The results of such an integrated analysis will inevitably yield complex and multi-scaled results. A remaining challenge is to graphically depict the results in a way that is simple enough to understand, yet that retains enough of the complexity to make an informed decision. In current ERAs, assessors usually compare an exposure level to a no-effect level. In Europe, the Predicted Environmental Concentration/Predicted No-Effect Concentration (PEC/PNEC) ratio is often used. The PEC is often derived from mechanistic fate models and can usually be tailored for local environments. The PNEC is typically derived via the application of an assessment (or uncertainty) factor to the most sensitive species or to a species sensitivity distribution and therefore, does not account for environmental variability. It is also important to note that the usual PEC/PNEC ratio is an indication of an exceeded threshold and not a quantification of a risk. The value of this ratio does not explicitly account for uncertainties or variabilities and tells us very little about the nature or level of effect and the likelihood of an undesired event. Further, the relationship between the PEC/PNEC ratio and the level of effect is unknown43,44.

The method presented here has the potential to overcome the limitations associated with the PEC/PNEC ratio and similar methods as it is focused on a quantitative measure of effects and it enables the uncertainty and variability in effects and exposure to be quantified and could, ultimately, serve as a replacement. Prevalence plots present an endpoint or an effect size as a function of its cumulative prevalence (Fig. 1). They (i) provide an estimate of risk by using more integrated biological endpoints, (ii) bring greater ecological relevance to risk assessments, and (iii) aid more transparent risk communication by using relevant effect size (e.g. assessor-defined reduction in population biomass) instead of a significant statistical effect (e.g. difference in means of two populations associated with p-values). Prevalence plots can either use “raw” data to represent the effects of the stressor on an endpoint or data scaled by baseline condition to represent the relative impact of the stressor (effect size). Such a plot enables a rapid and meaningful understanding of the effects of stressors and incorporates relevant ecological factors. The endpoints and effect sizes can be tailored depending on one’s needs from rather basic ones such as a brood-size or decrease in population growth rate to more elaborate metrics such as a population biomass or difference in a biodiversity indicator, or even a really complex one such as a score representing a population or ecosystem structure (e.g. Ecological Integrity Assessment45,46). Likewise, the prevalence axis can be drawn according to one’s needs. It can indeed represent various scales of study such as the prevalence of an effect size in a portion of a freshwater habitat or the prevalence of an effect size in river basins within a region. This type of plot could therefore be used by various communities such as a risk assessor interested in the effect of chemicals discharged on the whole ecosystem of a river or an academic assessing the effect of pollution on a particular species worldwide.

Figure 1 Prevalence plots. The prevalence plot present an endpoint (e.g. brood-size, population biomass; see Fig. 3) or an effect size (e.g. loss of biomass, index relative to the population structure; see Fig. 4) as a function of a cumulative prevalence for this effect (e.g. proportion of a river, hydrogeographic basin) for a selected stress level (e.g. chemical stress, temperature stress). The map was created using GIMP 2.8.14 (www.gimp.org). Full size image

The Ecological Simulation Model.

To produce a conceptual working example of the prevalence plot, we simulated the response of a population of Daphnia magna exposed to stressors using a modified version of the DEB-IBM (Dynamic Energy Budget model coupled with an Individual Based Model) published by Martin et al.47 to represent the effect size. DEB theory48 is based on a mathematical description of the uptake and use of energy within an organism. Energy allocation can be affected by chemicals acting via various physiological modes of action (pMoA)49 or by environmental parameters such as temperature or food availability which can affect all the energy fluxes in an organism48 (Table 1). The DEB model used in this study is a simplified standard version but it is readily able to relate a stressor level to physiological effects, more complex implementations can handle more subtle effects such as a receptor-mediated effect [ref. 48, see p. 244]. An IBM is used to translate the changes in growth, reproduction, and survival to population endpoints pertinent to support risk assessment such as the population biomass or abundance or the population structure34,50.

Table 1 Examples of integration rules. Full size table

We demonstrate the integration of multiple stressors by varying three conditions in the environment, namely food availability, temperature, and degree of chemical stress. To combine their effects, we modified the DEB part of the DEB-IBM model to account for variability in temperature by adjusting DEB rates according to an Arrhenius relationship

with the initial value of the parameter, T the actual temperature (K), T ref the reference temperature (K), and T A the Arrhenius temperature (K) [ref. 48, see p. 17]. The DEB-IBM model already accounts for food availability47 and provides an implementation of equations for modelling chemical stress via different pMoAs41. We selected pMoA maintenance (i.e. increase of maintenance costs) as our example stressor.

