Package 'cvasi'

Description

The model is a mechanistic combined toxicokinetic-toxicodynamic (TK/TD) and growth model for algae. It follows the concept of a simplified algae model described in Rendal et al. (2023). The model simulates the development of algal biomass. The growth of the algae population is simulated on the basis of growth rates, which are, in contrast to the Weber model, independent on environmental conditions which are usually optimal in laboratory effect studies. The toxicodynamic sub-model describes the effects of growth-inhibiting substances through a corresponding reduction in the photosynthesis rate on the basis of either external or internal concentrations (depending on user choice of 'scaled' parameter setting).

Usage

Algae_Simple()

Value

an S4 object of type AlgaeSimpleScenario

State variables

The model has two state variables:

• A, Biomass (ug fresh wt/mL, cells/mL *10^4)

• Dw, only used if scaled = 1

Model parameters

• Growth model

  • mu_max, Maximum growth rate (d-1)

• Concentration response (Toxicodynamics)

  • EC_50, Effect concentration of 50% inhibition of growth rate (ug L-1)

  • b, slope of concentration effect curve at EC_50 (-)

  • dose_response, shape of the dose response curve (0 = logit, 1 = probit)

• External concentration (Toxicokinetics)

  • kD, dominant rate constant of toxicant in aquatic environments (d-1)

  • scaled, 0 = no internal scaled damage / 1 = yes (-)

Forcings

Simplified model without additional forcings for e.g. irradiation or temperature as implemented in Algae_Weber. A constant growth over time is assumed. In case that growth is time dependent, a forcing variable (f_growth) can be set. Forcing time-series are represented by data.frame objects consisting of two columns. The first for time and the second for a scaling factor of mu_max. The input format for all forcings is a list of the data frames. If f_growth is not set, a default scaling factor of 1 is used.

Parameter boundaries

Upper and lower parameter boundaries are set by default for each parameter. This, to avoid extreme values during calibration (particularly likelihood profiling)

Simulation output

Simulation results will contain the state variables biomass (A) and in case of scaled damage the damage concentration (Dw). The derivatives are also available as additional output.

• nout >= 2

  • dA, biomass derivative (µg)

  • dDw, damage concentration derivative (ug L-1)

References

Weber D, Schaeffer D, Dorgerloh M, Bruns E, Goerlitz G, Hammel K, Preuss TG and Ratte HT, 2012. Combination of a higher-tier flow-through system and population modeling to assess the effects of time-variable exposure of isoproturon on the green algae Desmodesmus subspictatus and Pseudokirchneriella subcapitata. Environmental Toxicology and Chemistry, 31, 899-908. doi:10.1002/etc.1765

See Also

Scenarios, Transferable

Other algae models: Algae-models, Algae_TKTD(), Algae_Weber()

Description

The model is a mechanistic combined toxicokinetic-toxicodynamic (TK/TD) and growth model for algae. The model simulates the development of algal biomass under laboratory and environmental conditions. The growth of the algae population is simulated on the basis of growth rates, which are dependent on environmental conditions (radiation, temperature and phosphorus). The model is a variant of the Algae_Weber() model (Weber 2012) as cited in EFSA TKTD opinion (2018). This Algae model, Algae_TKTD(), provides an additional possibility (probit) to simulate the dose-response curve and considers a scaled internal damage instead of the external concentration.

Usage

Algae_TKTD()

Value

an S4 object of type AlgaeTKTDScenario

State variables

The model has four state variables:

• A, Biomass (ug fresh wt/mL, cells/mL *10^4)

• Q, Mass of phosphorous internal (ug P/ug fresh wt)

• P, Mass of phosphorous external (ug P/L)

• Dw, Damage concentration (ug/L)

Model parameters

• Growth model

  • mu_max, Maximum growth rate (d-1)

  • Q_min, Minimum intracellular P (ug P/ug fresh wt)

  • Q_max, Maximum intracellular P (ug P/ug fresh wt)

  • v_max, Maximum P-uptake rate at non-limited growth (ug P/ug fresh wt/d)

  • k_s, Half-saturation constant for extracellular P (mg P/L)

  • m_max, Natural mortality rate (1/d)

  • I_opt, Optimum light intensity for growth (uE/m²/s)

  • T_opt, Optimum temperature for growth (°C)

  • T_max, Maximum temperature for growth (°C)

  • T_min, Minimum temperature for growth (°C)

• Concentration response (Toxicodynamics)

  • EC_50, Effect concentration of 50% inhibition of growth rate (ug L-1)

  • b, slope of concentration effect curve at EC_50 (-)

  • dose_resp, shape of the dose response curve (0 = logit, 1 = probit)

• External concentration (Toxicokinetics)

  • kD, dominant rate constant (d-1)

Forcings

Besides exposure events (Cw), the Algae model requires two environmental properties as time-series input: Irradiance (I, uE/m²/s) and temperature (T_act, deg C). Forcings time-series are represented by data.frame objects consisting of two columns. The first for time and the second for the environmental factor in question. The input format for all forcings is a list of the data frames.

Simulation output

Simulation results will contain the state variables Biomass (A), mass of internal phosphorous (Q), mass of external phosphorous (P) and the damage concentration (Dw). The derivatives are also available as additional output.

• nout >= 4

  • dA, biomass derivative (µg)

  • dQ, internal phosphorous derivative (mg P/ug fresh wt)

  • dP, external phosphorous derivative (mg P L-1)

  • dDw, damage concentration derivative (ug L-1)

References

Weber D, Schaeffer D, Dorgerloh M, Bruns E, Goerlitz G, Hammel K, Preuss TG and Ratte HT, 2012. Combination of a higher-tier flow-through system and population modeling to assess the effects of time-variable exposure of isoproturon on the green algae Desmodesmus subspictatus and Pseudokirchneriella subcapitata. Environmental Toxicology and Chemistry, 31, 899-908. doi:10.1002/etc.1765

See Also

Scenarios, Transferable

Other algae models: Algae-models, Algae_Simple(), Algae_Weber()

Description

The model is a mechanistic combined toxicokinetic-toxicodynamic (TK/TD) and growth model for algae. The model simulates the development of algal biomass under laboratory and environmental conditions and was developed by Weber et al. (2012) as cited in EFSA TKTD opinion (2018). The growth of the algae population is simulated on the basis of growth rates, which are dependent on environmental conditions (radiation, temperature and phosphorus). The toxicodynamic sub-model describes the effects of growth-inhibiting substances through a corresponding reduction in the photosynthesis rate on the basis of internal concentrations. (the implementation of Weber et al. (2012) is followed where units differ with EFSA)

Usage

Algae_Weber()

Value

an S4 object of type AlgaeWeberScenario

State variables

The model has four state variables:

• A, Biomass (ug fresh wt/mL, cells/mL *10^4)

• Q, Mass of phosphorous internal (mg P/L, or ug P/mL)

• P, Mass of phosphorous external (mg P/L, or ug P/mL)

• C, external substance concentration (ug/L)

Model parameters

• Growth model

  • mu_max, Maximum growth rate (d-1)

  • Q_min, Minimum intracellular P (ug P/ug fresh wt)

  • Q_max, Maximum intracellular P (ug P/ug fresh wt)

  • v_max, Maximum P-uptake rate at non-limited growth (ug P/ug fresh wt/d)

  • k_s, Half-saturation constant for extracellular P (mg P/L)

  • m_max, Natural mortality rate (1/d)

  • I_opt, Optimum light intensity for growth (uE/m²/s)

  • T_opt, Optimum temperature for growth (°C)

  • T_max, Maximum temperature for growth (°C)

  • T_min, Minimum temperature for growth (°C)

  • D, Dilution rate (1/d)

  • R_0, Influx concentration of P (mg P/L)

• Concentration response (Toxicodynamics)

  • EC_50, Effect concentration of 50% inhibition of growth rate (ug/L)

  • b, slope of concentration effect curve at EC_50 (-)

• External concentration (Toxicokinetics)

  • k, Degradation rate of toxicant in aquatic environments (d-1)

Forcings

Besides exposure events (C_in), the Algae model requires three environmental properties as time-series input: Irradiance (I, uE/m²/s) and temperature (T_act, deg C). Forcings time-series are represented by data.frame objects consisting of two columns. The first for time and the second for the environmental factor in question. The input format for all forcings is a list of the data frames.

Simulation output

Simulation results will contain the state variables Biomass (A), mass of internal phosphorous (Q), mass of external phosphorous (P) and the external concentration (C). The derivatives are also available as additional output.

• nout >= 4

  • dA, biomass derivative (µg)

  • dQ, internal phosphorous derivative (mg P/ug fresh wt)

  • dP, external phosphorous derivative (mg P L-1)

  • dC, external concentration derivative (ug L-1)

Parameter boundaries

Default values for parameter boundaries are set for all parameters by expert judgement, for calibration purposes. Values can be access from the object, and defaults overwritten.

References

Weber D, Schaeffer D, Dorgerloh M, Bruns E, Goerlitz G, Hammel K, Preuss TG and Ratte HT, 2012. Combination of a higher-tier flow-through system and population modeling to assess the effects of time-variable exposure of isoproturon on the green algae Desmodesmus subspictatus and Pseudokirchneriella subcapitata. Environmental Toxicology and Chemistry, 31, 899-908. doi:10.1002/etc.1765

EFSA PPR Panel (EFSA Panel on Plant Protection Products and their Residues), Ockleford C, Adriaanse P, Berny P, Brock T, Duquesne S, Grilli S, Hernandez-Jerez AF, Bennekou SH,Klein M, Kuhl T, Laskowski R, Machera K, Pelkonen O, Pieper S, Smith RH, Stemmer M, Sundh I, Tiktak A,Topping CJ, Wolterink G, Cedergreen N, Charles S, Focks A, Reed M, Arena M, Ippolito A, Byers H andTeodorovic I, 2018. Scientific Opinion on the state of the art of Toxicokinetic/Toxicodynamic (TKTD)effect models for regulatory risk assessment of pesticides for aquatic organisms. EFSA Journal, 16(8), 5377. doi:10.2903/j.efsa.2018.5377

See Also

Scenarios, Transferable

Other algae models: Algae-models, Algae_Simple(), Algae_TKTD()

Description

Overview of supported Algae models

Details

• Algae_Weber() by Weber et al. (2012)

• Algae_TKTD() based on Weber et al. (2012), but with scaled damage

• Algae_Simple() Simple growth model without additional forcing variables

Biomass transfer

Models supporting biomass transfer can be instructed to move a fixed amount of biomass to a new medium after a period of time. This feature replicates a procedure occurring in e.g. Lemna effect studies and may be necessary to recreate study results.

The biomass transfer feature assumes that always a fixed amount of biomass is transferred. Transfers can occur at any fixed point in time or in regular intervals. During a transfer, the biomass is reset to the transferred amount and additional compartments can be scaled 1:1 accordingly, to e.g. reflect the change in internal toxicant mass when biomass is modified. Transfer settings can be modified using set_transfer().

Any transfer time point must also be an output time point. If a transfer occurs, simulation results of that time point will report the model state before the transfer. Be aware that in order to use transfers at regular intervals, the simulation must start at time point zero.

References

Weber D, Schaeffer D, Dorgerloh M, Bruns E, Goerlitz G, Hammel K, Preuss TG and Ratte HT, 2012. Combination of a higher-tier flow-through system and population modeling to assess the effects of time-variable exposure of isoproturon on the green algae Desmodesmus subspictatus and Pseudokirchneriella subcapitata. Environmental Toxicology and Chemistry, 31, 899-908. doi:10.1002/etc.1765

EFSA Panel on Plant Protection Products and their Residues, 2018. Scientific opinion on the state of the art of Toxicokinetic/Toxicodynamic (TKTD) effect models for regulatory risk assessment of pesticides for aquatic organisms. EFSA journal 16:5377 doi:10.2903/j.efsa.2018.5377

See Also

Lemna-models, Transferable

Other algae models: Algae_Simple(), Algae_TKTD(), Algae_Weber()

Other scenarios: DEB-models, GUTS-RED-models, Lemna-models, Macrophyte-models, Myriophyllum-models, Scenarios, Transferable

Description

Species parameters were collected from the AddMyPet database entry on Americamysis bahia (Opossum shrimp). The exposure series consists of a constant exposure resulting in medium effects on length and reproduction.

Usage

americamysis

Format

An object of class DebAbj of length 1.

Source

https://www.bio.vu.nl/thb/deb/deblab/add_my_pet/entries_web/Americamysis_bahia/Americamysis_bahia_res.html

See Also

DEB_abj()

Description

Cache control simulations

Usage

cache_controls(x, windows, skipZeroExposure = FALSE, ...)

Arguments

Value

Modified scenario objects

Description

The function calibrate() performs the calibration (fitting) of model parameters to observed data. The data can originate from one or more experiments or trials. Experimental conditions, such as model parameters and exposure level, can differ between trials; fitting can be performed on all datasets at the same time.

Usage

calibrate(x, ...)

## S4 method for signature 'EffectScenario'
calibrate(
  x,
  par,
  data,
  endpoint = deprecated(),
  output,
  by,
  metric_fun = deprecated(),
  err_fun,
  as_tibble = deprecated(),
  catch_errors = deprecated(),
  verbose = TRUE,
  ...
)

## S4 method for signature 'CalibrationSet'
calibrate(x, par, output, err_fun, verbose = TRUE, ...)

## S4 method for signature 'list'
calibrate(
  x,
  par,
  endpoint = deprecated(),
  output,
  metric_fun = deprecated(),
  metric_total = deprecated(),
  err_fun,
  as_tibble = deprecated(),
  catch_errors = deprecated(),
  verbose = TRUE,
  ...
)

Arguments

Details

Fitting of model parameters can be performed in two ways:

1. A single scenario is fitted to a single dataset. The dataset must represent a time-series of an output variable of the model, e.g. observed biomass over time (effect data). The dataset can represent results of one or more experimental replicates under identical conditions.

2. One or more datasets of observed data are fitted each to a scenario which describes the experimental conditions during observation, such as exposure level and environmental properties. Each combination of dataset and scenario is represented by a calibration set. During fitting, all calibration sets are evaluated and a total error term is calculated over all observed and predicted values.

