Geoscience Reference
In-Depth Information
also takes into account the interactions between the dynamics of the different
municipalities, particularly through the term A
i
that is evolutive.
Microsimulation: an individual-centered model in social science
The two previous cases are based on the hypothesis that a law can be formulated
at the level of spatial units apprehended in aggregated form. This assumes either that
the individuals' behaviors are homogeneous, or that the individuals' characteristics
compensate for each other and that they are seldom determinant relatively to the
general tendency. Sherlock Holmes summarizes well this point of view: “While the
individual man is an insoluble puzzle, in the aggregate he becomes a mathematical
certainty. You can, for example, never fore-tell what any one man will do, but you
can say with precision what an average number will be up to. Individuals vary, but
percentages remain constant” (Sir A.C. Doyle, quoted by Haag [HAA 89]). Other
researchers have an opposite view, stating that it is essential to apprehend logics in
change (here fertility, mortality and migration) at the finest level of the individuals.
The microsimulation models describe these behaviors with rules operating at the
level of individuals, and the evolution of the different municipal populations is then
obtained by simple aggregation (see Chapter 4).
Cellular automata (CA) and multiagent systems (MASs)
These methods are also individual-centered from a methodological point of view,
but the elementary entities are not necessarily individuals as in the previous case.
This will be illustrated in Chapter 4.
The models developed with these formalisms are based on rules. An emblematic
example of CAs is the game of life [GAR 70]. The entities are the cells of a grid that
can have two states, those of dead or alive. The transition from a state in t to a state
in t+1 is defined by the following set of rules based on the neighborhood of the cell:
(1) if a dead cell is surrounded by three neighboring living cells, it “is born”; (2) if a
living cell is surrounded by two or three living neighbors, it remains alive; (3) if a
living cell is surrounded by less than two neighboring cells, it dies by isolation; if it
has more than three neighboring living cells it dies by congestion. These simple
rules are sufficient to make a great diversity of spatial and temporal configurations
emerge. The central mechanism of CAs, which make change in a place (cell)
dependent on the neighboring places' (cells')status, meets the basic assumptions of
geographers on the functioning of geographical space [TOB 79, COU 85, WHI 93,
BAT 05]. Therefore, CA is a dynamic modeling tool privileged in the discipline.
While CAs enable simulating the states and evolutions of space portions, MASs
formalize the interactions between autonomous agents located in an environment
they perceive and on which they can act [FER 95]. This formalism is particularly
well-adapted when faced with a system in which it is assumed that the interactions
