Geoscience Reference
In-Depth Information
4.3.1.
Modeling the diffusion of a migratory wave front
The process of diffusion is intrinsically spatio-temporal: a phenomenon, such as
the adoption of an innovation or an epidemic, for example, appears at a given time,
in a given place and spreads progressively to other places, starting from interactions
between individuals. The first to have modeled this phenomenon in geography is
Torsten Hägerstrand. In his first works in the 1950s at the University of Lund, he
used Monte Carlo simulations in order to study migrations and diffusion of
innovations as spatial processes. In both cases, his questioning is anchored in the
empirical case of Asby (the innovation involving the improvement methods of
grazing in small farms), the Swedish village of his childhood [HAG 53]. Since that
time, he clearly favors an approach of phenomena at the level of the individual, by
grasping the logic of his/her intentions and his/her actions. He would then formalize
this concern in his development of “time-geography”. Since the 1950s, in his works
that put forward the importance of exchanges of information on the diffusion of
innovations, Hägerstrand considers that it is essential to introduce randomness in
any rule that brings individuals to take a decision involving change. In the
simulations that he was carrying out at that time without computers, Hägerstrand
introduced this randomness using a dice within the Monte Carlo method.
The Monte Carlo method allows simulating non-deterministic phenomena.
Therefore, it is frequently applied in the microsimulation models presented above. If
an individual possessing a certain profile has 80% chances not to move house, 15%
chances to change residence within the same municipality and 5% chances to
migrate out of the municipality, a number between 1 and 100 is pulled out in a
random distribution. If the number is in the [1, 80] interval, the individual is
simulated as not changing residence, if it is in the [81, 95] interval the individual is
considered to be changing residence within its municipality, and finally if the pulled
out number is in the [96,100] interval, he/she is considered as a migrant. The
operation of drawing lots is repeated for each individual constituting the sample and
this for each event that has to be simulated. Moeckel
et al.
[MOE 03] use a process
that falls within the same principle to proceed to the spatial distribution of a
synthetic population within a metropolis. An interval of values is assigned to each
cell as a function of the density of the built area. A draw is then carried out for each
individual, and this is located in the cell corresponding to the number drawn. The
method can also be used to simulate the choice of localization. This method is
conventional whenever it is wished to introduce a random mechanism in a behavior.
It has notably been used to simulate migrations.
Such a procedure was used by Young [YOU 02] to explore the colonization of
empty spaces by migration. He considered a homogeneous geographical space upon
which agents move around. These represent either individuals or groups (hunters-