Observed data

Experimental, or effect, data must be supplied as a data.frame in long format with at least two columns: the first column contains numeric timestamps and the remaining columns must contain the observed quantity. The dataset must contain a column that which matches with the contents of parameter output.

As an example, the simulation result of Lemna_Schmitt model contains the output column biomass (BM), amongst others. To fit model parameters of said Lemna_Schmitt scenario based on observed biomass, the observed data must contain a column named BM which represents the observed biomass. A minimal observed dataset could look like this:

observed <- data.frame(time=c(0,  7, 14, 21),
                       BM=c( 12, 23, 37, 56))

Error function

By default, the total sum of squared errors is used as the target function which is minimized during fitting. A custom error function can be supplied by the user: The function must accept four vectorized arguments and return a numeric of length one, i.e. the total error value which gets minimized by calibrate().

Example of a custom error function which returns the sum of absolute errors:

my_absolute_error <- function(observed, predicted, weights, tags) {
  sum(abs(observed - predicted))
}

The arguments to the error function will contain all observed and predicted values, as well as any weights and tags that were defined by the calibration sets. As tags are optional, the fourth argument may be a list containing NULL values. The fourth argument can be used to pass additional information to the error function: For example, the tag may identify the study from where the data originates from and the error function could group and evaluate the data accordingly.

Value

A list of fitted parameters (as produced by stats::optim()) is returned.

Methods (by class)

• calibrate(EffectScenario): Fit single scenario using a dataset

• calibrate(CalibrationSet): Fit using a CalibrationSet

• calibrate(list): Fit using a list of caliset objects

Examples

library(dplyr)

# Get observed biomass during control experiment by Schmitt et al. (2013)
observed <- Schmitt2013 %>%
  filter(ID == "T0") %>%
  select(t, BM=obs)

# Create a scenario that represents conditions during experiment
scenario <- metsulfuron %>%
  set_param(c(k_phot_fix=TRUE, k_resp=0, Emax=1)) %>%
  set_init(c(BM=12)) %>%
  set_noexposure()

# Fit parameter 'k_phot_max' to observed biomass growth from experiment
calibrate(
  scenario,
  par=c(k_phot_max=1),
  data=observed,
  output="BM",
  method="Brent", # Brent is recommended for one-dimensional optimization
  lower=0,        # lower parameter boundary
  upper=0.5       # upper parameter boundary
) -> fit
fit$par

Description

A calibration set combines a scenario, observed data, and an optional weighting factor into one object. The calibration set is used to fit model parameters to observed data using calibrate().

Usage

caliset(scenario, data, weight = 1.0, tag = NULL)

Arguments

Details

A calibration set usually represents a single experiment or trial. Multiple experimental replicates can be combined into a single set, if model parameters are identical between trials. If model parameters were modified during a trial, e.g. a pump failure occurred or flow rates changed, this can be represented by using a scenario sequence instead of a basic scenario. Please refer to sequence() for details.

Weighting

An optional weighting factor can be used to scale the error term of a whole set or of individual data points when fitting parameters using e.g. calibrate().

The vector of weights must either be of length one or have the same length as the dataset. In the former case, the same weight will be applied to all values in the dataset. In the latter, individual weights are applied for each data point.

Value

caliset() returns a calibration set object

Examples

library(dplyr)

# Get observed biomass during control experiment by Schmitt et al. (2013)
observed <- Schmitt2013 %>%
  filter(ID == "T0") %>%
  select(t, BM=obs)

# Create a scenario that represents conditions during experiment
scenario <- metsulfuron %>%
  set_param(c(k_phot_fix=TRUE, k_resp=0, Emax=1)) %>%
  set_init(c(BM=12)) %>%
  set_noexposure()

# Create a calibration set
cs <- caliset(scenario, observed)

# Fit parameter 'k_phot_max' to observed biomass growth from experiment
calibrate(
  cs,
  par=c(k_phot_max=1),
  output="BM",
  method="Brent", # Brent is recommended for one-dimensional optimization
  lower=0,        # lower parameter boundary
  upper=0.5       # upper parameter boundary
) -> fit
fit$par

Description

Creates a DEB abj scenario. The abj model with type M acceleration is like model std, but acceleration occurs between birth and metamorphosis (V1-morph). Isomorphy is assumed before and after acceleration. Metamorphosis is before puberty and occurs at maturity E_Hj, which might or might not correspond with changes in morphology. The abj model is a one-parameter extension of model std (DEB Wiki).

Usage

DEB_abj()

Details

State variables

The following list describes the default names and standard units of the model's state variables:

• L, structural length (cm)

• E, energy reserve (J)

• H, energy invested in maturity (J)

• R, reproduction buffer (J)

• cV, internal concentration (C)

• Lmax, maximum structural length (cm)

All state variables are initialized with zero. See set_init() on how to set the initial state.

Parameters

The following model parameters are required:

• p_M, vol-spec somatic maintenance (J/d.cm^3)

• v, energy conductance (cm/d)

• k_J, maturity maint rate coefficient (1/d)

• p_Am, surface-area specific maximum assimilation rate (J/d.cm^2)

• kap, allocation fraction to soma (-)

• E_G, spec cost for structure (J/cm^3)

• f, scaled functional response (-)

• E_Hj, maturity at metamorphosis (J)

• E_Hp, maturity at puberty (J)

• kap_R, reproduction efficiency (-)

• L_b, structural length at birth (cm)

• L_j, structural length at metamorphosis (cm)

• ke, elimination rate constant (d-1)

• c0, no-effect concentration sub-lethal (C)

• cT, tolerance concentration (C)

• MoA, mode of action switch (-)

Mode of Actions

Any combination of the following mode of actions (MoA) can be considered by the model:

• MoA = 1: effect on feeding

• MoA = 2: effect on maintenance costs

• MoA = 4: effect on overhead costs for making an egg

• MoA = 8: hazard during oogenesis

• MoA = 16: energy conductance

To activate more than one MoA, simply add up the corresponding codes. To disable all MoAs, set the parameter to zero. See also set_mode_of_action().

Effects

The state variables L (structural length) and R (reproduction buffer) are set as effect endpoints by default. All state variables are available as potential endpoints. The list of considered endpoints can be modified by using set_endpoints().

To calculate effects, each DEB scenario is simulated twice: One simulation which considers exposure to a toxicant and one simulation without exposure, i.e. a control. See also effect().

Value

an S4 object of type DebAbj

See Also

Other DEB models: DEB-models, DEBtox()

Examples

# Create an abj scenario from scratch and simulate it
DEB_abj() %>%
  set_init(c(L=0.02,E=0.1,H=0.01)) %>%
  set_param(c(p_M=3000,v=0.02,k_J=0.6,p_Am=300,kap=0.9,E_G=4000,f=1,
              E_Hj=0.05,E_Hp=0.3,kap_R=0.9,ke=1,c0=0,cT=1,L_b=0.02,
              L_j=0.04,MoA=0)) %>%
  set_exposure(no_exposure()) %>%
  set_times(0:10) %>%
  simulate()

# Print information about sample scenario 'americamysis'
americamysis

# Simulate 'americamysis' scenario
americamysis %>% simulate()

Description

Supported models:

• DEB_abj

• DEBtox

See Also

Other DEB models: DEB_abj(), DEBtox()

Other scenarios: Algae-models, GUTS-RED-models, Lemna-models, Macrophyte-models, Myriophyllum-models, Scenarios, Transferable

Description

Creates a DEBtox scenario as described by Jager (2020). It represents a simplified DEBtox model based on DEBkiss. In the BYOM application [link], this model is referred to as DEBtox 2019, version 4.7. It supports an optional feature of the ERA special model variant, which can consider a reference Lm parameter to compare results of multiple datasets.

Usage

DEBtox()

DEB_Daphnia()

Details

State variables

The following list describes the names and units of the model's state variables:

• D, scaled damage ([C])

• L, body length (mm)

• R, cumulative reproduction (-)

• S, survival probability (-)

State variables D, L, and R are initialized with zero. Variable S is initialized with one (1.0). See set_init() on how to set the initial state manually.

Parameters

The following parameters are required:

• General

  • L0, body length at start (mm)

  • Lp, body length at puberty (mm)

  • Lm, maximum body length (mm)

  • rB, von Bertalanffy growth rate constant (1/d)

  • Rm, maximum reproduction rate (#/d)

  • f, scaled functional response (-)

  • hb, background hazard rate (d-1)

  • a, Weibull background hazard coefficient (-). Set to 1 to disable.

• Extra parameters

  • Lf, body length at half-saturation feeding (mm)

  • Lj, body length at which acceleration stops (mm)

  • Tlag, lag time for start development (d)

• TK/TD parameters

  • kd, dominant rate constant (d-1)

  • zb, effect threshold energy budget ([C])

  • bb, effect strength energy-budget effects (1/[C])

  • zs, effect threshold survival ([C])

  • bs, effect strength survival (1/([C] d))

• Other parameters (formerly globals in BYOM)

  • FBV, dry weight egg as fraction of structural body weight (-)

  • KRV, part. coeff. repro buffer and structure (kg/kg) (for losses with reproduction)

  • kap, approximation for kappa (for starvation response)

  • yP, product of yVA and yAV (for starvation response)

  • Lm_ref, optional reference max length for scaling rate constants (mm). Set to zero to disable the reference length. Disabled by default.

  • len, a switch to control body length dynamics: 1 organism can shrink, 2 organism cannot shrink. Default value is 1.

  • Tbp, optional brood-pouch delay (d). Set to NA or zero to disable. Default value is 0.

  • MoA, mode of action switches (-). Default value is 0.

  • FB, feedback on damage dynamics switches (-). Default value is 0.

A reference Lm_ref is needed to properly compare different data sets, or when calibrating on more than one data set. If Lm differs, one would not want to have different rate constants at the same length.

Mode of Action

Any combination of the following mode of actions (MoA) can be considered by the model:

• MoA = 1: assimilation/feeding

• MoA = 2: costs for maintenance

• MoA = 4: costs for growth and reproduction

• MoA = 8: costs for reproduction

• MoA = 16: hazard for reproduction

To activate more than one mode of action, simply add up the corresponding codes and set parameter MoA to the desired value. To disable all mode of actions, set parameter MoA to zero. See also set_moa().

As an example, to consider effects on feeding and maintenance, set the mode of action to three (3):

DEBtox() %>% set_param(c(MoA=3))

Feedbacks

Any combination of the following damage feedbacks can be considered by the model:

• 1: surf:vol scaling uptake rate

• 2: surf:vol scaling elimination rate

• 4: growth dilution

• 8: losses with reproduction

To activate more than one feedback, simply add up the corresponding codes. To disable all feedbacks, set the parameter to zero.

Effects

The state variables L (body length), R (cumulative reproduction), and S (survival probability) are set as effect endpoints by default. All state variables are available as potential endpoints. The list of considered endpoints can be modified by using set_endpoints().

To calculate effects, each DEBtox scenario is simulated twice: One simulation which considers exposure to a toxicant and one simulation without exposure, i.e. a control. See also effect().

Output variables

The following intermediary model variables can be added to the model output on demand. Simply set the optional parameter nout to the required output level and pass it to simulate().

• nout >= 1: f, actual scaled response

• nout >= 2: fR, actual f considering starvation

• nout >= 3: kd, actual kd

• nout >= 4: s, stress level

• nout >= 5: h, hazard rate

• nout >= 6: sA, stress factor on assimilation/feeding

• nout >= 7: sM, stress factor on maintenance

• nout >= 8: sG, stress factor on growth costs

• nout >= 9: sR, stress factor on reproduction costs

• nout >= 10: sH, stress factor on hazard to reproduction

• nout >= 11: xu, damage feedback factor for surf:vol scaling uptake rate

• nout >= 12: xe, damage feedback factor for surf:vol scaling elimination rate

• nout >= 13: xG, damage feedback factor for growth dilution

• nout >= 14: xR, damage feedback factor for losses with repro

Model history and changes

• cvasi v1.0.0

  • The DEB_Daphnia() model implemented BYOM's DEBtox 2019 model version 4.5

• cvasi v1.2.0

  • The model equations were updated to conform with BYOM's DEBtox 2019 version 4.7. This introduced a new model parameter a, the Weibull background hazard coefficient, and limited the maximum hazard rate to 99% per hour.

  • The scenario constructor was renamed to DEBtox().

  • Additional intermediary model variables available as optional simulation output

Value

an S4 object of type DebTox

Functions

• DEB_Daphnia(): Deprecated model variant of DEBtox()

References

Jager T, 2020: Revisiting simplified DEBtox models for analysing ecotoxicity data. Ecol Model 416. doi:10.1016/j.ecolmodel.2019.108904

Romoli et al., 2024: Environmental risk assessment with energy budget models: a comparison between two models of different complexity. Environ Toxicol Chem 43(2):440-449. doi:10.1002/etc.5795

See Also

Other DEB models: DEB-models, DEB_abj()

Description

Species and substance parameters were collected from test runs of the original DEBtox Daphnia model.

Usage

dmagna

Format

An object of class DebTox of length 1.

See Also

DEBtox()

Description

Returns a data.frame with points on the dose response curve for the given effect scenario.

Usage

dose_response(
  scenario,
  range = c(1, 99),
  n = 20,
  strategy = c("exponential", "decadic", "vanilla"),
  verbose = FALSE,
  ...
)

Arguments

Details

Derives a dose response curve from a scenario. The result will cover the requested range of effect levels. The tested multiplication factors can be chosen by different strategies, i.e. a vanilla approach using a fixed set of factors, or decadic and exponential approaches employing logarithmic and exponential factor scaling, respectively.

Value

data.frame with two columns, i.e. factor and effect

Examples

# basic dose response curve
minnow_sd %>% dose_response()

# modify the minimum number of points on the curve
minnow_sd %>% dose_response(n=10)

# select a subset of the effect range
minnow_sd %>% dose_response(range=c(10,20))

# use an alternative strategy for the selection of multiplication factors
minnow_sd %>% dose_response(strategy="decadic")

# provide additional output how multiplication factors were selected
minnow_sd %>% dose_response(verbose=TRUE)

Description

Derives the effect level due to toxicant exposure in the supplied scenarios. Either relative to a control scenario or derived directly from model endpoints, depending on model type. For scenarios with moving exposure windows, the maximum effect is returned.

