Uncertainties in Data and Spurious Correlations Related to the Redfield Ratio

Spurious correlations is a fundamental problem in situations where the y‐variable is a function of x, such as ratios u/x versus x or u, or products, such as u × x versus x or u, or expressions such as (u–x) versus x. The theory of spurious correlations was developed more than 100 years ago and yet there are numerous papers in aquatic ecology presenting results as if they were mechanistically meaningful when they, in fact, are clearly spurious. This is specifically so in contexts related to some of the most important issues in aquatic ecology namely the question of “limiting” nutrient and the Redfield ratio, defined as either TN/TP or DIN/DIP (TN = total‐N, TP = total‐P, DIN = dissolved inorganic N, DIP dissolved inorganic P). We have demonstrated by systematic tests using randomly generated data that the patterns in spurious relationships can be identical to patterns in empirical data that have been interpretated in mechanistic terms. We have collected empirical data from the Baltic Sea, Kattegat and Skagerack and tested those data to see if spurious relationships exist. The r2 ‐values vary from 0.90 (TN/TP versus TP), 0.67 (DIN/DIP versus DIN), 0.40 (DIN/DIP versus DIP) to 0.014 (TN/TP versus TN). Very little mechanistic understanding about “limiting nutrient” and/or the role of TN/TP or DIN/DIP‐ratios can be deduced from these – and similar results – because they are spurious. We have also shown that the ratios TN/TP and DIN/DIP have significantly higher coefficients of variations (CV) than TN, TP, DIN and DIP individually. This explains why these ratios generally are poor predictors in contexts of nutrient limitation and in modeling of primary production. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)