Development and Validation of a Mixture Toxicity Implementation in the Dynamic Energy Budget–Individual‐Based Model: Effects of Copper and Zinc on Daphnia magna Populations

Abstract

Mechanistic population models are gaining considerable interest in ecological risk assessment. The dynamic energy budget approach for toxicity (DEBtox) and the general unified threshold model for survival (GUTS) are wellestablished theoretical frameworks that describe sublethal and lethal effects of a chemical stressor, respectively. However, there have been limited applications of these models for mixtures of chemicals, especially to predict long-term effects on populations. We used DEBtox and GUTS in an individual-based model (IBM) framework to predict both single and combined effects of copper and zinc on Daphnia magna populations. The model was calibrated based on standard chronic toxicity test results with the single substances. A mixture toxicity implementation based on the general independent action model for mixtures was developed and validated with data from a population experiment with copper and zinc mixtures. Populationlevel effects of exposure to individual metals were accurately predicted by DEB-IBM. The DEB-IBM framework also allowed us to identify the potential mechanisms underlying these observations. Under independent action the DEB-IBM was able to predict the population dynamics observed in populations exposed to the single metals and their mixtures (R 2 > 65% in all treatments). Our modeling shows that it is possible to extrapolate from single-substance effects at the individual level to mixture toxicity effects at the population level, without the need for mixture toxicity data at the individual level from standard mixture toxicity tests. The application of such modeling techniques can increase the ecological realism in risk assessment.

Interactive Metal Mixture Toxicity to Daphnia magna Populations as an Emergent Property in a Dynamic Energy Budget Individual‐Based Model

“…Our identified pMoAs were not in agreement with those reported in previous studies on D. magna . However, these amounted to a relatively small number of studies that also used different approaches for parameter estimation (Cu and Zn: Ashauer & Jager, 2018 and Vlaeminck et al, 2021; Ni: Pereira et al, 2019). A hypothesis that might explain this deviation, and which has not been considered so far, is that pMoAs in a population context might be different from those in an individual context, for example, due to physiological adaptation of animals under long‐term exposure or mediated by crowding.…”

“…Pereira et al (2019) used an individual‐based model (IBM) based on the DEB theory (DEB‐IBM) to extrapolate Ni toxicity from individuals to populations at different temperatures, and correctly predicted the absence of effects on the population level when exposed to the median effective concentration for reproduction on the individual level. Vlaeminck et al (2021) applied the same approach to prediction of Cu–Zn mixture toxicity to D. magna populations from individual‐level, single‐metal toxicity.…”

“…Individual‐based models facilitate the use of mechanistic effect modeling with respect to ecological interactions (Martin et al, 2012; Pereira et al, 2019; Vlaeminck et al, 2021). Calibration of IBMs typically relies on numerical optimization algorithms such as approximate Bayesian computation (Van der Vaart et al, 2015).…”

Predicting Combined Effects of Chemical Stressors: Population‐Level Effects of Organic Chemical Mixtures with a Dynamic Energy Budget Individual‐Based Model

“…An IBM implementation based on the DEB theory (DEB-IBM) was used to predict population-level of mixtures to D. magna populations. Details on the DEB-IBM model structure can be found in the TRACE document provided by Vlaeminck et al (2021). The DEB model for D. magna is used as a foundation.…”

“…Mixture toxicity in DEB-IBM. To predict mixture toxicity effects, two approaches at the damage level were considered, as discussed by Vlaeminck et al (2021): IA and damage addition (DA). The IA model assumes that each of two compounds in a mixture exerts an effect that is independent of the other compound.…”