EC_x-SyS

Version 2021.09

EC_x-SyS is a model for tri-phasic concentration-response relationships where hormetic and subhormetic effects are observed at low concentrations. It expands the Stress Addition Model (SAM) by introducing system stress (SyS) which is negatively correlated with toxicant stress.

For details see: Liess, M., Henz, S., Knillmann, S. (2019). Predicting low-concentration effects of pesticides. Scientific Reports 9, 15248.
For more information contact: matthias.liess@ufz.de

Data

Concentration: Toxicant concentrations. The value highlighted in bold marks the concentration where the peak of the hormesis likely occurs. This can be changed via Concentration_Hormesis in the Parameters section.
Survival_{Tox observed:} Measured survival under toxicant stress without environmental stress.
Survival_{Tox+Env observed:} Measured survival under toxicant stress in the presence of an environmental stressor.
Survival_Tox+Sys: Modeled survival related to toxicant and system stress conditions without environmental stress.
Survival_Tox+Env+Sys: Modeled survival in the presence of toxicant, environmental and system stress.

Parameters

Concentration_Hormesis: The concentration where hormesis occurs. Must be greater than Concentration₂ and less than Concentration_Max. If the supplied data contain no hormesis then enter the concentration after which there is a sharp decline or "step" in the survival. See publication for details.
Survival_Max: The theoretical maximum value of the survival. Default is 100.
Beta p: The shape parameter p of the beta distribution. Default is 3.2.
Beta q: The shape parameter q of the beta distribution. Default is 3.2.

Plots

Plot Survival

The modeled concentration-response relationships. Dots mark the measured survival. Triangles indicate different lethal concentrations (LC₁, LC₅, LC₁₀ and LC₅₀₎. Move the mouse over the triangles or see table LC Values for details).

Survival_Tox+SyS: The modeled survival resulting from toxicant and system stress.
Survival_Tox: The modeled survival under toxicant stress alone (without SyS).
Survival LL5_Tox: A smoothed five-parameter log-logistic (LL5) curve fitted to the measured survival without environmental stress. Computed the same way as Survival_Tox in the SAM Calculator with both options Smooth Curve and Asymmetric Curve enabled. For details see the SAM documentation.
Survival_Tox+Env+SyS: The modeled survival resulting from toxicant, environmental and system stress.
Survival_Tox+Env: The modeled survival resulting from toxicant and environmental stress (without SyS).
Survival LL5_Tox+Env: A smoothed five-parameter log-logistic (LL5) curve fitted to the measured survival with environmental stress. Computed the same way as Survival_Tox+Env in the SAM Calculator with both options Smooth Curve and Asymmetric Curve enabled. For details see the SAM documentation.
(¹,²)

Plot Stress

The relationship between toxicant concentration and stress. Dots mark the values estimated from the measured survival. Lines show the fitted stress used to model the survival.

Stress_Tox+Sys: The sum of toxicant and system stress.
Stress_Tox: The stress induced by contamination with a toxicant.
System Stress_Tox: System stress under toxicant stress conditions without environmental stress.
Stress_Tox+Env+Sys: The total stress as a combination of toxicant, environmental and system stress.
Stress_Tox+Env: The combined toxicant and environmental stress.
Stress_Env: The stress induced by an environmental stressor.
System Stress_Tox+Env: System stress in the presence of toxicant and environmental stress.

Plot Values

LC Values

Lethal concentrations (LC₁, LC₅, LC₁₀ and LC₅₀₎ and corresponding survival. Displayed values are rounded to 6 decimal digits. However, you can copy the exact values to your clipboard. (¹,²)

Curve Points Survival

Toxicant concentrations and corresponding survival used to plot the curves. (¹)

Curve Points Stress

Toxicant concentrations and corresponding stress used to plot the curves.

Notes

¹) Please note that the curves Survival LL5_Tox and Survival LL5_Tox+Env are calculated in the same way as the survival in the SAM calculation file with the options Smooth Curve and Asymmetric Curve turned on. However, here survival values are scaled to {0..1} before the curve fitting algorithm is applied which might lead to slightly different results for curve points and LC-values.
²) LC-Values are approximated by a linear interpolation of all plot values.

References

Liess, M., Henz, S., Knillmann, S. (2019). Predicting low-concentration effects of pesticides. Scientific Reports 9, 15248.
For more information contact: matthias.liess@ufz.de