The misuse of ratios in ecological stoichiometry

Abstract

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.

First report on the occurrence of a single species cyanobacterial bloom in a lake in Cyprus: Monitoring and treatment with hydrogen peroxide releasing granules

“…Monitoring is useful for building predictive models as early response tools to avoid cyanotoxins contamination of source waters used for recreational activities and drinking water. Correlations between nutrients and eutrophication have been developed recently [46] with the DIN:TP and NO 3 -:TP mass ratio to be the most promising ratios, as con rmed also in our case. While these ratios are proving to be promising for understanding the eutrophic status of surface waters, they should be applied with caution after careful examination of each waterbody's unique characteristics (depth, size, water temperature etc.).…”

Toward Determining the Spatio-Temporal Variability of Upper-Ocean Ecosystem Stoichiometry From Satellite Remote Sensing

“…This larger range reveals a relatively large uncertainty in r C:P in the subtropics. Here, we used range instead of arithmetic standard deviation as a measure of uncertainty because the ratios by their nature do not follow normal distributions (Isles, 2020) and the sample size is small (n = 4). We show the uncertainty of r C:P expressed in terms of geometric standard deviation from the mean in Supplementary Figure 5.…”

“…We use the median satellite-informed phytoplankton C:P and POC:POP values from four satellite products (CAFE, VGPM, Eppley-VGPM, and CbPM) for comparison with the data. Here, we use the median rather than the mean as the measure of average C:P across satellite products because the ratios by their nature do not follow normal distributions (Isles, 2020).…”

Rain-fed streams dilute inorganic nutrients but subsidise organic matter-associated nutrients in coastal waters of the northeast Pacific Ocean

“…All statistical analyses were completed in R (R Core Team, 2019), using packages vegan (Oksanen et al, 2018), dplyr (Wickham et al, 2019), lme (Bates et al, 2015) and lsmeans (Lenth, 2016). Stoichiometric ratios were log-transformed prior to the calculation of summary statistics presented in figures in acknowledgement of the inherent non-normality of ratio data (Isles, 2020). Mean concentrations presented in figures and tables were then re-transformed to non-log scale to facilitate comparisons with literature values.…”