Usage

effect(x, factor = 1, max_only = TRUE, ep_only = FALSE, marginal_effect, ...)

Arguments

Details

By default, only the maximum effect in all moving exposure windows will be returned. If argument max_only=FALSE is set, the returned table will be converted to long-format and will contain effect levels for each assessed exposure window.

Output formatting

Start and end time of exposure windows can be disabled by setting ep_only=TRUE. Effect levels smaller than a certain threshold can be automatically set to zero (0.0) to avoid spurious effect levels introduced by numerical errors. Set marginal_effect to an adequate value less than 1%.

Computational efficiency

Calculations can be sped up by providing a data.frame of pre-calculated control scenarios for each assessed time window. As control scenarios are by definition independent of any exposure multiplication factor, they can be reused for repeated calculations, e.g. to derive effect profiles or dose-response relationships.

Value

a tibble, by default containing scenarios, effect levels, and the exposure window where the maximum effect level occurred. The number of columns depends on the enabled effect endpoints and function arguments.

By default, the first column, named scenarios, contains the original scenario objects that were the basis of the calculation. For each effect endpoint, it will be followed by one column with the maximum effect level and two columns containing start and end time of the associated exposure window. If exposure windows are disabled, the columns will just contain the start and end time of the simulation. The effect level column will have the name of the effect endpoint, start and end time will additionally have the suffixes .dat.start and .dat.end, respectively.

Description

Derives one or more EPx/LPx values for the supplied effect scenarios, i.e. it calculates the multiplication factors of an exposure profile that cause x% of effect. Scenarios are processed in parallel, if possible.

Usage

epx(
  scenarios,
  level = c(10, 50),
  effect_tolerance = 0.001,
  factor_cutoff = NA,
  min_factor = 1e-30,
  max_factor = 1e+30,
  verbose = FALSE,
  ep_only = FALSE,
  long_format = FALSE,
  ...
)

Arguments

Details

To estimate EPx values, a binary search on multiplication factors is conducted. The algorithm can achieve arbitrary precision in terms of effects. The same approach is implemented in the morse package in the MFx() function. Convergence is often achieved in less than 10 iterations per effect level and endpoint.

Internally, a knowledge base of all tried factors and resulting effect levels is kept to speed up convergence if more than one endpoint or effect level was requested. The algorithm will automatically sweep the range of multiplication factors as needed but hard cutoff values are implemented to avoid infinite loops; the algorithm will halt with an error message if tried factors are smaller than 1e-30 or greater than 1e30.

Numerical precision

The precision of reported EPx values is controlled by the argument effect_tolerance and is given as the upper absolute error threshold of effects that is deemed acceptable. The default value of 0.001 ensures that a derived EPx will result in an effect of x% ± 0.1. Decreasing the effect_tolerance will result in additional model iterations and longer runtime. Setting an extremely small tolerance value may lead to a breakdown of the algorithm due to the occurrence of extremely small, quasi-random numerical errors in simulation results.

Value

The original tibble with additional columns named after the request effect levels, e.g. L.EP10. If no tibble was used as argument, then a new one is created. The first column scenario will contain the supplied EffectScenario objects.

Examples

minnow_sd %>% epx()
minnow_sd %>% epx(level=c(10,23,42))

# displays infos about tested multiplication factors
minnow_sd %>% epx(verbose=TRUE)

# return results as a table in wide format
minnow_sd %>% epx(long_format=TRUE)

Description

Calls epx() to calculate the EPx value (i.e. the multiplication factors of an exposure profile that cause x% of effect) for moving windows with length window_length that move timesteps defined by window_interval.

Usage

epx_mtw(
  x,
  level = c(10, 50),
  factor_cutoff = 1000,
  window_length = 7,
  window_interval = 1,
  ...
)

Arguments

Value

a tibble with five columns

• window.start

• window.end

• endpoint

• level

• EPx

Examples

metsulfuron %>%
  set_window(length=7, interval=1) %>%
  epx_mtw()

Description

The function is aimed at getting an idea of how the parameter space of a model behaves, so that parameter identifiability problems and correlations between parameters can be explored. Therefore, the function samples a large number of parameter sets by randomly drawing from each parameter's 95% confidence interval (generated by lik_profile()). It then checks how many of the parameter sets are within acceptable limits by comparing the likelihood ratio of a parameter set vs. the original parameter set against a chi-square distribution as degrees of freedom (df) the total number of profile parameters (outer rim) or one df (inner rim). If needed, the function resamples until at least nr_accept parameters sets are within the inner rim

Usage

explore_space(
  x,
  par,
  res,
  output,
  sample_size = 1000,
  max_runs = 30,
  nr_accept = 100,
  sample_factor = 1.2
)

Arguments

Value

a list containing a plot to explore the parameter space, and the data.frame supporting it

Examples

library(dplyr)
# Example with Lemna model - physiological params
# Before applying the function, a model needs to be calibrated and its parameters profiled
# Inputs for likelihood profiling

# exposure - control run
exp <- Schmitt2013 %>%
  filter(ID == "T0") %>%
  select(time=t, conc)

# observations - control run
obs <- Schmitt2013 %>%
  filter(ID == "T0") %>%
  select(t, BM=obs)

# parameters after calibration
params <- c(
  k_phot_max = 5.663571,
  k_resp = 1.938689,
  Topt = 26.7
)

# set parameter boundaries (if different from defaults)
bounds <- list(
  k_resp = list(0, 10),
  k_phot_max = list(0, 30),
  Topt = list(20, 30)
)

# update metsulfuron
myscenario <- metsulfuron %>%
  set_init(c(BM = 5, E = 1, M_int = 0)) %>%
  set_param(list(
    k_0 = 5E-5,
    a_k = 0.25,
    BM50 = 17600,
    mass_per_frond = 0.1
  )) %>%
  set_exposure(exp) %>%
  set_param(params) %>%
  set_bounds(bounds)

# Likelihood profiling
res <- lik_profile(
  x = myscenario,
  data = obs,
  output = "BM",
  par = params,
  refit = FALSE,
  type = "fine",
  method = "Brent"
)
# plot
plot_lik_profile(res)

# parameter space explorer
set.seed(1) # for reproducibility
res_space <- explore_space(
  x = list(caliset(myscenario, obs)),
  par = params,
  res = res,
  output = "BM",
  sample_size = 1000,
  max_runs = 20,
  nr_accept = 100)

plot_param_space(res_space)

Description

Creates an object that encapsulates an exposure time-series with its metadata, such as formatted datetime strings and file name where the series was loaded from. no_exposure() is shorthand to create a time-series of constant zero exposure.

Usage

ExposureSeries(series, dates, file, meta, context)

Arguments

Value

an S4 object of type ExposureSeries

Slots

dates

original time points of time-series, e.g. time stamps of the form ⁠2000-01-01 12:00⁠

file

character, file name where data originates from, may be empty

meta

list, contains metadata

context

list, contains contextual metadata, such as project ids

series

data.frame containing the actual time-series

See Also

no_exposure()

Description

A mechanistic combined toxicokinetic-toxicodynamic (TK/TD) and growth model for the aquatic macrophytes Lemna spp. as published by Klein et al. (2021).

Usage

focusd1

Format

An object of class LemnaSetacScenario of length 1.

Details

The scenario will simulate a period of 365 days, a start population of 80 g/m² dry weight, variable environmental conditions, and a complex, time-varying exposure pattern.

The scenario setup was published by Hommen et al. (2015). Exposure pattern and substance specific parameters are of exemplary character and represent the herbicide metsulfuron-methyl. The parameters were derived by Schmitt et al. (2013) based on literature data.

References

Hommen U., Schmitt W., Heine S., Brock Theo CM., Duquesne S., Manson P., Meregalli G., Ochoa-Acuña H., van Vliet P., Arts G., 2015: How TK-TD and Population Models for Aquatic Macrophytes Could Support the Risk Assessment for Plant Protection Products. Integr Environ Assess Manag 12(1), pp. 82-95. doi:10.1002/ieam.1715

Klein J., Cedergreen N., Heine S., Reichenberger S., Rendal C., Schmitt W., Hommen U., 2021: Refined description of the Lemna TKTD growth model based on Schmitt et al. (2013) - equation system and default parameters. Report of the working group Lemna of the SETAC Europe Interest Group Effect Modeling. Version 1, uploaded on 22. Sept. 2021. https://www.setac.org/group/effect-modeling.html

Schmitt W., Bruns E., Dollinger M., Sowig P., 2013: Mechanistic TK/TD-model simulating the effect of growth inhibitors on Lemna populations. Ecol Model 255, pp. 1-10. doi:10.1016/j.ecolmodel.2013.01.017

See Also

Lemna-models

Examples

# Simulate the example scenario
focusd1 %>% simulate()

Description

Generic to calculate effects for a particular scenario

Usage

fx(scenario, ...)

## S4 method for signature 'ANY'
fx(scenario, ...)

## S4 method for signature 'GutsRedSd'
fx(scenario, ...)

## S4 method for signature 'GutsRedIt'
fx(scenario, ...)

## S4 method for signature 'Lemna'
fx(scenario, ...)

## S4 method for signature 'Myriophyllum'
fx(scenario, ...)

## S4 method for signature 'Algae'
fx(scenario, ...)

Arguments

Value

numeric named vector

Methods (by class)

• fx(ANY): Use state variables at end of simulation

• fx(GutsRedSd): Effect at end of simulation of GUTS-RED-models

• fx(GutsRedIt): Effect at end of simulation of GUTS-RED-models

• fx(Lemna): Effect at end of simulation of Lemna-models

• fx(Myriophyllum): Effect at end of simulation of Macrophyte-models

• fx(Algae): Effect at end of simulation of Algae-models

Description

Returns the unique model name that is associated with a scenario, e.g. GUTS-RED-IT. The function supports vectorized arguments.

Usage

get_model(x)

Arguments

Value

vector of character

Examples

# returns `GUTS-RED-IT`
get_model(minnow_it)

Description

Returns the user-defined, custom tag of a scenario, if available. Tags can be helpful to quickly distinguish scenarios of the same model type. The function supports vectorized inputs.

Usage

get_tag(x)

Arguments

Value

vector of character

See Also

set_tag()

Examples

# returns `fathead minnow`
get_tag(minnow_it)

# update or set a tag
myscenario <- minnow_it %>% set_tag("My Custom Tag")
# returns `My Custom Tag`
get_tag(myscenario)

Description

Reduced General Unified Threshold models of Survival (GUTS) with individual tolerance (IT).

Usage

GUTS_RED_IT(param, init)

Arguments

Value

an S4 object of type GutsRedIt

Simulation output

The return value of simulate() will contain values for the state variables, as well as an additional column S which represents the survival probability for each time point. S is calculated as described in EFSA (2018) as S = (1- F(t)). The background hazard rate hb is already considered in state variable H and therefore does not occur as an additional term to derive S.

State variables

The following list describes the default names and standard units of GUTS-RED state variables:

• D, scaled damage (conc)

• H, cumulative hazard (-)

The state variables are initialized with zero by default.

IT model parameters

• kd, dominant rate constant (time^-1)

• hb, background hazard rate (time^-1)

• alpha, median of thresholds (conc)

• beta, shape parameter (-)

Effects

The effect endpoint L (lethality) is available for GUTS-RED models. A value of zero (0.0) denotes no effect on organism survival. A value of one (1.0) denotes a lethality rate of 100%, i.e. no survivors.

The survival probability S is available in the return value of simulate().

References

EFSA PPR Panel (EFSA Panel on Plant Protection Products and their Residues), Ockleford C, Adriaanse P, Berny P, et al., 2018: Scientific Opinion on the state of the art of Toxicokinetic/Toxicodynamic (TKTD) effect models for regulatory risk assessment of pesticides for aquatic organisms. EFSA Journal 2018; 16(8):5377, 188 pp. doi:10.2903/j.efsa.2018.5377

See Also

Other GUTS-RED models: GUTS-RED-models, GUTS_RED_SD()

Description

Reduced General Unified Threshold models of Survival (GUTS) with stochastic death (SD).

Usage

GUTS_RED_SD(param, init)

Arguments

Value

an S4 object of type GutsRedSd

Simulation output

The return value of simulate() will contain values for the state variables, as well as an additional column S which represents the survival probability for each time point. S is calculated as described in EFSA (2018) as S = exp(-H). The background hazard rate hb is already considered in state variable H and therefore does not occur as an additional term to derive S.

State variables

The following list describes the default names and standard units of GUTS-RED state variables:

• D, scaled damage (conc)

• H, cumulative hazard (-)

The state variables are initialized with zero by default.

SD model parameters

• kd, dominant rate constant (time^-1)

• hb, background hazard rate (time^-1)

• z, threshold for effects (conc)

• kk, killing rate constant (time^-1)

Effects

The effect endpoint L (lethality) is available for GUTS-RED models. A value of zero (0.0) denotes no effect on organism survival. A value of one (1.0) denotes a lethality rate of 100%, i.e. no survivors.

The survival probability S is available in the return value of simulate().

References

EFSA PPR Panel (EFSA Panel on Plant Protection Products and their Residues), Ockleford C, Adriaanse P, Berny P, et al., 2018: Scientific Opinion on the state of the art of Toxicokinetic/Toxicodynamic (TKTD) effect models for regulatory risk assessment of pesticides for aquatic organisms. EFSA Journal 2018; 16(8):5377, 188 pp. doi:10.2903/j.efsa.2018.5377

See Also

Other GUTS-RED models: GUTS-RED-models, GUTS_RED_IT()

Description

Reduced General Unified Threshold models of Survival (GUTS) with stochastic death (SD) and individual tolerance (IT)

Details

The TKTD models GUTS-RED-SD and GUTS-RED-IT were described by EFSA (2018). GUTS-RED models assume a one-compartment model which directly links external concentration to the scaled damage. The scaled damage is given in units of concentration, equal to the units of measurement in the external medium, e.g. ug/L. The damage dynamics is connected to an individual hazard state variable, resulting in simulated mortality when an internal damage threshold is exceeded. The death mechanisms stochastic death (SD) and individual threshold (IT) are extreme cases of the GUTS theory.

