Main panels: eigenvalues for heterogeneous density (A), heterogeneous activation (B), or combined (C). For each, the manipulated ratio is set as 1:2. For simplicity, the example considers 1D regions. Orange markers show eigenvalues from the baseline region, which is identical for all panels. Blue markers show eigenvalues from the second region with higher density, activation, or both, respectively. Markers connected by the grey line show the combined set of sorted eigenvalues from both regions. Insets: cumulative allocation for the set of eigenvalues marked by the red ellipse in the main panel. Horizontal orange lines indicate eigenvalues from and therefore allocation to the orange region, whilst vertical blue lines indicate allocation to the blue region. (A) Heterogeneous density. Increased receptor density in the blue region causes higher spatial correlations between neighbouring receptors and therefore larger eigenvalues, leading to a scaling of the eigenvalue curve. Increased density also leads to a larger number of receptors in the blue region, increasing the number of eigenvalues from this region and the total number of eigenvalues considered. (B) Heterogeneous activation. Increased variance in the blue region leads to a scaling of the eigenvalue curve. However, the number of receptors in the blue region is not affected, explaining differences observed compared to (A). (C) Heterogeneous density and activation. Effects from (A) and (B) are combined, leading to a double scaling of the eigenvalue curve, plus an increase in the total number of eigenvalues.