Figure 6

The Herfindahl index decreases monotonically with the fraction of migrants.

Note: In the main plot bullets represent the value of the normalized diversification index n_h for different province and different years as a function of the fraction of migrants Γ present in the same province in the same year. Green squares represent binned data and the solid red line is the related best fit (R²≈0.93). This is a linear curve (in log-log scale) y=p₁x+p₂, with p₁=−0.21±0.01 and p₂=−5.47±0.01. The fitting has also been performed for data of n_h pertaining to any single province and any single year, hence obtaining p₁(y,p). These values have been averaged over the provinces to get $\overline{p_1}(y)={\sum }_{p\mathrm{=1}}^{N_{\mathrm{\backslash scale\; 120\%p}}}{p}_1(y,p)/N_p$ which is shown in the inset (the line is a guide for the eye). This plot shows that the monotonicity of n_h with respect to Γ (that is,$\overline{p_1}\mathrm{<0}$) is robust with respect to the year; the same holds even when we average over the year, namely it is robust with respect to the province.