A Modular Modelling Framework for Hypotheses Testing in the Simulation of Urbanisation
Abstract
:1. Introduction
2. A Catalogue of Possible Mechanisms of Urbanisation
“It may also be useful to think of complex geographical models as extensions of thought experiments, where the necessary and contingent implications of theories can be examined. Further, admitting that “all models are wrong” is akin to the realisation in post-structural social science that multiple competing accounts of the same settings are possible, and that faced with a diversity of accounts the context and intent of each must be an important element in the evaluation process”([7] p. 291).
2.1. Competing Theories
- Spatial Interactions and diffusion allow for the exchange of informations, monies, goods and people. It thus makes cities co-evolve in time and adapt collectively to changing economic and innovation cycles through competition and cooperation, resulting in some complementarity of their specialisation. These local interactions and their consequences on the regular organisation of the system as a whole under spatial constraints could be thought of as “complex systems effects”.
- Size effects like agglomeration economies and urbanisation externalities illustrate a very direct and self-reinforcing cause for hierarchical differentiation.
- Site effects explain the spatial location of growth processes around resource-rich areas for the related innovation cycle.
- Situation effects illustrate the importance of the neighbouring relational environment (potential field, network accessibility, etc.) on a city’s pattern of growth.
- Territorial effects account for some exogenous (policy) shocks and the solidarity of urban trajectories in a common political space (through redistributive processes for example).
2.2. Empirical Results from the Literature
- Spatial Interactions are tricky to measure because of the variety and non-commensurability of flows circulating between cities at various temporalities. Until recently, the diffusion of innovations (agricultural techniques [40], telephone lines [41] or newspapers [42]) served as a proxy for these interactions. Since the development of various volumes of high velocity data, actual interactions (like phone calls [43]) have confirmed for example the relevance of the gravity model to describe inter-city interactions.
- Size effects on urban growth and differentiation were revealed by a persistent empirical correlation between growth rates and city sizes over long periods of time. All over the 19th century, Robson ([41] p. 79) measured a positive coefficient between the log of English and Welsh cities’ population and their gross ten-year growth rates (from a minimum of +1.47 between 1861 and 1871 to a maximum of +8.53 points in percentage between 1821 and 1831). This correlation is found for French cities as well [44]. The size effect finally relates to the stability of the rank position of large cities (by comparison with the fluctuations of smaller cities).
- Site effects were classically approached by estimating the surplus of growth associated with a localised resource (typically, deposits of natural materials, such as coal or gas). In the Soviet urban system of the 1920s–1930s, the location of a city on a coal deposit was associated with a surplus of 1.15 points in percentage of average demographic growth per annum, everything else being equal. A surplus over 0.5 point is observed nowadays (1989–2010) for oil and gas deposits [45]. In the USA, Black and Henderson [46] estimate that the coastal location (e.g., a resource for tourism) is associated with a significantly higher ten-year growth rates of three to five points.
- Situation effects can be revealed by the spatial autocorrelation of growth or the co-evolution between transportation networks and urban networks. In the first case, Hernando et al. [47] found a characteristic distance for spatial autocorrelation of growth rates of 215 km for American counties and of 80 km for Spanish cities. As for transportation dynamics, Bretagnolle [48] measured the correlation between accessibility and growth rates for French cities in the last two centuries. She finds that cities that were weakly connected (by any transportation network: road, rail or air) in 1900 and stayed isolated in 2002 grew slower (0.94% on average per annum between 1900 and 2002) than cities that became motorway nodes (1.21%) or multimodal hubs (1.69%). Likewise, well connected cities at the beginning of the period tended to grow faster than the first category.
- Territorial effects can be approached empirically by relating political statuses to dynamics of growth. In developing countries, regional capitals were found to grow significantly faster by 0.5 to 1 point of annual average growth rate in the 1960s [49] and the 1990s [50]. In the Former Soviet Union, the regional status of capital has proven important to predict urban growth [51], the coefficient regressed against growth rates over time ranges from +0.24 point between 1989 and 2002 to +1.88 between 1926 and 1939 [45]. Besides, cities that belong to the same territory have shown an increased pattern of synchronicity in their growth and decline trajectories from the 1980s on, suggesting evidence of both political shocks and territorial solidarity in the spatial distribution of urban growth.
2.3. A Case Study : The Former Soviet Union
3. Modular Multimodelling Experiment
3.1. Overview
- Each city updates its economic variables based on its current population;
- Cities interact (i.e., exchange product) with other cities according to they supply, demand and distance;
- Each city updates its wealth based on the results of its interactions;
- A simulation step ends when each city updates its population.
3.2. Design Concepts
3.3. Implementing Mechanisms as Building Blocks (Details)
3.3.1. The Baseline Model
- Each city interacts with other cities according to the intensity of their potential Equation (9). For two distinct cities i and j, the computation of the interaction potential consists in confronting the supply of i Equation (11) to the demand of j with an equation borrowed to the gravity model Equation (12).
