Figure 2

The fraction of migrants in each Spanish province grows monotonically with time.

Note: We collect the historical series for the fraction of migrants γ in each Spanish province over the period 1998–2012 and we consider Γ≡γ(1−γ) representing the fraction of potential native-immigrant pairs. For small γ (and this is the case for Spain in the time window considered), γ≈Γ. In this figure we show Γ versus time t for the three largest provinces (from top to bottom: Madrid, Barcelona, Valencia) and for various countries of origin (depicted in different colours as shown by the legend). Notice that, Γ grows monotonically with t, and this is found also for the rest of Spanish provinces. Through the monotonicity of Γ(t) we can invert the function to obtain t(Γ). The latter can then be plugged into the dynamics of trade Y(t) to obtain the evolution Y(Γ), as reported in Figs. 3 and 4.