The research, led by Simon Hansul of the Institute of Mathematics at Universität Osnabrück together with colleagues from the Institute for Game and Wildlife Research in Spain and the European Food Safety Authority in Italy, focused on the Iberian painted frog, Discoglossus galganoi. This species was chosen partly because earlier experimental work had generated unusually rich toxicity data for two very different agrochemicals: 2,4-dichlorophenoxyacetic acid, a widely used herbicide better known as 2,4-D, and flupyradifurone, a systemic insecticide sold under the brand name Sivanto Prime. Because those experiments had been designed with mechanistic modelling in mind, they offered the team the best currently available foundation for testing whether a predictive model could be calibrated on single-substance data and then trusted to forecast mixture effects without ever having tested the mixture itself during calibration.

At the heart of the approach lies a class of models known as dynamic energy budget models, or DEB models. Rather than describing toxicity statistically, as a curve fit to observed mortality or growth reduction, DEB models treat the animal as a system of mass and energy fluxes. Food is ingested and assimilated, and the assimilated resources are then divided among the fundamental processes of life: somatic maintenance, growth, maturation and reproduction. Chemicals enter this machinery through what modellers call a physiological mode of action, or PMoA. A substance might reduce the efficiency with which food is converted into new tissue, increase the ongoing costs of keeping the body running, reduce assimilation itself, or shift the allocation of resources between growth and maturation. Each of these hypotheses produces a characteristically different signature in the life history of the animal, and that is precisely what makes the framework so powerful for diagnosis as well as prediction.

Amphibians, however, pose a unique challenge for such models because of metamorphosis. The team therefore built on an amphibian-specific extension called AmphiDEB-TKTD, which adds a metamorphic reserve compartment to the standard energy budget. As a tadpole approaches metamorphic climax, a defined fraction of its biomass is set aside in this reserve, feeding is progressively shut down, and the reserve is burned to fuel the dramatic reorganisation of the body that turns an aquatic larva into a terrestrial juvenile. Metamorphosis is, by definition, complete when the reserve is exhausted. This structure allowed the model to track growth, the timing of metamorphosis and body mass through the larval period and into the newly formed froglet, connecting endpoints that conventional toxicity testing treats as separate measurements.

The toxicological half of the model is deliberately minimal. External concentrations in the water are linked to an abstract quantity called scaled damage, which rises and falls with its own characteristic rate constant and is assumed to be proportional to the toxicologically relevant internal concentration, without requiring direct measurements of the chemical inside the animal. Damage is then translated into an effect on a specific energy flux through a log-logistic relationship with two parameters: a sensitivity, interpretable as the damage level that halves the affected flux, and a slope describing how sharply the response intensifies. For 2,4-D, exposure caused growth to stagnate at the highest sublethal concentration alongside a clear delay in metamorphosis. For flupyradifurone, growth was affected but the timing of metamorphosis was not, and was even slightly advanced. These contrasting fingerprints became the raw material for inferring mechanisms.

When the researchers fitted alternative modes of action to the single-substance data, the differences proved diagnostic. An increased-maintenance mode of action, like that proposed for 2,4-D, drains energy continuously across the entire growth curve and directly slows both growth and maturation, producing stunted larvae and delayed metamorphosis together. A decreased-growth-efficiency mode of action, by contrast, weakens energy conversion only indirectly and actually reduces maintenance costs as growth slows, so it produces shrinking larvae with little delay in development, which matched flupyradifurone. Candidate modes of action involving reduced assimilation or shifted allocation toward maturation were systematically ruled out because they predicted patterns, such as premature metamorphosis or severe shrinkage, that the data did not show. Crucially, a cross-validation against data collected at Gosner stage 46, the point at which the front legs emerge and the animal completes its transformation, confirmed the assignments: the mode of action inferred from larvae up to stage 42 correctly predicted what would happen in the froglet, with mean absolute prediction errors of roughly 22 percent for timing and 17 percent for mass in the case of 2,4-D.