For this exercise, we defined our simulation scenarios with a minimal level of complexity, only considering variations in temperature, food availability, and chemical stress. To illustrate the impact of multiple stressors we chose to simulate the D. magna population in two scenarios – one within the temperature tolerance range (Temperate scenario), and another approaching and exceeding the temperature tolerance (Tropical scenario). While not ecologically realistic, this artificial example provides a clear illustrative example of how a chemical stressor can impact the overall performance of populations that are already under pressure from other unrelated stressors. For simplicity, the scenarios are identical with exception of the temperature distribution.

The temperature distributions were based on the temperature recorded in the river Thames from 1974 to 2005 (from 2.0 °C to 26.5 °C) for the Temperate scenario and from the river Brahmaputra from 1979 to 1995 (from 19.6 °C to 34.0 °C) for the Tropical scenario55. The amount of food available in the two scenarios is driven by an arbitrary uniform distribution of the resource dilution rate implemented in the DEB-IBM we used47 (from 0.005 to 0.1 by 0.005 increments). To represent chemical exposure and impact on a test species, we applied chemical stress levels ranging from 0 to 1.5 in 0.1 increments. This corresponds to an expected reduction of the reproduction outputs compared to the control of respectively 0% to 95% in the OECD Daphnia magna reproduction test (assuming ad libitum food at 20 °C) [ref. 47, see SI]. In this illustrative example we have used an arbitrary stress level as described above. In practice, such stress levels can be derived from the predicted environmental concentrations in complex exposure models such as the ScenAT56. For further information on extrapolating from an external concentration to the chemical stress level, one can refer to Jager and Zimmer 201241.

The DEB-IBM simulation allowed the D. magna population to reach steady-state over the first 150 days of the simulation at which point a constant level of chemical stress was applied until the end of the simulation at 600 days. Outputs were recorded between day 300 and day 600. This allowed sufficient time for the model to reach its new steady-state while avoiding the recording of transient dynamics47. Monte-Carlo simulations were used to simulate the D. magna population at different combinations of food availability, temperature, and chemical stress level. Each combination consisted of one constant value of food availability, of temperature, and of chemical stress. Thus the simulations do not account for seasonal or other temporal effects. Each combination was simulated three times whilst sampling DEB model parameters to account for inter-individual variability (See Supporting Information). The parameters used for the DEB-IBM simulation are presented in Table S1. It is important to note that we did not account for correlations that may exist between the temperature level and the food availability in these conceptual environmental scenarios. Further, our choice to assess the system at steady-state is appropriate for some questions, but may not be suitable for others where the interest might be in system resilience or structure.

Visualising the Model Output in Prevalence Plots.

As an endpoint for our analysis we choose the population biomass calculated as the average sum of the adult individuals’ cubic length over 300 days47 relative to the water body volume simulated. In the prevalence plot, an endpoint can be based on the raw value compared to a baseline condition or as an effect size, thus relative to the baseline condition, using for our case study:

where “i” is the ith combination of environmental parameters. The prevalence plots are based on the frequency distribution of the population biomass for each stress level. This frequency distribution can represent the raw (Fig. 2) or the effect-size data (Fig. S1). The prevalence plots are then constructed by plotting the increasing cumulative sum of the frequency distribution for each range of stress level and for either the raw or the effect-size data. Plotting the cumulative probability on the y-axis is common in probabilistic risk assessment21 and environmental fate studies57, hence we followed the same convention.

Figure 2 Raw prevalence histogram. Prevalence distribution of the population biomass (mm3 L−1) for the Temperate (dark grey) and the Tropical (light grey) conceptual scenarios for the five ranges of chemical stress level. The arrows in the “Medium high” and “High” panels denote a prevalence of 76% and 100% respectively. Full size image

In our study, the cumulative prevalence represents the proportion of all water bodies in a specific location in the Temperate or Tropical scenario having a certain D. magna biomass or less. Because our interest is in the contribution of chemical stress to the overall biomass, each plotted line represents a given level of chemical stress. To compare different stressor levels we plot multiple lines. If the question asked concerns one of the other factors, here food availability or temperature, one can plot a line for each level of food availability or each temperature (Fig. 1). In practice it is best to define ranges for the factor being plotted to reduce the number of plotted lines to a manageable number. Thus, we decided to plot the contribution of five ranges of chemical stress (no-chemical 0, low 0.1–0.2, medium low 0.3–0.7, medium high 0.8–1.2, and high 1.3–1.5).