For SD models, the threshold parameter for lethal effects is fixed and identical for all individuals of a group, meaning that the variance of the threshold values is zero. Hence, the killing rate relates the probability of a mortality event in proportion to the scaled damage. For IT models, the thresholds for effects are distributed among individuals of a group. Mortality of an individual follows immediately once the individual's tolerance is exceeded. Meaning in model terms that the killing rate is set to infinity (EFSA 2018).

State variables

The following list describes the default names and standard units of GUTS-RED state variables:

• D, scaled damage (conc)

• H, cumulative hazard (-)

The state variables are initialized with zero by default.

SD model parameters

• kd, dominant rate constant (time^-1)

• hb, background hazard rate (time^-1)

• z, threshold for effects (conc)

• kk, killing rate constant (time^-1)

IT model parameters

• kd, dominant rate constant (time^-1)

• hb, background hazard rate (time^-1)

• alpha, median of thresholds (conc)

• beta, shape parameter (-)

Effects

The effect endpoint L (lethality) is available for GUTS-RED models. A value of zero (0.0) denotes no effect on organism survival. A value of one (1.0) denotes a lethality rate of 100%, i.e. no survivors.

The survival probability S is available in the return value of simulate().

References

EFSA PPR Panel (EFSA Panel on Plant Protection Products and their Residues), Ockleford C, Adriaanse P, Berny P, et al., 2018: Scientific Opinion on the state of the art of Toxicokinetic/Toxicodynamic (TKTD) effect models for regulatory risk assessment of pesticides for aquatic organisms. EFSA Journal 2018; 16(8):5377, 188 pp. doi:10.2903/j.efsa.2018.5377

See Also

Other GUTS-RED models: GUTS_RED_IT(), GUTS_RED_SD()

Other scenarios: Algae-models, DEB-models, Lemna-models, Macrophyte-models, Myriophyllum-models, Scenarios, Transferable

Description

Read several exposure profiles at their corresponding paths at 'pathtofiles'. The exposure profiles are read for each file that are character seperated text files in a table format. The expected table format includes the columns time and conc for the concentration at each timestep.

Usage

import_exposure_text(pathtofiles, profileNames = NA, sep = "\t")

Arguments

Value

list of exposure profiles

Description

Read all TOXSWA files within a SWASH project directory.

Usage

import_swash(swash_dir)

Arguments

Value

a list of exposure profiles each with two columns (time and concentration)

Description

Read several TOXSWA exposure profiles from out-files at their corresponding paths given by'pathtofiles'.

Usage

import_toxswa(pathtofiles, profileNames = NA)

Arguments

Value

list of exposure profiles each with two columns (time and concentration)

Description

Test if argument is a DEB model

Usage

is_DEB(x)

Arguments

Value

vector of logical values

Description

Test if argument is a GUTS model

Usage

is_GUTS(x)

is_GUTS_IT(x)

is_GUTS_SD(x)

Arguments

Value

vector of logical values

Functions

• is_GUTS_IT(): Test if argument is a GUTS-IT model

• is_GUTS_SD(): Test if argument is a GUTS-IT model

Examples

# returns `TRUE`
is_GUTS(minnow_it)
is_GUTS(GUTS_RED_IT())

# returns `c(TRUE,TRUE,TRUE)`
is_GUTS(c(minnow_it, minnow_it, minnow_it))

# returns `FALSE`
is_GUTS_SD(minnow_it)

Description

Also returns TRUE for LemnaThreshold models

Usage

is_Lemna(x)

Arguments

Value

vector of logical values

See Also

is_LemnaThreshold()

Description

Test if argument is a LemnaThreshold model

Usage

is_LemnaThreshold(x)

Arguments

Value

vector of logical values

See Also

is_Lemna()

Description

Supports vectorized arguments.

Usage

is_scenario(x)

Arguments

Value

vector of logical values

Examples

# returns `TRUE`
is_scenario(minnow_it)

# returns `FALSE`
is_scenario(list())

Description

The model is a mechanistic combined toxicokinetic-toxicodynamic (TK/TD) and growth model for the aquatic macrophytes Lemna spp. The model simulates the development of Lemna biomass under laboratory and environmental conditions and was developed by Schmitt et al. (2013). Growth of the Lemna population is simulated on basis of photosynthesis and respiration rates which are functions of environmental conditions. The toxicodynamic sub-model describes the effects of growth-inhibiting substances by a respective reduction in the photosynthesis rate based on internal concentrations. This is the historical version of the Lemna model. For current uses, we recommend the Lemna (SETAC) model, which is a more recent version of the Schmitt model.

Usage

Lemna_Schmitt(param, init)

Lemna_SchmittThold(param, init)

Arguments

Details

Constructors to ease creation of scenarios based on the Lemna model by Schmitt et al. (2013). A variant of this Lemna model, Lemna_SchmittThold(), provides an additional cumulative exposure threshold parameter. The Lemna biomass stops growing if the integral of exposure over time exceeds the threshold. The integral of exposure is internally accounted for by an additional state variable AUC (Area Under Curve).

Value

an S4 object of type LemnaSchmittScenario

Functions

• Lemna_SchmittThold(): model variant with cumulative exposure threshold

State variables

The following list describes the default names and standard units of the model's state variables:

• BM, g_dw/m2, dry weight biomass per square meter

• E, -, effect [0,1]

• M_int, ug, internal toxicant mass

• AUC, ug/L, cumulative exposure (only for LemnaThreshold model)

Biomass (BM) and internal toxicant mass (M_int) are initialized to zero by default. See set_init() on how to set the initial states.

Model parameters

The following model parameters are required:

• Fate and biomass

  • k_phot_fix, logical, TRUE then k_phot_max is not changed by environmental factors, else FALSE

  • k_phot_max, 1/d, maximum photosynthesis rate

  • k_resp, 1/d, respiration rate

  • k_loss, 1/d, rate of loss (e.g. flow rate)

  • mass_per_frond, g_dw/frond, dry weight per frond

  • BMw2BMd, g_fw/g_dw, Fresh weight/dry weight

• Effect

  • Emax, -, maximum effect [0,1]

  • EC50, ug/L, midpoint of effect curve

  • b, -, slope of effect curve

• Toxicokinetics

  • P_up, cm/d, Permeability for uptake

  • AperBM, cm2/g_dw, A_leaf / d_leaf = 1/d_leaf (for circular disc, d=0.05 cm)

  • Kbm, -, Biomass(fw) : water partition coefficient

  • P_Temp, logical, TRUE to enable temperature dependence of cuticle permeability, else FALSE

  • MolWeight, g/mol, Molmass of molecule (determines Q10_permeability)

• Temperature dependence

  • Tmin, deg C, minimum temperature for growth

  • Tmax, deg C, maximum temperature for growth

  • Topt, deg C, optimal temperature for growth

  • t_ref, deg C, reference temperature for respiration rate

  • Q10, -, temperature dependence factor for respiration rate

• Light dependence

  • k_0, 1/d, light dependence: intercept of linear part

  • a_k, (1/d)/(kJ/m2.d), light dependence: slope of linear part

• Phosphorus dependence (Hill like dep.)

  • C_P, mg/L, phosphorus concentration in water

  • CP50, mg/L, phosphorus conc. where growth rate is halfed

  • a_p, -, Hill coefficient

  • KiP, mg/L, p-inhibition constant for very high p-conc.

• Nitrogen dependence (Hill like dep.)

  • C_N, mg/L, nitrogen concentration in water

  • CN50, mg/L, n-conc. where growth rate is halfed

  • a_N, -, Hill coefficient

  • KiN, mg/L, n-inhibition constant for very high p-conc.

• Density dependence

  • BM50, g_dw/m2, cut off BM

The Lemna_SchmittThold model requires the following additional parameter:

• threshold, ug/L, cumulative exposure threshold

Forcings

Besides exposure, the Lemna model requires two environmental properties as time-series input: global radiation (rad, kJ/m2.d) and temperature (temp, deg C). Forcings time-series are represented by data.frame objects consisting of two columns. The first for time and the second for the environmental factor in question.

Entries of the data.frame need to be ordered chronologically. A time-series can consist of only a single row; in this case it will represent constant environmental conditions. See scenarios for more details.

Effects

Supported effect endpoints include BM (biomass) and r (average growth rate during simulation). The effect on biomass is calculated from the last state of a simulation. Be aware that endpoint r is incompatible with frond transfers.

Parameter boundaries

Default values for parameter boundaries are set for all parameters by expert judgement, for calibration purposes. Values can be access from the object, and defaults overwritten.

Simulation output

Simulation results will contain two additional columns besides state variables:

• C_int, ug/L, internal concentration of toxicant

• FrondNo, -, number of fronds

It is possible to amend the output of simulate() with additional model quantities that are not state variables, for e.g. debugging purposes or to analyze model behavior. To enable or disable additional outputs, use the optional argument nout of simulate(), see examples below. nout=1 enables reporting of internal concentration (C_int), nout=14 enables all additional outputs, and nout=0 will disable additional outputs.

The available output levels are as follows:

• nout=1

  • C_int, internal concentration (ug/L)

• nout=2

  • FrondNo, number of fronds (-)

• nout=3

  • C_int_u, unbound internal concentration (ug/l)

• nout=8, growth and TK/TD

  • BM_fresh, fresh weight biomass (g_fw/m2)

  • k_photo_eff, current photosynthesis rate (1/d)

  • k_resp_eff, current respiration rate (1/d)

  • f_Eff, toxic effect factor (-)

  • P_up_eff, current permeability for uptake (cm/d)

• nout=11, environmental factors

  • actConc, current toxicant concentration in surrounding medium (ug/L)

  • actTemp, current environmental temperature (deg C)

  • actRad, current environmental radiation (kJ/m2.d)

• nout=14, derivatives

  • ⁠d BM/dt⁠, current change in state variable BM

  • ⁠d E/dt⁠, current change in effect

  • ⁠d M_int/dt⁠, current change in internal toxicant mass

Biomass transfer

Models supporting biomass transfer can be instructed to move a fixed amount of biomass to a new medium after a period of time. This feature replicates a procedure occurring in e.g. Lemna effect studies and may be necessary to recreate study results.

The biomass transfer feature assumes that always a fixed amount of biomass is transferred. Transfers can occur at any fixed point in time or in regular intervals. During a transfer, the biomass is reset to the transferred amount and additional compartments can be scaled 1:1 accordingly, to e.g. reflect the change in internal toxicant mass when biomass is modified. Transfer settings can be modified using set_transfer().

Any transfer time point must also be an output time point. If a transfer occurs, simulation results of that time point will report the model state before the transfer. Be aware that in order to use transfers at regular intervals, the simulation must start at time point zero.

References

Schmitt W., Bruns E., Dollinger M., and Sowig P., 2013: Mechanistic TK/TD-model simulating the effect of growth inhibitors on Lemna populations. Ecol Model 255, pp. 1-10. doi:10.1016/j.ecolmodel.2013.01.017

See Also

Lemna-models, Macrophyte-models, Transferable, Scenarios

Other Lemna models: Lemna-models, Lemna_SETAC()

Other macrophyte models: Lemna_SETAC(), Macrophyte-models, Myrio(), Myrio_log()

Description

The model was described and published by the SETAC Europe Interest Group Effect Modeling (Klein et al. 2022). It is based on the Lemna model by Schmitt (2013). The model is a mechanistic combined toxicokinetic-toxicodynamic (TK/TD) and growth model for the aquatic macrophytes Lemna spp.. The model simulates the development of Lemna biomass under laboratory and environmental conditions. Growth of the Lemna population is simulated on basis of photosynthesis and respiration rates which are functions of environmental conditions. The toxicodynamic sub-model describes the effects of growth-inhibiting substances by a respective reduction in the photosynthesis rate based on internal concentrations.

Usage

Lemna_SETAC()

Value

an S4 object of type LemnaSetacScenario

State variables

The model has two state variables:

• BM, Biomass (g dw m-2)

• M_int, Mass of toxicant in plant population (mass per m2, e.g. ug m-2)

Model parameters

• Growth model

  • k_photo_fixed, Model switch for unlimited growth conditions (TRUE/FALSE)

  • k_photo_max, Maximum photosynthesis rate (d-1)

  • k_loss, Reference loss rate (d-1)

  • BM_threshold, Lower biomass abundance threshold, (g dw m-2)

  • BM_min, Reservoir for biomass recovery, (g dw m-2)

• Temperature response of photosynthesis

  • T_opt, Optimum growth temperature (°C)

  • T_min, Minimum growth temperature (°C)

  • T_max, Maximum growth temperature (°C)

• Temperature response of biomass loss rate

  • Q10, Temperature coefficient (-)

  • T_ref, Reference temperature for response=1 (°C)

• Irradiance reponse of photosynthesis

  • alpha, Slope of irradiance response (m2 d kJ-1)

  • beta, Intercept of irradiance response (-)

• Nutrient response of photosynthesis

  • N_50, Half-saturation constant of Nitrogen (mg N L-1)

  • P_50, Half-saturation constant of Phosphorus (mg P L-1)

• Density dependence of photosynthesis

  • BM_L, Carrying capacity (g dw m-2)

• Concentration response (Toxicodynamics)

  • EC50_int, Internal concentration resulting in 50% effect (ug L-1)

  • E_max, Maximum inhibition (-)

  • b, Slope parameter (-)

• Internal concentration (Toxicokinetics)

  • P, Permeability (cm d-1)

  • r_A_DW, Area per dry-weight ratio (cm2 g-1)

  • r_FW_DW, Fresh weight per dry weight ratio (-)

  • r_FW_V, Fresh weight density (g cm-3)

  • r_DW_FN, Dry weight per frond ratio (g dw)

  • K_pw, Partitioning coefficient plant:water (-)

  • k_met, Metabolisation rate (d-1)

Forcings

Besides exposure, the model requires four environmental properties as time-series input:

• tmp, temperature (°C)

• irr, irradiance (kJ m-2 d-1)

• P, Phosphorus concentration (mg P L-1)

• N, Nitrogen concentration (mg N L-1)

Forcings time-series are represented by data.frame objects consisting of two columns. The first for time and the second for the environmental factor in question.

Entries of the data.frame need to be ordered chronologically. A time-series can consist of only a single row; in this case it will represent constant environmental conditions. See scenarios for more details.

Effects

Supported effect endpoints include BM (biomass) and r (average growth rate during simulation). The effect on biomass is calculated from the last state of a simulation. Be aware that endpoint r is incompatible with biomass transfers.

