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Séminaire interactif sur l'auto-organisation, cartographie cognitive, systèmes urbains et régionaux, et information spatiale, Paris, 17-18 mai 1998

Modelling within a self-organising or a microsimulation framework: opposite or complementary approaches?

Modéliser dans le cadre des théories de l'auto-organisation ou de la microsimulation : des approches opposées ou complémentaires ?
Lena Sanders


In this note I will shortly focus on the question of scale in the modelling of populations’ spatial mobility. Let us simply consider the case of three organisational levels : at the top, a region as a whole, for instance a country or a group of countries (macro-level), at an intermediate level a set of spatial units, for example the departments or the communes (meso-level) and at the bottom the individuals (micro-level). The question is, for a specific problem, to choose the most adapted level to develop a model. In many circumstances, there is no ambiguity, the level is induced by the problem. But in other cases, there is a possible choice. For example, if one wants to understand and to simulate the spatial redistribution of the population within a regional system during a certain period of time, the result of the model is expected to be given at a meso-level, but the model can be developed either within the framework of microsimulation, or within that of synergetics, each implying its proper philosophy. One privileges hypotheses on individuals’ behaviour, the other focuses on processes that refer to a meso-level logic. The aim here is to underline what conceptual differences are induced by these two approaches.

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From the individual to the group: agregation or synergy

1At first sight, the problem is similar in both approaches : in order to simulate the changing number of inhabitants of the different areas, between time t and t+t’, it is necessary to estimate the number of births and deaths in the areas, as well as the number of outmigrants and inmigrants from and to each area. In the microsimulation approach, the only way to properly estimate these figures is to aggregate the events that have occurred on an individual level. The modelling of these events constitutes then the core of the simulation. The hypothesis is that the diversity and the interdependency of individual behaviour and decisions is such that it has to be taken into account in order to simulate the change at an upper aggregate level. It is then necessary to reproduce the individual biographies, to simulate the series of events which lead to a demographic event as birth or death, or to the decision to move from one area to another. The passage to the meso-level is done by counting how many people are touched by demographic and mobility events during the concerned period.

2Using the framework of synergetics, one also starts from the individual level. Indeed, the master equation which is often used, expresses the relation between the change in the probability of observing a specific distribution of the total population between the different areas, and the individual probabilities of moving. When it comes to application, a series of assumptions are generally made : the population is homogeneous regarding behaviour, the individuals decisions are independent of each other and the decisions are supposed to only depend on the situation at t and not on previous history (Haag, 1989). If these assumptions hold, one obtains a convenient framework to simulate directly the change in each area of the regional system. The model focus on three aspects which could in some sense be interpreted from an individual point of view : the global propensity of the individuals to move, the individuals level of preference for each area, the different facilities of exchanges between couples of areas. Nevertheless, applications show that those aspects are merely related to the meso-level logic. The preferences which are computed for each date for each area are strongly related to the economic structure of the area (Sanders 1992). The mutual facility of connections between couples of areas is partly related to physical distance and to the existence of infrastructure, partly to cultural similarities and traditions of interaction (previous moves for example).

Opposite driving forces

3The philosophical differences between the two approaches appear very well when considering the assumptions made in the synergetics approach in order to build the mean value equation from the master equation. First, one supposes homogeneity in the individual behaviour, at least inside a given group. On the contrary, the microsimulation supposes diversity, and argue that the only way of taking this diversity into account, is to consider each individual in the simulation. A few variables of age, sex, family structure, educational level, profession, will characterise quite different types of individuals. In addition the simulation is based on a probabilistic approach that can give two different behaviours for two similar individuals. Second, the synergetics approach supposes independence between the individual decisions whereas the ambition of the microsimulation is to take into account the interdependence between individuals decisions. An example is : if the random drawing makes a particular individual move from area i between time t and t+t’, and if that individual has a family all the other members of the family will also deterministically move. Third, there is the Markow assumption which says that decisions made at time t do not depend on previous history. The ambition for microsimulation is to take into account past events, which is a central cause of diversity. A simple example is that the probability to have a child between t and t+t’, will differ, for the same age, according to the number of already existing children in the family.

