Refined data analysis for local marriages in France.

<p>Panel <i>a</i>: log-log scale plot of LM_{<i>α</i>_<i>i</i>,<i>y</i>} versus Γ_{<i>α</i>_<i>i</i>,<i>y</i>}, where different regions are denoted in different colours and symbols, as explained in the legend. These data are properly binned (green squares) and best-fitted (solid line) by , in agreement with the theoretical result (2). The best-fit coefficients are <i>a</i> = 1.87 and <i>b</i> = −4.38 ⋅ 10⁻⁴. The parameter <i>b</i> is introduced to account for the error (calculated in terms of the standard deviation) associated to binned data, which is ≈ 5%. In general, the various regions seem to be homogeneously scattered around the best-fit curve. In the insets we show, as examples, the data pertaining to two selected regions, namely Limousin (upper inset) and Provence-Alpes-Cote d’Azur (lower inset). Notice that for both the insets, the best-fit previously obtained for the whole data set (solid line) still provides a proper fit. Panel <i>b</i>: For each region we calculate <i>ρ</i>_<i>α</i>, as defined in the text and deepened in the Theoretical Protocol Section. The horizontal line is drawn as a reference for the unitary value. Notice that the largest deviation from the unitary value is for Corsica. From this plot we can distinguish regions displaying a relatively large number of marriages (i.e., <i>ρ</i>_<i>α</i> > 1) and regions displaying a relatively small number of marriages (i.e., <i>ρ</i>_<i>α</i> < 1). This division is highlighted in the colormap presented in panel <i>c</i>. Interestingly, regions exhibiting analogous deviations share a certain degree of geographical proximity: regions with <i>ρ</i>_<i>α</i> > 1 (dark shading) correspond to the North-Eastern border of France, while regions with <i>ρ</i>_<i>α</i> < 1 (bright shading) correspond to the Center-Western part of France. Panel <i>d</i>: the two clusters of regions highlighted are analyzed separately. For each we bin the related raw data and get a best fit, still according to the function , obtaining <i>a</i>_<i>up</i> = 1.90 and <i>b</i>_<i>up</i> = −6.5 ⋅ 10⁻⁵ (<i>R</i>² = 0.97) for the set of regions with <i>ρ</i>_<i>α</i> > 1, and <i>a</i>_<i>down</i> = 1.68 and <i>b</i>_<i>down</i> = −2.2610⁻⁴ (<i>R</i>² = 0.98) for the set of regions with <i>ρ</i>_<i>α</i> < 1; notice that <i>a</i>_<i>up</i>/<i>a</i>_<i>down</i> ≈ 1.1. Binned data for the former set (triangles) and for the latter set (square) are shown in the main panel, together with the related best fits, in a log-log scale plot. These fits are slightly better that the one obtained at the country level, suggesting that possible internal heterogeneities may be rather limited. In the insets we compare these best fits with raw data for two regions (Aquitaine and Auvergne) with <i>ρ</i>_<i>α</i> > 1 (upper inset) and two regions (Alsace and Franche-Comté) with <i>ρ</i>_<i>α</i> < 1 (lower inset). Notice that in both cases data points overlap both curves, again suggesting that the division highlighted here is rather mild.