MARIUS is a model of urban evolution in the post-Soviet space. It aims at simulating the socio-economic evolution of cities, the hierarchical and functional structuration of the geographical system resulting from their interactions at macro level, and their diversified trajectories over several decades at micro-level, while being as parsimonious as possible. For this purpose, we tackled the evaluation process alongside model-building, and prepared a path for progressively complexifying the model’s structure based on statistical findings . We start from a generic model that would suit other systems of cities and add mechanisms specific to the post-Soviet space when necessary (that is, if the generic mechanisms prove unable to match the observations).
The simplest model of urban evolution that satisfies criteria of proximity to data and realism of micro-dynamics is composed of a restricted set of mechanisms :
– scaling laws for modeling the inequalities of production and consumption capacities in cities according to their size;
– a gravity model computing the interaction potentials of pairs of cities on an abstract market (summarizing exchanges of diversified goods, services, information and capital);
– an advantage modelled for cities exchanging large quantities of value with a large pool of partners, representing the spillovers of information and technology that are associated to interactions;
– a fixed cost for each transaction that constrains the potential network of cities’ interaction according to the profitability of each potential exchange;
– a mechanism of conversion between gains in wealth and evolution of population in the city that is non linear with city size.
The calibrated model that produces the best results is obtained after intensive parameter search with genetic algorithms (100 000 generations) distributed on a computer grid with the OpenMOLE software.
Source : DARIUS 2014 . GibratSimulator . Cities in the graphs are sorted by size. (each point represents one urban agglomeration)
This figure demonstrates that we were able to simulate with this model the degree and trend of hierarchization process among the 1145 cities of the Soviet Union from 1959 to 1989, much better than using a classical model (Gibrat’s) and by including strong interaction hypotheses (yet with 8 parameters instead of 2 in Gibrat’case). Moreover, this model results from a trial and error process of examining the model outputs, evaluating them against empirical data and theoretical findings, refining the evaluation criteria and finally complexifying the model in order to meet the requirements of this new evaluation method.
It would be unrealistic to pretend using the model for reconstructing the evolution during the last two decades that followed rather unpredictable political events. But it is likely that once having introduced exogeneously in the model the corresponding bifurcation in economic rules, the model would help predicting the probable evolution of cities in countries of former Soviet Union in a rather accurate way.
Clémentine Cottineau, Paul Chapron and Romain Reuillon.