4To summarise, in the synergetic approach the individuals are seen as bringing out a kind of consensus in their decisions, whereas in microsimulation the individuals are considered in their individuality and in the interdependence of their biographies. In the first case the mean behaviour has a significance, in the second the individual diversity is the main feature. None of these approaches is deterministic, but chance is introduced at different levels. In the microsimulation, at each period of time, each individual is submitted to a probabilistic drawing. The probability to move for example, will vary according to age, profession etc., but whatever the individual’s situation, he or she can decide to move. Chance is then affected to the occurrence of each event at the level of each individual. In the synergetics approach the stochastic component is introduced at the meso-level, where it stands for the diversity at the lower level. It supposes that diversity only creates a simple difference, more or less random, with the deterministic trajectory which is determined through a meso-level logic.

5Which one of the two approaches would give the most plausible predictions on the growth or decline of the different areas forming the regional system under study? For instance, in one case the simulated changes are the result of mechanisms which refer to meso-level processes as complementarity, competition, saturation, segregation etc. They are modelled using differential equations applied to the meso-level variables of the system. Those variables are economic and social profile of the areas, initial spatial distribution of the population, relative locations and accessibility of the areas. The dynamics that are generated are a combination of slow dynamics, with quite regular and foreseen changes, and more sudden and unpredictable changes at bifurcation points. In the microsimulation case, the meso-level changes are the result of the aggregation of all individual changes due to individual causes : age, marriage, loss of job, search for the first job etc. These changes are modelled through ageing mechanisms, transition probabilities and events. They occur through quicker dynamics, but at the aggregate level there are compensation effects between the individuals specificities, so their aggregation produces also slower dynamics.

Complementary tools for complementary objectives

6In the microsimulation approach, the meso-level mechanisms appear either as constraints that will restrict the individuals’ behaviour, or as new structures produced by converging micro-level decisions. As a constraint, it is taken into account in the rules of the model (for example such periurban area is very attractive because of the number of new vacant housings), and as a result, it is given by the number of people moving to that area. In a meso-level model, the aim is in fact to predict these " constraints " and to integrate the factors that will favour the construction of new housing in this periurban area (accessibility etc.). In that sense, the meso-level model tends to concentrate on the major trends of change, when these are considered as constraints in a micro-level model. Thus what is considered as " causes " in one model become constraints in the other. In the microsimulation the focus is more on the individual specificities and the model concerns mostly their decision process within the space of " freedom " which is left when the meso-level constraints are taken into account. Evidently the system of causalities will deeply differ.

7As the two models when pretend to respond to the same question the problem is to choose the relevant one. A few years ago, there was a technical limitation for microsimulation, but with the increasing computing capacities there is no limitation of that kind today. Geographers from Umeå for example apply a microsimulation model to the whole Swedish population, that is 10 millions people (Holm et al. 1995). However there is often a limitation in the availability of data at a micro level. Let us suppose in the following that we have to make a purely theoretical choice, without any technical or informational constraints. Perhaps the choice should depend on the weight of the " constraints " in different political and economical systems at a macro-level. Indeed, on one hand a vacant housing is a constraint for an individual who wants to move somewhere. But, on the other hand, several individuals searching for a house in a same area, induce a demand and promote new housing in this area. The first mechanism will play a greater role in a country where the urbanization is more planified, the second in countries with a more liberal functioning. This reveals a first complementarity : the choice of the model could depend on the specificity of the regional system under study, in terms of housing economy among others. A second complementarity can be seen through a possible coupling between these two kinds of models. A model of synergetics could be used to simulate how the " constraints " evolve through time, using meso-level mechanisms, and then a microsimulation model could be developed, using the constraints produced by the preceding model. This model could in turn simulate the effects of a change in attittudes of some groups of individuals, on the meso-level structure of the system. One could also suppose an even more intimate coupling. Indeed, the decision to leave depends possibly more on individual reasons than the choice of a destination which is more dependant on meso-level structures and constraints.

8Could it be possible to couple the logics of change at an individual level, with that operating at a meso-level ? It would suppose the ability to identify the respective weights of these logics according to different categories of individuals and different kinds of macro-level systems. It is not done yet.


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Clarke M., Holm E., 1987, Microsimulations methods in spatial analysis and planning, Geografiska Annaler, 69B, n°2, p145-164.

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Lena Sanders, « Modelling within a self-organising or a microsimulation framework: opposite or complementary approaches? », Cybergeo: European Journal of Geography [En ligne], Dossiers, document 90, mis en ligne le 24 mars 1999, consulté le 24 avril 2024. URL : ; DOI :

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Lena Sanders

Equipe P.A.R.I.S., CNRS-University of Paris I, France

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