Barriers to the Spatial Diffusion for the Demographic Transition in Western Europe

The zones exhibiting a major discontinuity, an abrupt change of the values taken by spatialized variable(s) generally delineate patterns and probably correspond to the zones of sharp changes for the causal variable(s) underlying the observed surface relief, or to barriers in dynamic processes. An example of this can be two contiguous areas of mortality generated by ecological and/or socio-economic factors. A rapid change of the factors on the map corresponds to a sharp change of the mortality. Such a change is observed today on the borders separating Western Europe from the Federation of Russia. The underlying causal variable(s), summarized by the ‘sanitary system’, changes sharply on the border zone (Labbé, 1993). Another example is the Trieste-St Petersburg line (Hajnal, 1965) which separates two huge zones of nuptiality, high in the east, low in the west. To detect the zones of major discontinuity for one or several superimposed variables, in the same geographic frame, i.e. for surfaces of variables, this is the goal of a technique of descriptive statist ics called Wombling (Womble, 1951; Adams, 1970; Barbujani, Oden, Sokal, 1989; Bocquet-Appel, 1993). One can summarize the Wombling analysis in the following way: when the studied area is divided into quadrats, of (preferentially small and) equal size, an estimator quantifies the rate of change in each quadrat for all the variables studied. To this end, the variables of interest are represented as quasi-continuous surfaces, whose local slopes measure the local rate of change. For each surface-variable, the rate of change is expressed by a vector currently known in analytical geometry