The misuse of ratios in ecological stoichiometry.

Ecological stoichiometry is concerned with the ratios of different elements, particularly carbon, nitrogen, and phosphorus. Ratios by their nature do not respond symmetrically to changes in the numerator and denominator and do not follow normal distributions; however, researchers frequently fail to consider these properties in their analyses, which has biased reported results. Calculating means, variance, or linear slopes based on untransformed ratios results in biased results. I demonstrate the consequences of these errors for inferences from stoichiometric analyses using simple examples and several large monitoring data sets. I then review 100 studies in ecological stoichiometry and find that misuse of ratio data is common, with 93% of studies containing at least one error. These errors may be problematic, particularly in large-scale meta-analyses summarizing data over large ranges. Fortunately, most of these mistakes can be easily avoided by first log transforming elemental ratios. I therefore recommend that, to ensure robust and reproducible results, researchers in ecological stoichiometry should adopt a convention of presenting stoichiometric ratio data as the logarithm of molar ratios in the future. The widespread use of untransformed nitrogen to phosphorus ratio as an indicator of nutrient limitation has likely exaggerated the importance of phosphorus limitation, particularly in freshwater systems.