicator (CSI), a measure proposed by Gargiulo et al. [30] which encapsulates the local properties of the system by averaging cell-level heterogeneity over all non-empty cells. Lower CSI values indicate higher heterogeneity. ...
One of the pressing social concerns of our time is the need for meaningful responses to migrants and refugees fleeing conflict and environmental catastrophe. We develop a computational model to model the influx of migrants into a city, varying the rates of entry, and find a nonlinear inverse relationship between the fraction of resident population whose tolerance levels are breached due to migrant entry and the average time to such tolerance breach. Essentially, beyond a certain rate of migrant entry, there is a rapid rise in the fraction of residents whose tolerances are breached, even as the average time to breach decreases. We also model an analytical approximation of the computational model and find qualitative correspondence in the observed phenomenology, with caveats. The sharp increase in the fraction of residents with tolerance breach could potentially underpin the intensity of resident responses to bursts of migrant entry into their cities. Given this nonlinear relationship, it is perhaps essential that responses to refugee situations are multicountry or global efforts so that sharp spikes of refugee migrations are equitably distributed among nations, potentially enabling all participating countries to avoid impacting resident tolerances beyond limits that are socially sustainable.
... Initially, agents are distributed equally across each of the M neighbourhoods, such that P(i) = P(j) for 1 i, j M. This model follows in the tradition of earlier metapopulation models [24] [25], where each location is a neighbourhood with a carrying capacity, as opposed to the classic Schelling model where each location in a lattice represents a single agent. However, our model also differs significantly from these models in that the dynamics are driven both by ethnicity and wealth considerations. ...
... Finally, we also compare the outcomes of our model to those of the metapopulation model of Gargiulo, Gandica, and Carletti [25]. In that model, agent movement is driven solely by ethnicity considerations (and not wealth), and it studies the outcomes on cell level ethnic heterogeneity as well as population heterogeneity. ...
... We seek to now measure these outcomes in our model and verify if these results are replicated. We use the definition of cell segregation indicator as provided by Gargiulo, Gandica, and Carletti [25]. Given that f i e 0 and f i e 1 are the fractions of e 0 and e 1 agents (as proportions of total e 0 and total e 1 agents respectively) in cell i, the cell segregation Ethnicity and wealth: The dynamics of dual segregation indicator CSI is defined as (Eq 9): ...
Creating inclusive cities requires meaningful responses to inequality and segregation. We build an agent-based model of interactions between wealth and ethnicity of agents to investigate ‘dual’ segregations—due to ethnicity and due to wealth. As agents are initially allowed to move into neighbourhoods they cannot afford, we find a regime where there is marginal increase in both wealth segregation and ethnic segregation. However, as more agents are progressively allowed entry into unaffordable neighbourhoods, we find that both wealth and ethnic segregations undergo sharp, non-linear transformations, but in opposite directions—wealth segregation shows a dramatic decline, while ethnic segregation an equally sharp upsurge. We argue that the decrease in wealth segregation does not merely accompany, but actually drives the increase in ethnic segregation. Essentially, as agents are progressively allowed into neighbourhoods in contravention of affordability, they create wealth configurations that enable a sharp decline in wealth segregation, which at the same time allow co-ethnics to spatially congregate despite differences in wealth, resulting in the abrupt worsening of ethnic segregation.
... The regular grid might be a reasonable approximation of the real world for many purposes, but human settlement shows much greater variation in local population density than can be modeled in a grid with only one resident per patch. Multiple residents per patch might be a fruitful route to more realistically model this variation [17]. ...
