Fig. 1

What lies beneath: co-expression can reflect different combinations of cell-state or compositional variation. Each panel shows a different scenario in which cell state and composition affect the expression of two genes (A and B), yielding different types of co-expression. Two cell types are colored in red and blue. In the top panel, both cell types have state-dependent variation that causes co-expression within each (r ~ 0.75). In addition, there is co-expression due to compositional variation (r ~ 0.75). In the bottom left panel only compositional variation is apparent (r ~ 0.65), there is no relationship between gene A and gene B within the cell types (r ~ 0). This is the opposite in the bottom right panel. Here, there is only variation within the cell types (r ~ 0.95) but no compositional effect across cell types (r ~ 0). The exact value the compositional correlations take would vary in real data since combinations of the underlying cell types would fill in intermediate points, but the three cases would still occur as described; other possibilities due to noise or other complex scenarios (e.g. Yule-Simpson effect) are also possible