Figure 5. Summary of relationship between pairwise and population metrics.

A change in r_sc mean and r_sc SD may correspond to changes in loading similarity, %sv, dimensionality, or a combination of the three. Shaded regions indicate the possible r_sc mean and r_sc SD values for different dimensionalities; increasing dimensionality tends to decrease r_sc mean and r_sc SD (shaded regions for larger dimensionalities become smaller). Within each shaded region, decreasing %sv decreases both r_sc mean and SD radially toward the origin. Finally, rotating co-fluctuation patterns such that the loadings are more similar (going from low to high loading similarity) results in moving clockwise along an arc such that r_sc mean increases and r_sc SD decreases. We also note two subtle trends. First, there are more possibilities for loading similarity to be low than high (Math Note E), suggesting that r_sc SD will generally tend to be larger than r_sc mean if neuronal activity varied along a randomly chosen co-fluctuation pattern (shading within each region is darker near the vertical axis than the horizontal axis). Second, this effect becomes exaggerated for higher dimensional neuronal activity, as many dimensions can have low loading similarity but only one dimension can have high loading similarity (Math Note E). Thus, it becomes progressively unlikely for r_sc SD to be 0 as dimensionality increases (shaded regions for larger dimensionalities lifted off the horizontal axis).