Simulation output

For reasons of convenience, the return value contains by default two additional variables derived from simulation results: the internal concentration C_int as well as the number of fronds FrondNo. These can be disabled by setting the argument nout = 0.

The available output levels are as follows:

• nout >= 1

  • C_int, internal concentration (mass per volume)

• nout >= 2

  • FrondNo, frond number (-)

• nout >= 4

  • f_loss, respiration dependency function (-)

  • f_photo, photosynthesis dependency function (-)

• nout >= 10

  • fT_photo, temperature response of photosynthesis (-)

  • fI_photo, irradiance response of photosynthesis (-)

  • fP_photo, phosphorus response of photosynthesis (-)

  • fN_photo, nitrogen response of photosynthesis (-)

  • fBM_photo, density response of photosynthesis (-)

  • fCint_photo, concentration response of photosynthesis (-)

• nout >= 16

  • C_int_unb, unbound internal concentration (mass per volume)

  • C_ext, external concentration (mass per volume)

  • Tmp, temperature (deg C)

  • Irr, irradiance (kJ m-2 d-1)

  • Phs, Phosphorus concentration (mg P L-1)

  • Ntr, Nitrogen concentration (mg N L-1)

• nout >= 18

  • dBM, biomass derivative (g dw m-2 d-1)

  • dM_int, mass of toxicant in plants derivative (mass per m2 d-1)

Biomass transfer

Models supporting biomass transfer can be instructed to move a fixed amount of biomass to a new medium after a period of time. This feature replicates a procedure occurring in e.g. Lemna effect studies and may be necessary to recreate study results.

The biomass transfer feature assumes that always a fixed amount of biomass is transferred. Transfers can occur at any fixed point in time or in regular intervals. During a transfer, the biomass is reset to the transferred amount and additional compartments can be scaled 1:1 accordingly, to e.g. reflect the change in internal toxicant mass when biomass is modified. Transfer settings can be modified using set_transfer().

Any transfer time point must also be an output time point. If a transfer occurs, simulation results of that time point will report the model state before the transfer. Be aware that in order to use transfers at regular intervals, the simulation must start at time point zero.

References

Klein J., Cedergreen N., Heine S., Reichenberger S., Rendal C., Schmitt W., Hommen U., 2021: Refined description of the Lemna TKTD growth model based on Schmitt et al. (2013) - equation system and default parameters. Report of the working group Lemna of the SETAC Europe Interest Group Effect Modeling. Version 1, uploaded on 22. Sept. 2021. https://www.setac.org/group/effect-modeling.html

Schmitt W., Bruns E., Dollinger M., and Sowig P., 2013: Mechanistic TK/TD-model simulating the effect of growth inhibitors on Lemna populations. Ecol Model 255, pp. 1-10. doi:10.1016/j.ecolmodel.2013.01.017

See Also

Lemna-models, Macrophyte-models, Transferable, Scenarios

Other Lemna models: Lemna-models, Lemna_Schmitt()

Other macrophyte models: Lemna_Schmitt(), Macrophyte-models, Myrio(), Myrio_log()

Description

Overview of supported Lemna models

Details

• Lemna_Schmitt() by Schmitt et al. (2013)

• Lemna_SETAC() by Klein et al. (2021)

Biomass transfer

Models supporting biomass transfer can be instructed to move a fixed amount of biomass to a new medium after a period of time. This feature replicates a procedure occurring in e.g. Lemna effect studies and may be necessary to recreate study results.

The biomass transfer feature assumes that always a fixed amount of biomass is transferred. Transfers can occur at any fixed point in time or in regular intervals. During a transfer, the biomass is reset to the transferred amount and additional compartments can be scaled 1:1 accordingly, to e.g. reflect the change in internal toxicant mass when biomass is modified. Transfer settings can be modified using set_transfer().

Any transfer time point must also be an output time point. If a transfer occurs, simulation results of that time point will report the model state before the transfer. Be aware that in order to use transfers at regular intervals, the simulation must start at time point zero.

See Also

Macrophyte-models

Other Lemna models: Lemna_SETAC(), Lemna_Schmitt()

Other scenarios: Algae-models, DEB-models, GUTS-RED-models, Macrophyte-models, Myriophyllum-models, Scenarios, Transferable

Description

The aim of the function is two-fold: 1) estimate a 95% confidence around each parameter of a calibrated model, and 2) see if perhaps a local minimum was found rather than a global minimum. To achieve this, the likelihood profiling goes through every parameter one by one. For each parameter, the model is sequentially refit with the parameter value set to increasingly lower and higher values, and the likelihood of the model given the data calculated (using log_lik()). The likelihood is then compared to the likelihood of the original model (using a likelihood ratio). This leads to the development of a likelihood profile, from which a plot a 95% confidence interval for the parameter is derived.

The idea of the function is a variable stepwise algorithm: When the likelihood ratio changes very little (less than l_crit_min), the stepsize is increased (up to a maximum, specified by f_step_max). When the lik. ratio changes too much (more than l_crit_max), the algorithm tries again with a smaller stepsize (also bound to a minimum: f_step_min). Note that the stepsize is used as a fraction of the parameter value that is tried. To prevent very small stepsizes when the value goes towards zero (as can be the case for effect thresholds), an absolute minimum stepsize (f_step_abs), which is specified as a fraction of the best parameter value (Xhat) (unless it is zero, then algoritm takes something small).

The function was inspired by a MatLab BYOM v.6.8 procedure, created by Tjalling Jager. For details, please refer to BYOM (http://debtox.info/byom.html) as well as Jager (2021).

Usage

lik_profile(
  x,
  par,
  output,
  data = NULL,
  bounds = NULL,
  refit = TRUE,
  type = c("coarse", "fine"),
  break_prof = FALSE,
  ...
)

Arguments

Value

A list containing, for each parameter profiled, the likelihood profiling results as a dataframe; the 95% confidence interval; the original parameter value; the likelihood plot object; and the recalibrated parameter values (in case a lower optimum was found)

References

Jager T, 2021. Robust Likelihood-Based Optimization and Uncertainty Analysis of Toxicokinetic-Toxicodynamic Models. Integrated Environmental Assessment and Management 17:388-397. doi:10.1002/ieam.4333

Examples

# Example with Lemna model - physiological params
library(dplyr)

# exposure - control run
exp <- Schmitt2013 %>%
  filter(ID == "T0") %>%
  select(time=t, conc)

# observations - control run
obs <- Schmitt2013 %>%
  filter(ID == "T0") %>%
   select(t, BM=obs)

# update metsulfuron
myscenario <- metsulfuron %>%
  set_param(c(k_phot_fix = TRUE,Emax = 1)) %>%
  set_init(c(BM = 12)) %>%
  set_exposure(exp)

fit <- calibrate(
  x = myscenario,
  par = c(k_phot_max = 1),
  data = obs,
  output = "BM",
  lower=0,
  upper=1,
  method="Brent"
)

# Likelihood profiling

res <- lik_profile(
  x = myscenario,
  data = obs,
  output = "BM",
  par = fit$par,
  bounds = list(
    k_phot_max = list(0, 30)
  ),
  refit = FALSE,
  type = "fine",
  method = "Brent"
)
# plot
plot_lik_profile(res)

Description

Start and stop logging

Usage

log_enable(file = NULL, append = TRUE, envir = parent.frame())

log_disable()

Arguments

Value

no return value

Description

Log R environment properties

Usage

log_envir()

Value

no return value

Description

Calculates the sum of log likelihoods of each observation given the model parameterization (considering a normal distribution around the prediction for each datapoint)

Usage

log_lik(npars, obs, pred)

Arguments

Value

the log likelihood value

Examples

# observations
obs <- c(12, 38, 92, 176, 176, 627, 1283, 2640)
# intercept, a, and slope, b, of a Poisson regression fitted through obs
pars <- c(a = 2, b = 0.73)
# predictions with the Poisson regression
pred <- c(15.43, 32.15, 66.99, 139.57, 290.82, 605.94, 1262.52, 2630.58)
# example plot
plot(seq(1:length(obs)), obs)
lines(seq(1:length(obs)), pred)
log_lik(
  npars = length(pars),
  obs = obs,
  pred = pred
)

Description

Message will only appear in the console or in log file if logging was enabled using log_enable().

Usage

log_msg(...)

Arguments

Value

no return value

Examples

log_msg("this message will not appear")

log_enable()
log_msg("this message will appear")
log_msg("a number of ","elements to ",42," concatenate")

Description

Log scenario properties

Usage

log_scenarios(x, header = TRUE)

Arguments

Value

unmodified argument x

Description

Population models of standard test macrophytes, such as Lemna spp.

Details

Available macrophyte models:

• Lemna

• Myriophyllum

Biomass transfer

Models supporting biomass transfer can be instructed to move a fixed amount of biomass to a new medium after a period of time. This feature replicates a procedure occurring in e.g. Lemna effect studies and may be necessary to recreate study results.

The biomass transfer feature assumes that always a fixed amount of biomass is transferred. Transfers can occur at any fixed point in time or in regular intervals. During a transfer, the biomass is reset to the transferred amount and additional compartments can be scaled 1:1 accordingly, to e.g. reflect the change in internal toxicant mass when biomass is modified. Transfer settings can be modified using set_transfer().

Any transfer time point must also be an output time point. If a transfer occurs, simulation results of that time point will report the model state before the transfer. Be aware that in order to use transfers at regular intervals, the simulation must start at time point zero.

See Also

Scenarios

Other macrophyte models: Lemna_SETAC(), Lemna_Schmitt(), Myrio(), Myrio_log()

Other scenarios: Algae-models, DEB-models, GUTS-RED-models, Lemna-models, Myriophyllum-models, Scenarios, Transferable

Description

Data set for the parametrisation of a mechanistic combined toxicokinetic-toxicodynamic (TK/TD) and growth model for the aquatic macrophytes Lemna spp. as published by Schmitt et al. (2013). The growth model was parameterised by Schmitt et al. based on these data while toxicokinetic and toxicodynamic parameters were determined by calibrating the model using substance specific effect data of metsulfuron-methyl.

Usage

metsulfuron

Format

An object of class LemnaSchmittScenario of length 1.

References

Schmitt W., Bruns E., Dollinger M., and Sowig P., 2013: Mechanistic TK/TD-model simulating the effect of growth inhibitors on Lemna populations. Ecol Model 255, pp. 1-10. doi:10.1016/j.ecolmodel.2013.01.017

See Also

Lemna-models

Description

The scenario consists of a parameterized GUTS-RED-IT model and a constant exposure series. Model parameters were derived from an acute fish toxicity study of the fathead minnow and chlorpyrifos by Geiger et al. (1988). The dataset is also referred to as GUTS Ring-test dataset C by EFSA (2018). Fitted parameters were estimated using the morse package.

Usage

minnow_it

Format

An object of class GutsRedIt of length 1.

Details

The background mortality rate (hb) was set to zero.

Source

https://mosaic.univ-lyon1.fr/guts

References

Geiger D.L., Call D.J., and Brooke L.T., 1988: Acute toxicities of organic chemicals to fathead minnows (Pimephales promelas): Volume IV, pp. 195-197. University of Wisconsin-Superior, Center for Lake Superior Environmental Studies. ISBN 9780961496838.

EFSA PPR Panel (EFSA Panel on Plant Protection Products and their Residues), Ockleford C, Adriaanse P, Berny P, et al., 2018: Scientific Opinion on the state of the art of Toxicokinetic/Toxicodynamic (TKTD) effect models for regulatory risk assessment of pesticides for aquatic organisms. EFSA Journal 2018; 16(8):5377, 188 pp. doi:10.2903/j.efsa.2018.5377

See Also

GUTS-RED-models

Description

The scenario consists of a parameterized GUTS-RED-SD model and a constant exposure series. Model parameters were derived from an acute fish toxicity study of the fathead minnow and chlorpyrifos by Geiger et al. (1988). The dataset is also referred to as GUTS Ring-test dataset C by EFSA (2018). Fitted parameters were estimated using the morse package.

Usage

minnow_sd

Format

An object of class GutsRedSd of length 1.

Details

The background mortality rate (hb) was set to zero.

Source

https://mosaic.univ-lyon1.fr/guts

References

Geiger D.L., Call D.J., and Brooke L.T., 1988: Acute toxicities of organic chemicals to fathead minnows (Pimephales promelas): Volume IV, pp. 195-197. University of Wisconsin-Superior, Center for Lake Superior Environmental Studies. ISBN 9780961496838.

EFSA PPR Panel (EFSA Panel on Plant Protection Products and their Residues), Ockleford C, Adriaanse P, Berny P, et al., 2018: Scientific Opinion on the state of the art of Toxicokinetic/Toxicodynamic (TKTD) effect models for regulatory risk assessment of pesticides for aquatic organisms. EFSA Journal 2018; 16(8):5377, 188 pp. doi:10.2903/j.efsa.2018.5377

See Also

GUTS-RED-models

Description

Loads GUTS model parameters which were fitted by the morse package.

Usage

morse(
  file,
  find.SD = TRUE,
  find.IT = TRUE,
  reset.hb = TRUE,
  params = c("estim", "all"),
  mcmc.size
)

Arguments

Value

vector of parameter_set objects

Examples

# import all parameter fits
try(morse("path/to/morse_fit.RData"))

# import parameters for a specific model
try(morse("path/to/morse_fit.RData", find.IT=TRUE, find.SD=FALSE))

# modify model objects
try(models %>% set_param(morse("path/to/morse_fit.RData")))

Description

The Myriophyllum model is derived from the Lemna TKTD model by Klein et al. (2021). The Myriophyllum model is mathematically equivalent to the Tier 2C version of the Lemna model by Klein et al. (2021), cf. Lemna_SETAC(). Recommended settings for Tier 2C are k_photo_fixed=TRUE and k_resp=0 (Klein et al. 2021). In particular, the growth model is a simple exponential growth model, which is considered to be the typical situation for a laboratory macrophyte study. Instead of frond numbers as for Lemna, the biomass is also returned as total shoot length (TSL) in simulation results. Consequently, the model has the additional parameter r_DW_TSL (dry weight per total shoot length ratio) instead of r_DW_FN (dry weight per frond number ratio).

