Evaluation of different averaging methods for calculation of ratios in nutrient data

Abstract

: Nutrient ratios are commonly used in ecology to investigate nutrient limitation in an aquatic environment. Ratios have distinct mathematical properties which should be considered when choosing an averaging method to avoid biased results. Herein, we estimated annual dissolved inorganic nitrogen to dissolved inorganic phosphorus ratios using long-term ecological (LTER) data from three sites in the German Bight by applying various measures of central tendency. Our aim was to examine the sensitivity of nutrient ratios to different modes of averaging and to define the most appropriate method for the calculation of nutrient relationships for stoichiometry. Our results demonstrate that the arithmetic mean of the raw data is upwardly biased, exaggerating the importance of phosphorus-deficient conditions. The geometric mean of the raw data and the arithmetic mean of log-transformed ratios are reliable calculations; however, the median is the most robust method to average nutrient ratios for skewed data. We recommend that ratio data should first be tested for normality, and that the methods used to determine nutrient ratios should be clearly stated, including which averaging method was used.