In Schelling's segregation model agents of two ethnic groups reside in a regular grid and aim to live in a neighborhood that matches the minimum desired fraction of members of the same ethnicity. The model shows that observed segregation can be the emergent result of people interacting under spatial constraints in pursuit of such homophily preferences. Even mild homophily preferences can generate high degrees of segregation at the macro level. In modern, ethnically diverse societies people might not define similarity based on ethnicity. Instead, shared tolerance towards ethnic diversity might play a more significant role, impacting segregation and integration patterns in societies. Bearing this consideration in mind, we extend Schelling's model by dividing the population of agents into value-oriented and ethnicity-oriented agents. Using parameter sweeping, we explore the consequences that the mutual adaptation of these two types of agents has on ethnic segregation, value segregation, and population density in the neighborhood. Such consequences are examined for equally sized ethnic groups and for majority-minority conditions. The introduction of value-oriented agents reduces total ethnic segregation when compared to Schelling's original model, but the new phenomenon of value segregation appears to be more pronounced than ethnic segregation. Furthermore, due to cross-contagion, stronger ethnic homophily preferences lead not only to greater ethnic segregation but also to more value segregation. Stronger value-orientation of the tolerant agents similarly leads to increased ethnic segregation of the ethnicity-oriented agents. Also, value-oriented agents tend to live in neighborhoods with more agents than ethnicity-oriented agents. In majority-minority settings, such effects appear to be more drastic for the minority than the majority ethnicity.
... The regular grid might be a reasonable approximation of the real world for many purposes, but human settlement shows much greater variation in local population density than can be modeled in a grid with only one resident per patch. Multiple residents per patch might be a fruitful route to more realistically model this variation [17]. ...
In Schelling’s segregation model, agents of two ethnic groups reside in a regular grid and aim to live in a neighborhood that matches the minimum desired fraction of members of the same ethnicity. The model shows that observed segregation can emerge from people interacting under spatial constraints following homophily preferences. Even mild preferences can generate high degrees of segregation at the macro level. In modern, ethnically diverse societies, people might not define similarity based on ethnicity. Instead, shared tolerance towards ethnic diversity might play a more significant role, impacting segregation and integration in societies. With this consideration, we extend Schelling’s model by dividing the population of agents into value-oriented and ethnicity-oriented agents. Using parameter sweeping, we explore the consequences that the mutual adaptation of these two types of agents has on ethnic segregation, value segregation, and population density in the neighborhood. We examine for equally sized ethnic groups and for majority–minority conditions. The introduction of value-oriented agents reduces total ethnic segregation compared to Schelling’s original model, but the new value segregation appears to be more pronounced than ethnic segregation. Due to spillover effects, stronger ethnic homophily preferences lead not only to greater ethnic segregation, but also to more value segregation. Stronger value-orientation of the tolerant agents similarly leads to increased ethnic segregation of the ethnicity-oriented agents. Also, value-oriented agents tend to live in neighborhoods with more agents than ethnicity-oriented agents. In majority–minority settings, such effects appear to be more drastic for the minority than the majority ethnicity.
Complex interactions are at the root of the population dynamics of many natural systems, particularly for being responsible for the allocation of species and individuals across apposite niches of the ecological landscapes. On the other side, the randomness that unavoidably characterises complex systems has increasingly challenged the niche paradigm providing alternative neutral theoretical models. We introduce a network-inspired metapopulation individual-based model (IBM), hereby named self-segregation, where the density of individuals in the hosting patches (local habitats) drives the individuals spatial assembling while still constrained by nodes’ saturation. In particular, we prove that the core–periphery structure of the networked landscape triggers the spontaneous emergence of vacant habitat patches, which segregate the population in multistable patterns of isolated (sub)communities separated by empty patches. Furthermore, a quantisation effect in the number of vacant patches is observed once the total system mass varies continuously, emphasising thus a striking feature of the robustness of population stationary distributions. Notably, our model reproduces the patch vacancy found in the fragmented habitat of the Glanville fritillary butterfly Melitaea cinxia, an endemic species of the Åland islands. We argue that such spontaneous breaking of the natural habitat supports the concept of the highly contentious (Grinnellian) niche vacancy and also suggests a new mechanism for the endogeneous habitat fragmentation and consequently the peripatric speciation.
In this work we characterize sudden increases in the land price of certain urban areas, a phenomenon causing gentrification, via an extended Schelling model. An initial price rise forces some of the disadvantaged inhabitants out of the area, creating vacancies which other groups find economically attractive. Intolerance issues forces further displacements, possibly giving rise to an avalanche. We consider how gradual changes in the economic environment affect the urban architecture through such avalanche processes, when agents may enter or leave the city freely. The avalanches are characterized by power-law histograms, as it is usually the case in self-organized critical phenomena.