Usage

Myrio()

Value

an S4 object of type MyrioExpScenario

State variables

The model has two state variables:

• BM, Biomass (g dw m-2 for field studies or mg dw for lab)

• M_int, Mass of toxicant in plant population (mass per m2, e.g. ug m-2)

Model parameters

• Growth model

  • k_photo_max, Maximum photosynthesis rate (d-1), default: 0.47

• Concentration response (Toxicodynamics)

  • EC50_int, Internal concentration resulting in 50% effect (ug L-1)

  • E_max, Maximum inhibition (-), default: 1

  • b, Slope parameter (-)

• Internal concentration (Toxicokinetics)

  • P, Permeability (cm d-1)

  • r_A_DW, Area per dry-weight ratio (cm2 g-1), default: 1000

  • r_FW_DW, Fresh weight per dry weight ratio (-), default: 16.7

  • r_FW_V, Fresh weight density (g cm-3), default: 1

  • r_DW_TSL, Dry weight per total shoot length ratio (g (field) or mg (lab) dw cm-1)

  • K_pw, Partitioning coefficient plant:water (-), default: 1

  • k_met, Metabolisation rate (d-1), default: 0

Environmental factors

None.

Parameter boundaries

Default values for parameter boundaries are set for all parameters by expert judgement, for calibration purposes. Values can be modified using set_bounds().

Simulation output

Simulation results will contain two additional columns besides state variables:

• C_int, internal concentration of toxicant (mass per volume)

• TSL, total shoot length (?)

The available output levels are as follows:

• nout >= 1

  • C_int, internal concentration (mass per volume)

• nout >= 2

  • TSL, total shoot length (?)

• nout >= 3

  • f_photo, photosynthesis dependency function (-)

• nout >= 5, growth and TK/TD

  • C_int_unb, unbound internal concentration (mass per volume)

  • C_ext, external concentration (mass per volume)

• nout >= 7, environmental factors

  • dBM, biomass derivative (g dw m-2 d-1)

  • dM_int, mass of toxicant in plants derivative (mass per m2 d-1)

Effects

Supported effect endpoints include BM (biomass) and r (average growth rate during simulation). The effect on biomass is calculated from the last state of a simulation. Be aware that endpoint r is incompatible with biomass transfers.

Biomass transfer

Models supporting biomass transfer can be instructed to move a fixed amount of biomass to a new medium after a period of time. This feature replicates a procedure occurring in e.g. Lemna effect studies and may be necessary to recreate study results.

The biomass transfer feature assumes that always a fixed amount of biomass is transferred. Transfers can occur at any fixed point in time or in regular intervals. During a transfer, the biomass is reset to the transferred amount and additional compartments can be scaled 1:1 accordingly, to e.g. reflect the change in internal toxicant mass when biomass is modified. Transfer settings can be modified using set_transfer().

Any transfer time point must also be an output time point. If a transfer occurs, simulation results of that time point will report the model state before the transfer. Be aware that in order to use transfers at regular intervals, the simulation must start at time point zero.

References

Klein J., Cedergreen N., Heine S., Reichenberger S., Rendal C., Schmitt W., Hommen U., 2021: Refined description of the Lemna TKTD growth model based on Schmitt et al. (2013) - equation system and default parameters. Report of the working group Lemna of the SETAC Europe Interest Group Effect Modeling. Version 1, uploaded on 22. Sept. 2021. https://www.setac.org/group/effect-modeling.html

See Also

Macrophyte-models, Transferable, Scenarios

Other Myriophyllum models: Myrio_log(), Myriophyllum-models

Other macrophyte models: Lemna_SETAC(), Lemna_Schmitt(), Macrophyte-models, Myrio_log()

Description

The Myriophyllum model is derived from the Lemna TKTD model by Klein et al. (2021). Myrio_log() modifies the Myrio() model to feature logistic growth, i.e. control growth is described by the differential equation ⁠d BM/dt = k_photo_max*BM*(1 - BM/BM_L)⁠ where BM_L is the carrying capacity.

Usage

Myrio_log()

Value

an S4 object of type MyrioLogScenario

Model parameters

• Growth model

  • k_photo_max, Maximum photosynthesis rate (d-1), default: 0.47

  • BM_L, Carrying capacity (g dw m-2)

• Concentration response (Toxicodynamics)

  • EC50_int, Internal concentration resulting in 50% effect (ug L-1)

  • E_max, Maximum inhibition (-), default: 1

  • b, Slope parameter (-)

• Internal concentration (Toxicokinetics)

  • P, Permeability (cm d-1)

  • r_A_DW, Area per dry-weight ratio (cm2 g-1), default: 1000

  • r_FW_DW, Fresh weight per dry weight ratio (-), default: 16.7

  • r_FW_V, Fresh weight density (g cm-3), default: 1

  • r_DW_TSL, Dry weight per total shoot length ratio (?)

  • K_pw, Partitioning coefficient plant:water (-), default: 1

  • k_met, Metabolisation rate (d-1), default: 0

State variables

The model has two state variables:

• BM, Biomass (g dw m-2 for field studies or mg dw for lab)

• M_int, Mass of toxicant in plant population (mass per m2, e.g. ug m-2)

Environmental factors

None.

Simulation output

Simulation results will contain two additional columns besides state variables:

• C_int, internal concentration of toxicant (mass per volume)

• TSL, total shoot length (?)

The available output levels are as follows:

• nout >= 1

  • C_int, internal concentration (mass per volume)

• nout >= 2

  • TSL, total shoot length (?)

• nout >= 3

  • f_photo, photosynthesis dependency function (-)

• nout >= 5, growth and TK/TD

  • C_int_unb, unbound internal concentration (mass per volume)

  • C_ext, external concentration (mass per volume)

• nout >= 7, environmental factors

  • dBM, biomass derivative (g dw m-2 d-1)

  • dM_int, mass of toxicant in plants derivative (mass per m2 d-1)

Effects

Supported effect endpoints include BM (biomass) and r (average growth rate during simulation). The effect on biomass is calculated from the last state of a simulation. Be aware that endpoint r is incompatible with biomass transfers.

Biomass transfer

Models supporting biomass transfer can be instructed to move a fixed amount of biomass to a new medium after a period of time. This feature replicates a procedure occurring in e.g. Lemna effect studies and may be necessary to recreate study results.

The biomass transfer feature assumes that always a fixed amount of biomass is transferred. Transfers can occur at any fixed point in time or in regular intervals. During a transfer, the biomass is reset to the transferred amount and additional compartments can be scaled 1:1 accordingly, to e.g. reflect the change in internal toxicant mass when biomass is modified. Transfer settings can be modified using set_transfer().

Any transfer time point must also be an output time point. If a transfer occurs, simulation results of that time point will report the model state before the transfer. Be aware that in order to use transfers at regular intervals, the simulation must start at time point zero.

Parameter boundaries

Default values for parameter boundaries are set for all parameters by expert judgement, for calibration purposes. Values can be modified using set_bounds().

References

Klein J., Cedergreen N., Heine S., Reichenberger S., Rendal C., Schmitt W., Hommen U., 2021: Refined description of the Lemna TKTD growth model based on Schmitt et al. (2013) - equation system and default parameters. Report of the working group Lemna of the SETAC Europe Interest Group Effect Modeling. Version 1, uploaded on 22. Sept. 2021. https://www.setac.org/group/effect-modeling.html

See Also

Transferable, Scenarios

Other Myriophyllum models: Myrio(), Myriophyllum-models

Other macrophyte models: Lemna_SETAC(), Lemna_Schmitt(), Macrophyte-models, Myrio()

Description

Supported models:

• Myrio(), with exponential growth

• Myrio_log(), with logistic growth

See Also

Lemna-models, Transferable

Other Myriophyllum models: Myrio(), Myrio_log()

Other scenarios: Algae-models, DEB-models, GUTS-RED-models, Lemna-models, Macrophyte-models, Scenarios, Transferable

Description

Creates an ExposureSeries with zero concentration. When setting the zero exposure, pay attention not to accidentally reset the output times of your scenario as the zero exposure series contains only a single time point. See the examples.

Usage

no_exposure()

Value

an S4 object of type ExposureSeries

See Also

set_noexposure()

Examples

# this will reset the output times of the sample scenario,
# simulate() will quit with an error
try(
  minnow_it %>%
    set_exposure(no_exposure()) %>%
    simulate()
)

# set zero exposure, but keep original output times
minnow_it %>%
  set_exposure(no_exposure(), reset_times=FALSE) %>%
  simulate()

Description

Set of model parameters

Usage

parameter_set(model, param = list(), tag = NA_character_)

Arguments

Value

an S4 object of type parameter_set

Slots

model

character, a string containing a model name, e.g. "GUTS-RED-IT"

tag

character, an optional identifier

param

named list of model parameters

Examples

# create a parameter set and assign it
ps <- parameter_set("GUTS-RED-IT", list(kd=0.12, hb=0.3))
GUTS_RED_IT() %>% set_param(ps)

# multiple scenarios can be modified at once
c(GUTS_RED_IT(), GUTS_RED_IT()) %>%
  set_param(ps)

# model names must match, otherwise an error will be raised
try(GUTS_RED_SD() %>% set_param(ps))

Description

In certain cases it might be beneficial to disable parallel execution of e.g. effect profile calculations. By disabling, all processes run sequentially and instantly pass messages to the console which would be delayed during parallel processing. This makes it easier to pinpoint problems within the data or algorithm.

Usage

pll_debug(state = TRUE)

Arguments

Value

no return value

Description

Plot EPx values

Usage

plot_epx(
  EPx_ts,
  exposure_ts,
  draw = TRUE,
  time_col = "time",
  conc_col = "conc",
  epx_x_title = "Start time",
  conc_y_title = "Exposure conc."
)

Arguments

Value

a grid of ggplots

Examples

ti <- 0:21
expo <- abs(0.01*ti + rnorm(length(ti), 0, 0.05))
exposure <- data.frame(time = ti, conc = expo)
metsulfuron_epx_mtw <- metsulfuron %>%
set_exposure(exposure) %>%
epx_mtw(level = 10, factor_cutoff = 1000)
metsulfuron_epx_mtw
plot_epx(EPx_ts = metsulfuron_epx_mtw,
exposure_ts = exposure, conc_y_title = "env. concentration [µg/L]")

Description

The function provides a combined plot of the likelihood profiles of all parameters profiled.

Usage

plot_lik_profile(x)

Arguments

Value

plots

Description

The function provides bivariate parameter space plots indicating parameter draws (from the 95%confidence intervals per parameter obtained through likelihood profiling) that fall within the inner rim (in green, i.e. parameter sets which are not significantly different from the original, based on a chi-square test). The original parameter set is also indicated (in orange), and, if different from the original set, the best fit parameter set is indicated (in red)

Usage

plot_param_space(x)

Arguments

Value

plots

Description

A sample of parameters representing the uncertainty within the dataset is passed to the function. All parameter combinations and exposure patterns are simulated and the range of predicted frond numbers is derived for a single study. The uncertainty is displayed by a Posterior Predictive Plot (PPC). The data (rs_mean, obs_mean and obs_full) must have the following format (col1 = time, col2 = data of interest, col3 = trial name). Data for uncertainties (rs_range) must have the format: col1 = time, col2 = lower boundaries, col3 = upper boundaries, col4 = trial. The user should take care of the input data and consider whether control data and data at time zero should be included in the model check.

Usage

plot_ppc(
  rs_mean,
  rs_range,
  col_number = 2,
  obs_mean = NULL,
  obs_full = NULL,
  xy_lim = NULL,
  study = NULL
)

Arguments

Value

a ggplot2 plot object

Description

The function expects a data.frame with four mandatory and one optional column. The mandatory columns are as follows:

• pred: mean of predictions e.g. frond number for lemna

• max: maximum of predictions

• min: minimum of predictions

• obs: observations The optional column is to be named study and contains a study identifier. If more than one study identifier is present in the table, individual studies will be plotted in different colors and a legend will be displayed. The function is called by plot_ppc where the column names are defined (see rs_ppc object).

Usage

plot_ppc_combi(table, xy_lim = NULL)

Arguments

Value

a ggplot2 plot object

Description

Sometimes it is helpful if the user can plot results of one effect scenario. This is for instance the case for test simulations or predictions for one profile. This function runs the simulation for one effect scenario and plots the results. Function plots the time (column 1) and the predictions (column 2, can be changed by the user plot_col)

Usage

plot_scenario(model_base, plot_col = 2, trial_number = NULL)

Arguments

Value

plot of the results for one ⁠effect scenario⁠

Examples

plot_scenario(metsulfuron)

Description

All parameter combinations and exposure patterns are simulated and the mean of predictions is derived for a single study. The uncertainty is passed to the function due to computation time. Results are displayed by plotting the time series including the uncertainty interval. Observation data can be optionally displayed. Data should be provided in long format. Function plots the time (column 1) and the predictions (column 2, can be changed by the user plot_col)

Usage

plot_sd(
  model_base,
  treatments,
  rs_mean,
  rs_range = NULL,
  obs_mean = NULL,
  obs_full = NULL,
  x_breaks = NULL,
  y_lim = NULL,
  grid_labels = NULL,
  grid_ncol = 2,
  plot_col = 2,
  y_title = NULL,
  ...
)

Arguments

Value

a ggplot2 plot object

Examples

set.seed(124)
exposure <- data.frame(
  time = 0:21,
  conc = rnorm(n = 22, mean = 0.1, sd = 0.06),
  trial = "T1"
)
forcings <- list(temp = 12, rad = 15000)
param <- list(EC50 = 0.3, b = 4.16, P_up = 0.0054)
inits <- list(BM = 0.0012, E = 1, M_int = 0)

scenario <- Lemna_Schmitt() %>%
  set_forcings(forcings) %>%
  set_param(param) %>%
  set_init(inits)

sim_result <- simulate_batch(
  model_base = scenario,
  treatments = exposure,
  param_sample = NULL
)

plot_sd(
  model_base = scenario,
  treatments = exposure,
  rs_mean = sim_result
)

Description

The method pulls available metadata from scenario objects and returns a table with additional columns. If the argument already was a data.frame object, the columns are appended. May overwrite existing columns of the same name.

