Dangerous relationships: biases in freshwater bioassessment based on observed to expected ratios

The ecological assessment of freshwaters is currently primarily based on biological communities and the reference condition approach (RCA). In the RCA, the communities in streams and lakes disturbed by humans are compared with communities in reference conditions with no or minimal anthropogenic influence. The currently favored rationale is using selected community metrics for which the expected values (E) for each site are typically estimated from environmental variables using a predictive model based on the reference data. The proportional differences between the observed values (O) and E are then derived, and the decision rules for status assessment are based on fixed (typically 10th or 25th) percentiles of the O/E ratios among reference sites. Based on mathematical formulations, illustrations by simulated data and real case studies representing such an assessment approach, we demonstrate that the use of a common quantile of O/E ratios will, under certain conditions, cause severe bias in decision making even if the predictive model would be unbiased. This is because the variance of O/E under these conditions, which seem to be quite common among the published applications, varies systematically with E. We propose a correction method for the bias and compare the novel approach to the conventional one in our case studies, with data from both reference and impacted sites. The results highlight a conceptual issue of employing ratios in the status assessment. In some cases using the absolute deviations instead provides a simple solution for the bias identified and might also be more ecologically relevant and defensible.