HUGIN ENCORE

A multi-level Bayesian network for predicting probabilistic risk of chemical mixtures

By: Jannicke Moe (Norwegian Institute for Water Research)
WWW: Anders L Madsen, Mark Christiansen (HUGIN EXPERT)

First version: June 2025
Latest update: May 2026

Chemical mixtures

Mixtures of chemical pollutants in the environment pose threats for aquatic ecosystems globally. There are endless possible combinations of substances in the environment, surpassing any available mixture toxicity data. Environmental risk assessment (ERA) for chemical mixture therefore requires pragmatic and robust computational approaches. Bayesian network (BN) methodology offers new opportunities for probabilistic risk characterisation for mixtures.

The two main mixture toxicity concepts are Concentration Addition (CA) and Independent Action (IA). CA typically predicts slightly higher mixture toxicity than IA, while a combination of CA and IA can give more accurate predictions. Traditionally, the CA method has been more commonly used because of the simpler calculation and the more protective outcome. However, the IA method can more easily be implemented in a probabilistic model.

Probabilistic risk calculation

The ENCORE Mixture BN Pilot is a multi-level probabilistic model developed for combining the CA and IA methods, implemented as an OOBN (Object-oriented Bayesian Network). The risk characterisation for a substance is based on a Risk Quotient (RQ), here calculated as the ratio RQ = PEC/HC5 ( = Predicted Environmental Concentration / Hazardous concentration to 5% of the species)

Environmental risk is here defined as the probability (P) of RQ exceeding a given threshold, P(RQ > Threshold_RQ).

A standard threshold for screening-level ERA is Threshold_RQ = 1. Here, the user can select alternative thresholds from 0.001 to 100). For example, Threshold_RQ = 0.1 can represent an early warning situation.

How to run the model

The BN can be run by setting evidence for input variables:

Further details about the approach can be found at the bottom of the page.

Inputs:

Scenarios

Spatial and temporal settings

Exceedance thresholds for Risk Quotients

Outputs:

Substance level

Fungicides

Probability of
RQ > Threshold_RQ

Herbicides

Probability of
RQ > Threshold_RQ

Insecticides

Probability of
RQ > Threshold_RQ

Outputs:

Group level

"Concentration Addition" (CA):

Probability of
SumRQ > Threshold_SumRQ

"Independent Action" (IA):

Probability of one or more
RQ > Threshold_RQ

Outputs:

Mixture level

"CA":

Probability of
SumSumRQ > Threshold_SumSumRQ

"IA":

Probability of one or more
RQ > Threshold_RQ

"CA + IA":

Probability of one or more
SumRQ > Threshold_SumRQ

Description of pilot study

Spatial extent: Belgium
Spatial resolution: River Basin District (5); Region (2)
Temporal extent: Year 2012
Spatial resolution: Month (12): Season (4)
Chemical substances: 15 pesticides (Chlorothalonil (chloro), Pyraclostrobin (pyracl), Tebuconazole (tebuco), Thiophanate-methyl (thioph), Trifloxystrobin (triflo), 2,4-Dichlorophenoxyacetic acid (24dich), Dicamba (dicamb), Dichlorprop (dichlo), Dimethenamid(-p) (dimete), Diuron (diuron), Glyphosate (glypho), MCPA (mcpaaa), Pendimethalin (pendim), Chlorpyrifos (chlorp), Dimethoate (dimeto))
Chemical groups: 3 groups (Fungicides, Herbicides, Insecticides)

Predicted environmental concentrations are obtained from the ENCORE fate model, a process-based model for simulating chemical concentrations in subcatchments of rivers across Europe.

Mixture risk calculation with the BN

The BN calculates environmental risk of chemical substances at three levels: substance, substance group, and mixture. The two calculation methods, "Concentration Addition" (CA) and "Independent Action" (IA), are generalisations of the concepts used in ecotoxicology.

  1. Substance level: calculation of risk for each substance
    Risk = P(RQ > Threshold_RQ)
  2. Group level: calculation of risk for multiple substances within a group
    CA:
    SumRQ = RQ1 + RQ2 + ... + RQn
    Risk = P(SumRQ > Threshold_SumRQ)
    IA:
    Risk = OR ((RQ1 > Threshold_RQ), (RQ2 > Threshold_RQ), ..., (RQn > Threshold_RQ))
    = 1 - (1-P(RQ1 > Threshold_RQ) × (1-P(RQ2 > Threshold_RQ) × ... × (1-P(RQn > Threshold_RQ))
  3. Mixture level: calculation of risk for multiple groups
    CA:
    SumSumRQ = SumRQ1 + SumRQ2 + SumRQ3
    Risk = P(SumSumRQ > Threshold_SumSumRQ)
    IA:
    Risk = OR ((RQ1 > Threshold_RQ), (RQ2 > Threshold_RQ), ..., (RQ15 > Threshold_RQ))
    CA + IA (=CA within groups + IA across groups):
    Risk = OR ((SumRQ1 > Threshold_SumRQ), (SumRQ2 > Threshold_SumRQ), (SumRQ3 > Threshold_SumRQ))

References
https://www.niva.no/en/projects/encore
Mentzel S, van Gils J, Grung M, Martins S, Verdonck F, Viaene KPJ, Vlaeminck K, Madsen AL, Snoj L, Šubelj G and Moe SJ (2026) Chemical exposure and risk in river basins: Bayesian integration of environmental model simulations and monitoring data. Frontiers in Freshwater Science 4:1789703. doi: 10.3389/ffwsc.2026.1789703
Moe et al. 2026. Chemical Mixtures in European River Basins: A Probabilistic Risk Model for Integrating Additive and Independent Effects. Poster presentation, SETAC Europe 2026.
https://setac.confex.com/setac/europe2026/meetingapp.cgi/Paper/32674

Acknowledgements
The project ENCORE (Environmental CO-exposure and Risk Estimation) is sponsored by the European Chemical Industry Council (CEFIC) as part of the Long Range Initiative (LRI) under project ECO-66 Next generation risk assessment methods supporting the identification of environmental co-exposures of potential concern.

Disclaimer
HUGIN EXPERT A/S takes no responsibility whatsoever for examples and information in examples published on this web site. ALL EXAMPLES ARE FOR DEMONSTRATION PURPOSES ONLY.