Usage

pull_metadata(x, model = TRUE, exposure = TRUE)

Arguments

Value

a data.frame

Examples

metsulfuron %>%
  pull_metadata()

Description

Data are from Weber 2012 publication.

Usage

Rsubcapitata

Format

An object of class AlgaeTKTDScenario of length 1.

References

Weber D, Schaeffer D, Dorgerloh M, Bruns E, Goerlitz G, Hammel K, Preuss TG and Ratte HT, 2012. Combination of a higher-tier flow-through system and population modeling to assess the effects of time-variable exposure of isoproturon on the green algae Desmodesmus subspictatus and Pseudokirchneriella subcapitata. Environmental Toxicology and Chemistry, 31, 899-908. doi:10.1002/etc.1765

See Also

Algae_TKTD

Description

The EffectScenario class is the base for all of the basic scenario types and models. It contains slots for data and settings that are required by most models such as a vector of model parameters and a vector of initial states. For each particular model, the class's slots are filled with certain default or fixed values. Some models derive from this class and add slots to store additional data.

Details

Certain behaviors that are required to model complex processes cannot be represented by a single EffectScenario. As an example, the parameters of a scenario are generally fixed during the simulated time period. In order to represent a change in parameter values, the original scenario would need to split into two scenarios A and B which differ by parameter values and simulated time period. By combining these scenarios to a scenario sequence, the sequence would be treated as a single, complex scenario. See sequence() for more information.

Parameters

Most parameters are represented by numerical types but other types are possible depending on model. Please refer to the model description which parameters are required and in which unit. Some or all parameters may be required to start a simulation. If required parameters are missing, simulation will fail with an error message.

Initial state

The initial state represents the starting values of state variables when starting a simulation. A scenario's default initial state may be insufficient to get sensible results. It is advisable to set an initial state explicitly when creating a new scenario, see set_init().

In theory, a scenario's state variables can be renamed by modifying the names of the initial state vector. However, this is strongly discouraged as this will affect other routines such as effect() and epx() and may render results useless.

Exposure

Exposure refers to the concentration of toxicant an organism is exposed to. In case of aquatic organisms, this would commonly be the concentration of a toxicant in water. Other interpretations are possible depending on model assumptions.

Exposure time-series are generally represented by a data.frame containing two columns. The first column representing time, the second representing the exposure level. The ordering of columns is mandatory. The column names are essentially irrelevant but sensible names may help documenting the scenario and its data. The rows must be ordered chronologically. A time-series can consist of only a single row; in this case it will represent constant exposure. Exposure time-series are set to a scenario using set_exposure().

Handling time-series is a costly task for the ODE solver due to consistency checks and interpolation between time steps. How the solver interpolates the time-series can be controlled by certain arguments to functions such as simulate() and effect(). Please refer to simulate() for a brief overview and deSolve::forcings for a detailed description.

Exposure time-series should be kept as short as possible and as complex as needed for optimal computational efficiency.

Environmental forcings

Forcings generally refer to model parameters that change over time as part of an external function such as environmental temperature and exposure levels. Due to the importance of exposure in regulatory assessments, this R package explicitly distinguishes between environmental forcings and exposure. However, the same restrictions and features apply to both of them.

Forcing time-series are handled the same way as exposure time-series, i.e. they are represented by a data.frame containing two columns. The first column representing time, the second representing the parameter that is a function of time. The ordering of columns is mandatory. The rows must be ordered chronologically. Forcings time-series are set using set_forcings(). Please refer to the Exposure section for more information on how time-series are handled.

Output times

A scenario's simulated time period is defined by its minimum and maximum output time. Simulation results will only be returned for the defined output times even though the ODE solver may use smaller time steps between output times. Output times can be explicitly set using set_times(). The number and distance of output times may have influence on the precision of simulation results and numerical stability, cf. simulate().

Be aware that set_exposure() will overwrite previously defined output times if not requested otherwise.

Effects

Generally, all state variables can be used as effect endpoints but models may provide additional endpoints. Use set_endpoints() to enable or disable endpoints for a scenario.

Some scenarios or models require control runs to calculate effects under exposure. Generally, control simulations will run automatically where needed. However, when conducting a large number of repeated simulations, e.g. when calculating effect profiles (EPx values) or simulating moving exposure windows, it may be computational efficient to run control simulations only once and cache their results within the scenario. Please refer to cache_controls() for details.

Moving exposure windows

The time frame relevant for effects may be much shorter than the assessed exposure time-series for certain organisms. This fact can be represented by moving exposure windows which divide a long time period in a number of consecutive windows of the same length. Each window is simulated individually and effects are calculated. By default, methods such as effect() will only return the maximum effect of all considered windows but detailed results can be presented on demand.

To use moving exposure windows, the exposure time-series must be regular, i.e. must have an equidistant step length in time. The length of the window is defined as the number of time steps of the exposure time-series. As an example, assume the time-series has daily granularity and a moving window of seven days length is required. In this case, the moving window must have a length of seven (7) time steps. If the exposure time-series had hourly granularity, the same window would need to have a length of 168 (=7*24) time steps. Please refer to set_window() for details.

Slots

name

character, unique model name

tag

character, an optional identifier

param

list of parameter key-value pairs

param.bounds

named list of parameter boundaries

param.req

character vector of required parameters

forcings

list of data.frames representing forcing time-series

forcings.req

character vector or required model forcings data, e.g. temperature

init

list of initial model states

times

numeric vector of output times, beginning and end also define the simulated period

endpoints

character vector of endpoints to calculate results for

exposure

data.frame with two columns representing an exposure time-series

control

list of named numerical vectors, contains the control values for all relevant moving windows

control.req

logical, if TRUE then control values are required to calculate effects

window.length

numeric, maximum length of the simulated period, if window.length is shorter than the exposure pattern, then all possible exposure sub-patterns are evaluated for effect calculation. This is also referred to as a moving window approach.

window.interval

numeric, interval determining distance between moving windows during effect calculation. First window starts at first time point in exposure pattern.

See Also

Other scenarios: Algae-models, DEB-models, GUTS-RED-models, Lemna-models, Macrophyte-models, Myriophyllum-models, Transferable

Description

Data are from Schmitt 2013 publication.

Usage

Schmitt2013

Format

An object of class data.frame with 56 rows and 4 columns.

References

Schmitt W., Bruns E., Dollinger M., and Sowig P., 2013: Mechanistic TK/TD-model simulating the effect of growth inhibitors on Lemna populations. Ecol Model 255, pp. 1-10. doi:10.1016/j.ecolmodel.2013.01.017

See Also

Lemna-models

Description

A sequence of scenarios is treated as a single scenario and each scenario is simulated one after the other. If scenario n in a sequence was simulated, scenario n+1 will start off in the model state where n had ended. Scenario sequences can be used to e.g. implement changes in model parameters over time.

Details

Requirements

All scenarios in a sequence must fulfill the following requirements:

• All scenarios must have identical state variables

• The output times of all scenarios must represent a continuous time series without gaps or overlaps

Limitations

Only simulation of sequences are supported, at the moment. Effects and effect profiles (EPx values) cannot be derived, yet.

Value

an S4 object of type ScenarioSequence

Examples

# create two scenarios that need to be simulated one after the other
scen1 <- minnow_it %>% set_times(0:3)
scen2 <- minnow_it %>% set_times(3:6) %>% set_param(c(kd=0))

# create a sequence and assign scenarios
sq <- sequence(list(scen1, scen2))

# simulate the sequence

simulate(sq)

Description

Modifies the boundaries of model parameters for one or more scenario or caliset objects.

Usage

set_bounds(x, bounds)

## S4 method for signature 'EffectScenario,list'
set_bounds(x, bounds)

## S4 method for signature 'CalibrationSet,list'
set_bounds(x, bounds)

## S4 method for signature 'list,list'
set_bounds(x, bounds)

Arguments

Value

scenario or caliset with modified parameter boundaries

Examples

metsulfuron %>%
   set_bounds(list(k_phot_max = c(0, 30),
                   k_resp = c(0, 10)))

Description

Effect endpoints calculated by functions such as effect() and epx() can be enabled and disabled. If an endpoint is not required for an assessment, it should be disabled for reasons of computational efficiency. Please refer to the model description for a list of available endpoints.

Usage

set_endpoints(x, endpoints)

Arguments

Value

Modified EffectScenario objects

Examples

# Only enable reproduction (R) endpoint for americamysis scenario
americamysis %>%
  set_endpoints("R") %>%
  effect()

# Enable endpoints length (L) and reproduction (R)
americamysis %>%
  set_endpoints(c("L","R")) %>%
  effect()

Description

Exposure refers to the toxicant concentration an organism is exposed to. In case of aquatic organisms, this would commonly be the concentration of a toxicant in water. Other interpretations are possible depending on model assumptions.

Usage

set_exposure(scenarios, series, ...)

## S4 method for signature 'ANY,ANY'
set_exposure(scenarios, series)

## S4 method for signature 'EffectScenario,data.frame'
set_exposure(scenarios, series, ...)

## S4 method for signature 'EffectScenario,ExposureSeries'
set_exposure(scenarios, series, reset_times = TRUE)

## S4 method for signature 'EffectScenario,list'
set_exposure(scenarios, series, ...)

## S4 method for signature 'list,list'
set_exposure(scenarios, series, ...)

## S4 method for signature 'list,ANY'
set_exposure(scenarios, series, ...)

Arguments

Details

Exposure time-series are generally represented by a data.frame containing two columns. The first column for time, the second representing the exposure level. The ordering of columns is mandatory. The column names are non-relevant but sensible names may help documenting the scenario and its data. The data.frame's rows must be ordered chronologically. A time-series can consist of only a single row; in this case it will represent constant exposure.

For convenience, a time-series with zero exposure can be set using set_noexposure().

Computational efficiency

Handling time-series is a costly task for the ODE solver due to consistency checks and interpolation between time steps. How the solver interpolates the time-series can be controlled by optional arguments to functions such as simulate() and effect(). Please refer to simulate() for a brief overview and deSolve::forcings for a detailed description.

Exposure time-series should be kept as short as possible and as complex as needed for optimal computational efficiency.

Output times

By default, the exposure time-series' time points will also be used as output times of the scenario. Any output times previously set by set_times() will be lost. If this behavior is undesired, set the function argument reset_times=FALSE.

Multiple exposure series and scenarios

The functions supports modifying multiple scenarios at once: by calling it with lists of scenario and ExposureSeries objects. The cartesian product of all scenarios and exposure series will be returned, iff the parameter expand = TRUE is set.

As an example for the expand mode, two scenarios A and B and one exposure series g will result in two scenarios Ag and Bg, both using exposure series g. Two scenarios A and B as well as two exposure seres g and h will result in four scenarios Ag,Ah,Bg, and Bh.

Value

list of EffectScenario objects

Examples

# set a data.frame as exposure series
Lemna_Schmitt() %>% set_exposure(data.frame(time=c(0, 1, 2, 3), conc=c(1, 1, 0, 0)))

# set one ExposureSeries
es1 <- ExposureSeries(data.frame(time=0, conc=0))
Lemna_Schmitt() %>% set_exposure(es1)

# set two ExposureSeries to create two scenarios
es2 <- ExposureSeries(data.frame(time=5:10, conc=1))
Lemna_Schmitt() %>% set_exposure(c(es1, es2))

# set one ExposureSeries without resetting existing output times
Lemna_Schmitt() %>%
  set_times(0:5) %>%
  set_exposure(es1, reset_times=FALSE)

Description

Parameters which change their value over time are referred to as forcings. If and what parameters can vary over time depends on the model in question. In many cases, forcings represent time-series of environmental properties.

Usage

set_forcings(x, ...)

## S4 method for signature 'EffectScenario'
set_forcings(x, ...)

## S4 method for signature 'list'
set_forcings(x, ...)

Arguments

Details

Forcing time-series are always represented by a data.frame containing two columns. The first column representing time, the second representing the parameter that is a function of time. The ordering of columns is mandatory. The column names are essentially irrelevant but may help documenting the scenario and its data. The rows must be ordered chronologically. A time-series can consist of only a single row; in this case it will represent constant conditions.

Handling forcing time-series is a costly task for the ODE solver due to consistency checks and interpolation between timesteps. How the solver interpolates the forcing time-series can be controlled by certain arguments to functions such as simulate() and effect(). Please refer to simulate() for a brief overview and deSolve::forcings for a detailed description.

Forcing time-series should be kept as short as possible and as complex as needed for optimal computational efficiency.

Value

Modified scenarios

Examples

# constant values will be automatically converted to a data.frame
Lemna_Schmitt() %>% set_forcings(temp=20) -> lemna
lemna@forcings

# setting multiple forcings at once
df <- data.frame(t=0:14, temp=rnorm(15, mean=20)) # random temperature series
Lemna_Schmitt() %>% set_forcings(temp=df, rad=15000) -> lemna
lemna@forcings

# forcings can also be supplied as a named list
Lemna_Schmitt() %>% set_forcings(list(temp=20, rad=15000)) -> lemna
lemna@forcings

Description

The initial state represents the starting values of a scenario's state variables when starting a simulation. A scenario's default initial state may be insufficient to get sensible results.

Usage

set_init(x, init)

## S4 method for signature 'vector'
set_init(x, init)

## S4 method for signature 'EffectScenario'
set_init(x, init)

Arguments

Details

In theory, a scenarios's state variables can be renamed by modifying the names of the initial state vector. However, this is strongly discouraged as this will affect other routines such as effect() and epx() and may render results useless.

Value

modified EffectScenario objects

Examples

# Set initial biomass to 1.0
metsulfuron %>% set_init(c(BM=1.0)) %>% simulate()

Description

Updates the model parameter MoA to a certain value

Usage

set_mode_of_action(x, code)

set_moa(x, code)

Arguments

Value

modified EffectScenario objects

Functions

• set_moa(): Shorthand version

Examples

# Set MoA=8, i.e. hazard during oogenesis
americamysis %>%
  set_mode_of_action(8) %>%
  effect(method="ode45")

# alternative approach using the parameter directly
americamysis %>%
  set_param(c(MoA=8)) %>%
  effect(method="ode45")

Description

The scenarios current exposure is replaced by a constant exposure time-series of value zero(0.0). Output times are unaffected.

