Fig. 7.

a Scaling of log-ratio variance using the proportionality coefficient. Shown are coefficients of gene pairs involving three genes with different variances versus their log-ratio variances (absolute data). The three genes have variances of the logged absolute data of 2.1 (blue), 0.39 (green) and 0.076 (red), respectively. Gene pairs with higher variance can have higher log-ratio variance to attain the same value of the coefficient. b Log-ratio (alr and clr) transformed gene expression scatter plots. The red lines are fits with a slope $\mathit{\beta }=1$ (the intercept is estimated by the mean over $Y_j-Y_i$). Upper panels A gene pair correctly identified as proportional (left) and incorrectly discarded (right). The same pair is shown in the first panel of Fig. 6. Lower panels A gene pair correctly discarded (left) and incorrectly identified as proportional (right) (colour figure online)