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).

Figure 1.

Scatter plots and fitted lines of hypothetical data of an effluent X (%) exposed to an measured endpoint Y. Current acute categorical (A) and proposed continuous (B) sampling design (n = 18), (C) smooth threshold, (D) critical concentration.

The same sampling effort for a test with 3 replicates of 5 concentrations plus 3 control replicates (n = 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 (n = 6) compared to the proposed continuous sampling design (n = 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) or critical concentration that cause an abrupt change in response, leading to an exponential decay of the measured endpoint almost to zero (Figure 1D). These critical concentrations may not be seen by current ECx and NOEC evaluations although they are much more ecologically relevant. The identification of these critical thresholds is extremely important especially at higher levels of biological organization (i.e., populations, communities, and ecosystems).

These points or zones at which there are abrupt changes in ecological relationships can be defined as ecological thresholds. This concept has been applied in pollution evaluation as “critical loads,” which represent the amount of a contaminant that an ecosystem can safely absorb before there is a change in ecosystem state and/or in a particular ecosystem function (Groffman et al. 2006). Critical loads have been extensively used in air pollution control in long-term monitoring programs in Europe (Long-Range Transboundary Air Pollution: http://www.unece.org/env/lrtap/) and in the United States (National Atmospheric Deposition Program: http://nadp.isws.illinois.edu/). Sonderegger et al. (2009) and Schmidt et al. (2010) have also shown useful and different applications of the concept of ecological thresholds in aquatic systems by evaluating the effects of metals on macrobenthic community composition.

Although there seems to be no consensus as to which statistical tools are most appropriate to identify these critical thresholds, different linear and nonlinear models have been used in other sciences, such as ecology (e.g., piecewise regression, logistic regression, nonparametric change point analysis). The 95% confidence interval still can be evaluated using some of these techniques. Ficetola and Denoël (2009) review examples of the differences between 3 analytical methods with simulated ecological data of habitat loss and species occurrence. The “significant zero crossing” method (SiZe) (Sonderegger et al. 2009) also provides a graphical representation of the threshold and how it responds to data variability providing insights into multiple thresholds. Although SiZe cannot provide estimates and confidence regions for the thresholds it detects, it has shown good potential in critical thresholds evaluation. Akaike's information criterion (AIC) can be used as well for model averaging and testing by the method of maximum likelihood, taking the predictions of all reasonable models into account (e.g., Schmidt et al. 2010).

More attention should be given to the concept of ecological thresholds in ecotoxicology and environmental risk assessment. Predicting critical concentrations for contaminants is not an easy task and a range of concentrations should be calculated based on a confidence interval. Thresholds at lower levels of biological organization (e.g., in organism level, such as reproduction and growth) should also be investigated by ecotoxicologists and efforts should be made to assess the relationships between thresholds at different levels of biological organization. Multispecies, in situ, and manipulative experiments could be used to search for ecological thresholds at higher levels of biological organization. A proper sampling design, which allows a complete evaluation of the dose response curve, should be used to identify those critical thresholds.

Assessment of dose as a continuous variable, increasing the number of replicates, is advisable at any level of biological organization. Regression analyses, which are also analyses of variance and also hypothesis testing, are more appropriate than ANOVA analyses. However, maybe we are not using the most appropriate and conservative metric (ECx) and experimental design for the curve fitting estimate.