Geoscience Reference
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- to model statistically the evolutions of spatial units and identify the
organization of differential evolution in space;
- to model spatial organizations (for example, using spatial autocorrelation) and
identify their evolution;
- to analyze and follow-up spatial associations (or in other words, correlations
between variables characterizing spatial units) in time.
This challenge may therefore constitute a goal as such or be integrated in a loop.
It can for example be used for creation of data and its explorations. Some
processings may be integrated in exploration methods. Finally, these approaches can
also be used in a preparatory step to other types of modeling.
2.1.4.
Identifying the underlying processes of change: simulation and scenario
testing (challenge 4)
Finally, the last step is the one that identifies and proposes explicit formulations of
the processes that lead to certain types of spatial organizations and to their evolution: it
concerns the implementation of dynamic models and simulation models. Let us recall
the example related to the demographic evolution of a spatial unit. In the most simple
case, where questioning focuses, for example, on the evolution of the population of a
given municipality K, the purpose is to identify the factors that explain this evolution.
Knowing the population at the date being considered as initial, the objective is to build
a model that allows explaining the shape of the municipality's trajectory. Various
frameworks and formalisms are possible. Here are a few examples:
Aggregated dynamic model
The evolution of the municipal population can be expressed based on a
difference equation or differential equation. The logistic model is a classic example:
dPK/dt = a PK (1 - PK/CK) for the differential equation version, in continuous
time
PK
t+1
= PK
t
+ a PK
t
(1 - PK
t
/CK) for the difference equation version, in discrete
time
where PK represents the population, CK is the carrying capacity of the spatial unit
considered, i.e. its demographic potential, and
a
is
a parameter measuring the overall
growth rate of the population. Such an equation translates the hypothesis of a strong
growth (of exponential nature) when the size of the population is much below the
carrying capacity, and a progressively much slower growth as the population gets
closer to this threshold (Figure 2.2).