3.3.2. Mechanism Increments
- The mechanism that accounts for interactions benefits at the intercity level is the one called bonus. It
“[...] features a non-zero sum game [...], rewarding cities who effectively interact with others rather than internally. We assume that the exchange of any unit of value is more profitable when it is done with another city, because of the potential spillovers of technology and information [54].”
- A mechanism related to situation advantages is called fixed costs. It ensures that the situation of each city in the system is taken into account in its interactions with other cities.
“Every interurban exchange generates a fixed cost (the value of which is described by the free parameter ). This implies two features that make the model more realistic: first, no exchange will take place between two cities if the potential transacted value is under a certain threshold ; second, cities will select only profitable partners and not exchange with every other cities. This mechanism plays the role of a condition before the exchange” [54].
- Site effects are targeted by the resource mechanism: site advantages are particularised in this model by natural resource deposits (more specifically: coal deposits C on the one hand, and oil and gas deposits O on the other hand). The assumption is made that if the city i is located on some coal or oil deposits ( or ), the city benefits from the advantage granted by the extraction activity. The capacity of extraction depends on the capital (wealth) of the city and takes the form of a wealth multiplier for each resource Equation (22) after Equation (14):
- Territorial and political effects are formalised by the redistribution mechanism. It allows for a redistribution of wealth between cities of the same territory R (region or State). To do so, territorial taxes are collected in each city , as a proportion of their wealth. The total amount of taxes collected is Equation (23):
- Finally, territorial and situation explanations are mixed in the urban transition mechanism. To account for the different opportunities of cities to attract rural migrants in the different regions, we model the evolution of the urban transition curves over time. As shown empirically [45], 100 out of the 108 regions of the Former Soviet Union have followed the scheme of the urban transition. It means that their urbanisation rate (in %) has followed a logistic function over time t Equation (27):
3.4. Technical Modular Implementation
Listing 1: Object oriented specialisation. abstract class C extends A with B { def a(x : Double) : Double def b(x : Double) : Double def c(x : Double) = /* Compute something using a and b * / } class C1 extends C { def a(x : Double) = /* Some implementation of a */ def b(x : Double) = /* Some implementation of b */ }
Listing 2: Mixin in Scala. trait A { def a(x : Double) : Double } trait B { def b(x : Double) : Double } trait C extends A with B { def c(x : Double) = /* Compute something using a and b */ } // Implementation 1 of trait A trait A1 extends A { def a(x : Double) = /* Some implementation */ } // Implementation 2 of trait A trait A2 extends A { // Parameter p0 used in this version of a def p0 : Double def a(x : Double) = /* Some implementation using p0 */ } // Implementation 2 of trait B trait B2 extends B { def b(x : Double) = /* Some implementation */ } val instance 1 = new C with A1 with B2 {} val instance 2 = new C with A2 with B2 { // Value for parameter p0 of trait A2 def p0 = 1.0 }
Listing 3: Example of generated code. def model (index : Int , parameters : Seq[Double]) = index match { case 0 => new Model with T11 with T21 with . . . { def p0 = parameters(0) def p1 = parameters(1) ... } case 1 => new Model with T11 with T22 with ... { def p0 = parameters(0) def p1 = parameters(1) ... } case 2 => ... }
3.5. Calibrating a Multi-Model
“Whatever changes occur in the institutional, political and social context of computational models, the question of how to learn from models remains. It is clear that assessment of the accuracy of a model as a representation must rest on argument about how competing theories are represented in its workings, with calibration and fitting procedures acting as a check on reasoning”([7] p. 291).
4. Results: Hypothesis Testing to Explain Urbanisation in the Former Soviet Union
- 1
- Which is the most parsimonious model to simulate the evolution of cities before and after the collapse of the Soviet Union? A way to answer this question is to restrict the set of results to the five model structures that correspond to the a mix of two mechanisms: the baseline model + one additional mechanism (for example: resource extraction). That leaves us with parameter sets and 250 performance values δ for each time period analysed. We look at the lowest distance to empirical data achieved in this set of results, and identify the corresponding model structure (the additional mechanism involved) and parameter values as the best performing ones.
