Providing reliable environmental quality standards (EQSs) is a challenging issue in environmental risk assessment (ERA). These EQSs are derived from toxicity endpoints estimated from dose-response models to identify and characterize the environmental hazard of chemical compounds released by human activities. These toxicity endpoints include the classicalx% effect/lethal concentrations at a specific timet(EC/LC(x,t)) and the new multiplication factors applied to environmental exposure profiles leading tox% effect reduction at a specific timet(MF(x,t), or denotedLP(x,t) by the EFSA). However, classical dose-response models used to estimate toxicity endpoints have some weaknesses, such as their dependency on observation time points, which are likely to differ between species (e.g., experiment duration). Furthermore, real-world exposure profiles are rarely constant over time, which makes the use of classical dose-response models difficult and may prevent the derivation ofMF(x,t). When dealing with survival or immobility toxicity test data, these issues can be overcome with the use of the general unified threshold model of survival (GUTS), a toxicokinetic-toxicodynamic (TKTD) model that provides an explicit framework to analyse both time- and concentration-dependent data sets as well as obtain a mechanistic derivation ofEC/LC(x,t) andMF(x,t) regardless ofxand at any timetof interest. In ERA, the assessment of a risk is inherently built upon probability distributions, such that the next critical step is to characterize the uncertainties of toxicity endpoints and, consequently, those of EQSs. With this perspective, we investigated the use of a Bayesian framework to obtain the uncertainties from the calibration process and to propagate them to model predictions, includingLC(x,t) andMF(x,t) derivations. We also explored the mathematical properties ofLC(x,t) andMF(x,t) as well as the impact of different experimental designs to provide some recommendations for a robust derivation of toxicity endpoints leading to reliable EQSs: avoid computingLC(x,t) andMF(x,t) for extremexvalues (0 or 100%), where uncertainty is maximal; computeMF(x,t) after a long period of time to take depuration time into account and test survival under pulses with different periods of time between them.

Raw data on the number of deaths at a country level generally indicate a spatially variable distribution of COVID-19 incidence. An important issue is whether this pattern is a consequence of environmental heterogeneities, such as the climatic conditions, during the course of the outbreak. Another fundamental issue is to understand the spatial spreading of COVID-19. To address these questions, we consider four candidate epidemiological models with varying complexity in terms of initial conditions, contact rates and non-local transmissions, and we fit them to French mortality data with a mixed probabilistic-ODE approach. Using statistical criteria, we select the model with non-local transmission corresponding to a diffusion on the graph of counties that depends on the geographic proximity, with time-dependent contact rate and spatially constant parameters. This suggests that in a geographically middle size centralized country such as France, once the epidemic is established, the effect of global processes such as restriction policies and sanitary measures overwhelms the effect of local factors. Additionally, this approach reveals the latent epidemiological dynamics including the local level of immunity, and allows us to evaluate the role of non-local interactions on the future spread of the disease.

Understanding pesticide impacts on populations of target/non‐target species and communities is a challenge to applied ecology. When predators that otherwise regulate pest densities ingest prey contaminated with pesticides, this can suppress predator populations by secondary poisoning. It is, however, unknown how species relationships and protocols of treatments (e.g. anticoagulant rodenticide [AR]) interact to affect pest regulation. To tackle this issue, we modelled a heuristic non‐spatialized system including montane water voles, specialist vole predators (stoats, weasels) and a generalist predator (red fox) which consumes voles, mustelids and other prey. By carrying out a broad‐range sensitivity analysis on poorly known toxicological parameters, we explored the impact of five farmer functional responses (defined by both AR quantity and threshold vole density above which AR spreading is prohibited) on predator–prey interactions, AR transfer across the trophic chain and population effects. Spreading AR to maintain low vole densities suppressed mustelid and fox populations, leading to vole population dynamics being entirely regulated by AR use. Such vole‐suppression treatment regimes inhibited predation ecosystem services and promoted pesticide dependence. Keeping vole density below acceptable bounds by spreading AR while maintaining sufficient voles as prey resources led to less AR being applied and extended periods without AR in the environment, benefiting predators while avoiding episodes with high vole density. This may meet farm production interests while minimizing the impact on mustelid and fox populations and associated ecosystem processes. These alternating phases of mustelids and farmer regulation highlight the consequence of intraguild relationship where mustelids may rescue foxes from poisoning. Both global and wide‐range sensitivity analysis illustrate the tightrope between predator–prey regulation and pesticide–pest regulation. Synthesis and applications. Different pesticide protocols lead to a rich variety of predator–prey dynamics in agro‐ecosystems. Our model reveals the need to maintain refuges with sufficient non‐poisoned voles for sustaining specialist mustelids, to conserve the predator community given the potential of secondary poisoning with rodenticides. We suggest that long periods without pesticide treatment are essential to maintain predator populations, and that practices of pesticides use that attempt to permanently suppress a pest over a large scale are counterproductive.

Field cultivation of Genetically Modified (GM) Bt-plants has a potential environmental risk toward non-target Lepidoptera (NTLs) larvae through the consumption of Bt-maize pollen. The Bt-maize Cry protein targeting Lepidoptera species detrimental to the crop is also expressed in pollen which is dispersed by wind and can thus reach habitats of NTLs. To better assess the current ecological risk of Bt-maize at landscape scales, we developed a spatially-explicit exposure-hazard model considering (i) the dynamics of pollen dispersal obtained by convolving GM plants emission with a dispersal kernel and (ii) a toxicokinetic-toxicodynamic (TKTD) model accounting for the impact of toxin ingestion on individual lethal effects. We simulated the model using real landscape observations in Catalonia (Spain): GM-maize locations, flowering dates, rainfall time series and larvae emergence date of the European peacock butterfly Aglais io. While in average, the additional mortality appears to be negligible, we show significant additional mortality at sub-population level, with for instance a mortality higher than 40% within the 10m for the 10% most Bt-sensitive individuals. Also, using Pareto optimality we capture the best trade-off between isolation distance and additional mortality: up to 50 m are required to significantly buffer Bt-pollen impact on NTLs survival at the individual level. Our study clears up the narrow line between diverging conclusions: those claiming no risk by only looking at the average regional effect of Bt on NTLs survival and those pointing out a significant threaten when considering the variability of individuals mortality.

The R-package rbioacc allows to analyse experimental data from bioaccumulation tests where organisms are exposed to a chemical (exposure) then put into clean media (depuration). Internal concentrations are measured over time during the experiment. rbioacc provides turnkey functions to visualise and analyse such data. Under a Bayesian framework, rbioacc fits a generic one-compartment toxicokinetic model built from the data. It provides TK parameter estimates (uptake and elimination rates) and standard bioaccumulation metrics. All parameter estimates, bioaccumulation metrics and predictions of internal concentrations are delivered with their uncertainty. Bioaccumulation metrics are provided in support of environmental risk assessment, in full compliance with regulatory requirements required to approve market release of chemical substances. This paper provides worked examples of the use of rbioacc from data collected through standard bioaccumulation tests, publicly available within the scientific literature. These examples constitute step-by-step user-guides to analyse any new data set, uploaded in the right format.