Proportionality: A Valid Alternative to Correlation for Relative Data
Fig 1
Why correlations between relative abundances tell us absolutely nothing.
These plots show two hypothetical mRNAs that are part of a larger total. (a) Seven pairs of relative abundances (mRNA1/total, mRNA2/total) are shown in red, representing the two mRNAs in seven different experimental conditions. The dotted reference line shows (mRNA1 + mRNA2)/total = 1.) Rays from origin through the red points show absolute abundances that could have given rise to these relative abundances, e.g., the blue, green or purple sets of points (whose Pearson correlations are −1, +1 and 0.0 respectively). (b) Relative abundances that are proportional must come from equivalent absolute abundances. Here the blue, green or purple sets of point pairs have the same proportionality as the pairs of relative abundances in red, though not necessarily the same order or dispersion.