With the mechanisms pinned down for each substance independently, the team turned to the real prize: predicting the binary mixture. Because the two pesticides operated through different modes of action, the model could apply their effects independently, multiplying the individual response factors within the energy budget equations. The experimental mixture data showed a striking dominance of 2,4-D, meaning that adding flupyradifurone on top of 2,4-D exposure changed essentially nothing about the observed response. The model anticipated this outcome accurately, and the reason follows directly from the biology of the two mechanisms. Flupyradifurone’s effect on growth efficiency fades in influence as individuals approach their maximum size and only indirectly touches maturation, whereas 2,4-D’s added maintenance costs propagate through the whole life history, swamping the contribution of the insecticide at the endpoints measured.

The authors are careful about the limits of what they have shown. The mixture validation involved only one pair of substances, and that pair conveniently acted through different modes of action. Whether the model performs equally well when two chemicals share the same mode of action, where the choice between independent action and damage-addition assumptions becomes critical, remains to be tested. The study also examined sublethal effects in a single species, and the model showed a tendency to under-predict reductions in mass at metamorphosis, which the authors attribute to simplifications in how the baseline model handles the energetics of metamorphic climax. Extending the framework to include lethal effects, additional species with contrasting life histories, and the interplay between chemical stress and environmental pressures such as pond drying and temperature are all flagged as necessary next steps before general claims about predictive capacity can be made.

Even with those caveats, the implications are considerable. Amphibians are currently not explicitly considered in chemical risk assessment; regulators assume that protection goals calibrated on fish, birds and mammals extend to frogs and salamanders. That assumption often holds for acute sensitivity, but it breaks down for some chemicals under long-term exposure, and it entirely misses metamorphosis, a physiological bottleneck during which mortality risk peaks and developmental timing can decide life or death. In ephemeral habitats like those D. galganoi inhabits, a pesticide-induced delay of even a few days in metamorphosis can mean that a pond dries before the tadpoles are ready to leave the water, converting a sublethal laboratory effect into outright mortality in the field. A model that can extrapolate from larval data to metamorph outcomes, and from single substances to mixtures, therefore promises to stretch scarce experimental resources much further and to reduce the need for animal testing, while also giving ecologists a mechanistic tool for thinking about how contamination reshapes amphibian populations.

The study also highlights a methodological lesson that reaches beyond amphibians. The choice of physiological mode of action turned out to matter enormously for extrapolating across life stages, and the authors found that data from later developmental stages carries disproportionate information for distinguishing between competing mechanisms. Standard quantitative goodness-of-fit metrics, which compare average errors, proved poorly suited to capturing whether a model reproduces the correct temporal dynamics, so the team leaned on careful visual evaluation of time series and suggest that future statistical developments, such as path signatures as summary statistics for time-ordered data, could help make mode-of-action selection more objective. Parameter identifiability posed its own challenges, with the damage rate constant and response slope far less well constrained than the sensitivity parameter, largely because effects appeared at only one test concentration an order of magnitude above the next. These are the growing pains of a young field, but the direction of travel is clear. By coupling the physics of energy flow through a developing organism to the dynamics of chemical damage, the AmphiDEB-TKTD framework turns ecotoxicology from a science of single-chemical snapshots into something closer to genuine forecasting, and it does so for a group of animals whose global decline has made better risk assessment an urgent necessity.

Subject of Research: Predictive mechanistic modelling of pesticide mixture toxicity to anuran larvae and metamorphs

Article Title: Predictive modelling of chemical mixture toxicity to amphibians in Discoglossus galganoi larvae and metamorphs

Article References: Predictive modelling of chemical mixture toxicity to amphibians in Discoglossus galganoi larvae and metamorphs. (n.d.). https://doi.org/10.3389/famrs.2026.1909160

Image Credits: AI Generated

DOI: 10.3389/famrs.2026.1909160

Keywords: amphibians, dynamic energy budget, TKTD modelling, mixture toxicity, pesticides, 2,4-D, flupyradifurone, Discoglossus galganoi, metamorphosis, physiological mode of action, environmental risk assessment, ecotoxicology