What does the ECx tell us about the curve? Thoughts into ecological thresholds

Criticisms regarding the use of no-observed effect concentration (NOEC) and lowest observed effect concentration (LOEC) in the field of ecotoxicology are not new. The limitations of this approach are already well established in the literature although it continues to be widely used. One of the key issues is that questions should be related to the dose response curve; the analysis of variance approach, used to estimate the NOEC and LOEC values, does not tell us anything about the curve. Regression analysis, such as the ECx evaluation, has been proposed as an alternative for the use NOEC (Landis and Chapman 2011). However, most of the techniques used to calculate the ECx (e.g., Probit, Logit, trimmed Spearman– Karber) have the same sampling design used in the NOEC and LOEC evaluation, in which concentration is treated as an categorical variable. In fact, if true replication is employed, it is possible to calculate the ECx and NOEC/LOEC for the same data set. So how can we have the same sampling design for 2 completely different questions? The current sampling design of ECx and the importance of the concept of ecological thresholds in ecotoxicology is discussed in this Learned Discourse. In the current calculation of ECx, usually 5 concentrations plus 1 control are used. Using this sampling design, normally there is a gap, sometimes a large one, between concentrations and little can be seen of the shape of curve (Figure 1A). To better understand the dose response curve, we should assess the concentration as a continuous variable, increasing the number of replicates throughout the concentrations. Regression analysis, as a continuous variables assessment, does not need replication at the same concentration but, for a robust analysis, it needs at least 10 replicates along the gradient so that a line can be fitted (Gotelli and Ellison 2004). The same sampling effort for a test with 3 replicates of 5 concentrations plus 3 control replicates (n1⁄4 18) distributed over different concentrations to generate a curve would enable a much more robust analysis (Figure 1B). Depending on the intrinsic variability of a particular test, i.e., whether data exhibit high variability, increasing sample size may be necessary to estimate the curve fitting. Another important feature is that smaller sample sizes usually result in wider confidence intervals because our estimates are less precise. Although replicates at the same concentration may result in more precise values at this specific concentration, the sample size normally used to estimate the confidence interval over the fitted curve is 3 times smaller (n1⁄4 6) compared to the proposed continuous sampling design (n1⁄4 18). Two or three concentrations plus control should be replicated (laboratory replicates) as part of an analytical procedure. Outliers are easily identified. Furthermore, we could visualize the shape of the curve before the logarithmic transformation of the concentrations. Generally, the dose response curve can be described as a sigmoid curve, however, depending on the measured endpoint and the contaminant, it can have different shapes and slopes. Looking at Figure 1A, we cannot be sure which is the best curve fitting estimate between Figure 1C or Figure 1D. Some of these curves may present a smooth slope (Figure 1C)