Patterns of molecular line ratios for M 51. Each molecular line is stacked by CO (1–0), and the line ratio is normalised by the mean stacked line ratio with CO (1–0). We colour-coded by the CO (1–0) line brightness of the stacked bin. The line ratios are roughly ordered from left to right by increasing critical density of the line entering in the numerator. We find an increase in the line ratio variations towards the right end of the plot. Such a trend is in agreement with the results from the models presented in Leroy et al. (2017).