Parameter Name | Value | Mechanism |
---|---|---|
economicMultiplier | 0.002193758 | Baseline |
populationToWealth | 1.000184755 | Baseline |
sizeEffectOnSupply | 1.053943022 | Baseline |
sizeEffectOnDemand | 1.000000000 | Baseline |
wealthToPopulation | 0.203567639 | Baseline |
distanceDecay | 1.872702086 | Baseline |
ruralMultiplier | 0.034975771 | UrbanTransition |
Normalized δ | n cities | Time steps |
0.01423387 | 1145 | 30 |
Parameter Name | Value | Mechanism |
---|---|---|
economicMultiplier | 0.502616330 | Baseline |
populationToWealth | 1.124963276 | Baseline |
sizeEffectOnSupply | 1.002982515 | Baseline |
sizeEffectOnDemand | 1.000808442 | Baseline |
wealthToPopulation | 0.699943763 | Baseline |
distanceDecay | 1.475836151 | Baseline |
oilAndGazEffect | 0.017066495 | Resources |
coalEffect | −0.011792670 | Resources |
Normalized δ | n cities | Time steps |
0.005180008 | 1822 | 21 |
- 2
- Which are the mechanisms (and mechanisms’ interactions) that are essential to model the Soviet and post-Soviet urbanisation patterns? To address this question, we statistically analyse the results of the multicalibration (3200 sets of parameters, the best 50 of each model structure for each time period) to evaluate the contribution of each mechanism (everything else being equal in the model structure) to the reduction of distance between simulated and observed demographic data for each city. More specifically, we regress the distance to data δ against the mechanism composition of the model, following Equation (30):
- 3
- What are the cities that resist modelling? In other words, what are the cities that are too specific to be modelled by any of the mechanisms implemented? To answer this last question, we statistically analyse the difference between the log of the population observed and the log of the population simulated at the last evaluation Census date for cities included in the simulation, with respect to their locational and functional attributes. The models for which we present the results below contains all the implemented mechanisms, and are applied to the two periods of enquiry.
Positive Residuals | ||
---|---|---|
City | Observed Pop. | Simulated Pop. |
Naberezhnye Tchelny | 500,000 | 30,000 |
Volgodonsk | 191,000 | 36,000 |
Chajkovskij | 86,000 | 19,000 |
Toljatti | 685,000 | 158,000 |
Bratsk | 285,000 | 73,000 |
Balakovo | 197,000 | 52,000 |
Tihvin | 71,000 | 20,000 |
Chervonograd | 72,000 | 21,000 |
Obninsk | 111,000 | 32,000 |
Staryjoskol | 174,000 | 53,000 |
Negative Residuals | ||
City | Observed Pop. | Simulated Pop. |
Zaozernyj | 16,000 | 54,000 |
Gremjachnsk | 21,000 | 56,000 |
Atakent/Ilitch | 15,000 | 38,000 |
Kizel | 37,000 | 88,000 |
Cheremhovo | 74,000 | 172,000 |
Ilanskij | 18,000 | 42,000 |
Gornoaltajsk | 46,000 | 102,000 |
Volchansk | 15,000 | 32,000 |
Zujevka | 16,000 | 35,000 |
Taldykorgai | 138,000 | 296,000 |
Positive Residuals | ||
---|---|---|
City | Observed Pop. | Simulated Pop. |
Mirnyja | 41,000 | 12,000 |
Sertolovo | 48,000 | 16,000 |
Beineu | 32,000 | 11,000 |
Govurdak | 76,000 | 28,000 |
Serdar/Gyzylarbat | 98,000 | 37,000 |
Bayramaly | 131,000 | 53,000 |
Sarov | 92,000 | 39,000 |
Turkmenabat/Tchardjou | 427,000 | 185,000 |
Astana/Tselinograd | 613,000 | 278,000 |
Dashougouz | 275,000 | 126,000 |
Sovetabad | 11,000 | 33,000 |
Zhanatas | 21,000 | 50,000 |
Krasnozavodsk | 13,000 | 31,000 |
Gagra | 11,000 | 25,000 |
Nevelsk | 12,000 | 26,000 |
Arkalyk | 28,000 | 59,000 |
Chyatura | 14,000 | 28,000 |
Aleksandrovsk Sahalinsk | 11,000 | 21,000 |
Uglegorsk | 10,000 | 20,000 |
Baikonyr | 36,000 | 67,000 |
5. Discussion
“Despite the fact that the experience of individual cities has become more varied internationally (at least within what might be called the mature economies) there is stronger evidence of a predictable pattern of change, determined by common causal factors, than might be expected given the diversity and variety of cities”([15] p. 1342).
6. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
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Cottineau, C.; Reuillon, R.; Chapron, P.; Rey-Coyrehourcq, S.; Pumain, D. A Modular Modelling Framework for Hypotheses Testing in the Simulation of Urbanisation. Systems 2015, 3, 348-377. https://doi.org/10.3390/systems3040348
Cottineau C, Reuillon R, Chapron P, Rey-Coyrehourcq S, Pumain D. A Modular Modelling Framework for Hypotheses Testing in the Simulation of Urbanisation. Systems. 2015; 3(4):348-377. https://doi.org/10.3390/systems3040348
Chicago/Turabian StyleCottineau, Clémentine, Romain Reuillon, Paul Chapron, Sébastien Rey-Coyrehourcq, and Denise Pumain. 2015. "A Modular Modelling Framework for Hypotheses Testing in the Simulation of Urbanisation" Systems 3, no. 4: 348-377. https://doi.org/10.3390/systems3040348