Usage

set_noexposure(x)

Arguments

Value

vector of scenarios

Examples

# Derive effect size in sample scenario without toxicant exposure
minnow_it %>%
  set_noexposure() %>%
  effect()

Description

Modifies the parameters of one or more EffectScenario objects.

Usage

set_param(x, param)

## S4 method for signature 'EffectScenario,vector'
set_param(x, param)

## S4 method for signature 'EffectScenario,parameter_set'
set_param(x, param)

## S4 method for signature 'list,parameter_set'
set_param(x, param)

## S4 method for signature 'list,vector'
set_param(x, param)

## S4 method for signature 'ScenarioSequence,vector'
set_param(x, param)

## S4 method for signature 'ScenarioSequence,parameter_set'
set_param(x, param)

Arguments

Details

Most parameters are represented by numerical types but other types are possible depending on model. Please refer to the model description which parameters are required and in which unit. Some or all parameters may be required to start a simulation. If required parameters are missing, simulation will fail with an error message.

Value

Vector of modified objects

Examples

Lemna_Schmitt() %>% set_param(c(Emax=1, EC50=0.12))

Description

Sets the user-defined, custom tag of a scenario. Tags can be helpful to quickly distinguish scenarios of the same model type.

Usage

set_tag(x, tag)

Arguments

Value

(vector of) modified EffectScenario objects

See Also

get_tag()

Examples

# set a custom tag
myscenario <- GUTS_RED_SD() %>% set_tag("My Custom Tag")

# returns `My Custom Tag`
get_tag(myscenario)

# the tag also appears in the scenario overview
myscenario

Description

Minimum and maximum output times define the simulated period for a scenario. Simulation results will be returned for each output time, see simulate().

Usage

set_times(x, times)

Arguments

Details

Be aware that output times may be modified by set_exposure(). Precision of simulation results may be influenced by chosen output times, see simulate() for more information.

Value

Vector of modified ExposureScenario objects

See Also

simulate()

Examples

# Set simulated period to [2,4] with output intervals of length 1
minnow_it %>% set_times(c(2,3,4))

# Decrease output interval length to 0.1
minnow_it %>% set_times(seq(2, 4, 0.1))

Description

A transfer refers to an event where a certain amount of biomass (BM) is moved to a new medium after a period of time. This feature replicates a procedure occurring e.g. in Lemna effect studies and may be necessary to recreate study results.

Usage

set_transfer(x, interval, times, biomass, scaled_comp)

## S4 method for signature 'ANY'
set_transfer(x, interval, times, biomass, scaled_comp)

## S4 method for signature 'Transferable'
set_transfer(x, interval, times, biomass, scaled_comp)

Arguments

Details

Any transfer time point must also be an output time point. If a transfer occurs, simulation results of that time point will report the model state before the transfer. Be aware that in order to use transfers at regular intervals, the simulation must start at time point zero.

Transferred biomass

At each transfer, a defined amount of biomass is transferred to a new medium. This is modeled by interrupting the simulation at a transfer time point, modifying the biomass level BM, and scaling affected compartments according to new biomass levels. Scaling of compartments depending on biomass, such as internal toxicant mass, is necessary to correctly reflect mass balances and concentrations over time.

Transferred biomass is set using the biomass parameter. Is is either a single numerical value in which case the same biomass level is set at each transfer. Or it is a vector of numerical values with the same length as the times parameter in which case a custom biomass level can be set for each transfer. Multiple biomass levels can only be set in conjunction with custom transfer time points.

Some scenario types define default values for transferred biomass based on common study set ups.

Regular and custom transfer time points

Transfers can occur either in regular intervals of time or at selected, custom time points. For regular intervals, the parameter interval is set to a single numeric value which has the same unit as the scenario's time dimension. As an example: if a scenario uses the unit of days for time, the transfer interval is also specified in days:

Transfers occurring at custom time points are set by passing a numerical vector to the parameter times. The time points' units must match with the unit of time in the scenario. A custom transfer time point must not occur at the starting time point of a simulation.

Affected compartments

Some compartments depend on biomass to correctly reflect mass balances and concentrations over time, such as internal toxicant mass. These compartments need to be scaled linearly to reflect the change in biomass levels. The parameter scaled_comp accepts a character vector of compartment names which are scaled at each transfer. This parameter should only be used with custom, user-defined models. If no compartment needs to be scaled, set or use the default value of character(0).

Value

Modified EffectScenario objects

See Also

Lemna_Schmitt()

Examples

# Simulate biomass transfer of 50 *g dw/m²* at a regular interval of 7 *days*
metsulfuron %>%
  set_transfer(interval=7, biomass=50) %>%
  simulate()

# Simulate irregular biomass transfers occuring at days 5, 10, and 12
metsulfuron %>%
  set_transfer(times=c(5,10,12), biomass=50) %>%
  simulate()

# Simulate irregular transfers with changing amounts of transferred biomass
metsulfuron %>%
  set_transfer(times=c(5,10,12), biomass=c(50,20,10)) %>%
  simulate()

Description

Exposure windows are defined as a period of time at the scale of the exposure series. As an example: if an exposure series has an hourly time step, a window length of 24 will consider the exposure within 24 hours intervals for effect calculation. The same applies for the window interval, i.e. the period between considered exposure windows. Set length=-1 to disable moving windows.

Usage

set_window(x, length, interval)

Arguments

Value

modified EffectScenario objects

Examples

# calculate the maximum effect for all windows of 10 days length
metsulfuron %>%
  set_window(length=10, interval=1) %>%
  effect()

Description

The supplied EffectScenario is passed on to the ODE solver for numerical integration. Internally, simulate() is split up into several functions dedicated to particular models, e.g. one for GUTS and one for Lemna type models. The package will take care of using the correct function for each model when simulate() is called.

Usage

simulate(x, ...)

## S4 method for signature 'EffectScenario'
simulate(x, ...)

## S4 method for signature 'Transferable'
simulate(x, ...)

## S4 method for signature 'ScenarioSequence'
simulate(x, ...)

Arguments

Details

Simulation results are returned as a time-series for each state variable. Some models provide additional properties describing the model state, e.g. the internal concentration of a toxicant within the organism. Refer to the respective scenario for more information.

Additional arguments to simulate() will be passed on to deSolve::ode() which enables control of the numerical integration parameters.

Output times and windows

The minimum and maximum of given time points generally define the simulated period. Function argument times overrides settings of the scenario, i.e. time points set in scenario@times. However, the simulation can be limited to a subset of time points by enabling a moving exposure window, see set_window().

Results will be returned for each time point. Precision of the numeric solver may be affected by chosen output times in certain cases. Hence, small deviations in results should be expected if different output times are set. This effect can be mitigated by either defining are sufficiently small time step for the solver using argument hmax or by decreasing the error tolerances atol and rtol. These arguments are passed to the solver, see e.g. deSolve::lsoda() for details.

Optional output variables

Some models support adding intermediary model variables to the return value of simulate(). Analyzing the additional outputs may be helpful to understand model behavior and support finding potential issues in model parameterization.

Optional outputs are enabled by setting the parameter nout to a value greater than zero. If nout is set to n, then the first n optional output columns will be returned along the normal simulation result.

Which optional outputs are available depends on the model/scenario at hand. Please refer to the model documentation for details. As an example, the GUTS-RED-IT model supports adding the external toxicant concentration to the output by setting nout=1:

minnow_it %>% simulate(nout=1)

Numerical precision and stability

Each model was assigned a default ODE solver which handles most of the occurring inputs well. In most cases, this will be an explicit numerical scheme of the Runge-Kutta family with variable step width. For certain extreme parameters settings, such as very high uptake/permeability of the contaminant or exposure series which represent step functions, the numerical approximation might deteriorate and yield invalid results. In this case try to decrease the allowed max step width by setting the argument hmax with various values. Start with hmax=1 and decrease the value by orders of 10. It is not possible or desirable to reduce hmax to extremely small values, as the ODE solver will require more CPU time and simulation will become inefficient.

Oftentimes, it will be computational more efficient to adapt the solver's error tolerances atol and rtol than reducing the step width hmax to achieve stable numerics. Start by decreasing deSolve's default values by orders of ten until the simulation yields acceptable results, see e.g. deSolve::lsoda() for more information on error tolerances.

As an alternative to adapting solver parameters, it might be worthwhile to try other numerical schemes which can handle stiff ODEs, such as Radau, LSODA, or LSODES. To change solvers, set the method argument. To select e.g. the Radau scheme, set method="radau". For LSODA, set method="lsoda". Radau performs better than LSODA in some cases, as the latter method can return biologically nonsensical results without raising an error. See deSolve::ode() for details on available ODE solvers.

Value

A data.frame with the time-series of simulation results

Examples

minnow_sd %>% simulate() # tidy syntax
simulate(minnow_sd) # base R syntax

# Set new output times
minnow_sd %>% simulate(times=c(0,4))

# Modify simulated time frame
minnow_sd %>% simulate(times=c(0,10))

# Use an alternative exposure profile than defined in the scenario
minnow_sd %>% set_exposure(data.frame(t=0,c=10), reset_times=FALSE) %>% simulate()

##
## Precision of results

# A large number of output times forces smaller solver time steps
minnow_it %>% simulate(times=seq(0,1,0.001)) %>% tail()

# Defining only two output times allows for larger solver time steps
minnow_it %>% simulate(times=c(0,1))

# The difference between results can be reduced by limiting the solver's
# maximum step length
minnow_it %>% simulate(times=c(0,1), hmax=0.001)

# The same numerical precision can be achieved by switching to
# the Radau scheme
minnow_it %>% simulate(times=c(0,1), method="radau")

# A very small step length may reduce the difference even further but may
# also exceed the allowed number of steps per output interval. The following
# simulation will be aborted with a solver error:
try(
  minnow_it %>% simulate(times=c(0,1), hmax=0.0001)
)

# However, the solver's max number of allowed steps can be increased:
minnow_it %>% simulate(times=c(0,1), hmax=0.0001, maxsteps=10^5)

Description

An effect scenario contains only one exposure level. Consequently, the simulation of an effect scenario (e.g. metsulfuron %>% simulate will return the results for one exposure level only). However, in a laboratory experiment examining the effects of different exposure levels on a biological system, a batch simulation approach would involve running multiple simulations with varying exposure or treatment conditions. To illustrate, if the objective is to examine the impact of a substance on cell growth, the simulation model could be designed to replicate the cell growth dynamics under varying concentrations of the substance. Each simulation run would represent a specific exposure level, ranging from low to high concentrations of the chemical. To simulate such a laboratory experiment, the simulate_batch function can be used. All exposure series are saved in the treatment argument. The first column contains the time, the second column the concentration, and the third column the trial name (exposure level, e.g. 'T1', 'T2', 'T3').

Usage

simulate_batch(model_base, treatments, param_sample = NULL)

Arguments

Value

a data.frame with simulation results

Examples

exposure <- data.frame(time = Schmitt2013$t,
            conc = Schmitt2013$conc,
           trial = Schmitt2013$ID)

sim_result <- simulate_batch(model_base = metsulfuron,
                            treatments = exposure)

Description

Please refer to the Modeling Howto vignette on how to implement custom models by overloading the solver function.

Usage

solver(scenario, times, ...)

## S4 method for signature 'ANY'
solver(scenario, times, ...)

## S4 method for signature 'GutsRedSd'
solver(scenario, times, ...)

## S4 method for signature 'GutsRedIt'
solver(scenario, times, ...)

## S4 method for signature 'LemnaSchmittScenario'
solver(scenario, times, ...)

## S4 method for signature 'LemnaSetacScenario'
solver(scenario, times, ...)

## S4 method for signature 'MyrioExpScenario'
solver(scenario, times, ...)

## S4 method for signature 'MyrioLogScenario'
solver(scenario, times, ...)

## S4 method for signature 'DebAbj'
solver(scenario, times, ...)

## S4 method for signature 'AlgaeWeberScenario'
solver(
  scenario,
  times,
  approx = c("linear", "constant"),
  f = 1,
  method = "lsoda",
  hmax = 0.1,
  ...
)

## S4 method for signature 'AlgaeTKTDScenario'
solver(
  scenario,
  times,
  approx = c("linear", "constant"),
  f = 1,
  method = "lsoda",
  hmax = 0.1,
  ...
)

## S4 method for signature 'AlgaeSimpleScenario'
solver(
  scenario,
  times,
  approx = c("linear", "constant"),
  f = 1,
  method = "ode45",
  hmax = 0.01,
  ...
)

## S4 method for signature 'DebTox'
solver(
  scenario,
  times,
  approx = c("linear", "constant"),
  f = 1,
  rule = 2,
  method = "ode45",
  ...
)

## S4 method for signature 'DebDaphnia'
solver(scenario, times, ...)

Arguments

Details

Please note that not all solvers support setting the parameters listed here. In addition, some solvers may set reasonable default values for e.g. maximum step length in time, but not all do. Please check the model documentation for details.

Value

data.frame with simulation results

Methods (by class)

• solver(ANY): Default solver, raises an error

• solver(GutsRedSd): Numerically integrates GUTS-RED-SD models

• solver(GutsRedIt): Numerically integrates GUTS-RED-IT models

• solver(LemnaSchmittScenario): Numerically integrates Lemna_Schmitt models

• solver(LemnaSetacScenario): Numerically integrates Lemna_SETAC models

• solver(MyrioExpScenario): Numerically integrates Myrio models

• solver(MyrioLogScenario): Numerically integrates Myrio_log models

• solver(DebAbj): Numerically integrates DEB_abj models

• solver(AlgaeWeberScenario): numerically integrates Algae_Weber models

• solver(AlgaeTKTDScenario): numerically integrates Algae_TKTD models

• solver(AlgaeSimpleScenario): numerically integrates Algae_Simple models

• solver(DebTox): Numerically integrates DEBtox scenarios

• solver(DebDaphnia): (deprecated) Numerically integrates DEBtox_Daphnia scenarios

Description

Deprecated function. Derives the survival rate of individuals for Reduced GUTS models. Was replaced by simulate().

Usage

survival(scenario, ...)

Arguments

Details

The survival rate describes the survival probability at each time point. The function simulates the GUTS scenario and appends a column survival to the simulation result. A value of one (1.0) denotes that all individuals survive. A value of zero (0.0) denotes that no individuals survived.

Only available for Reduced GUTS models, see GUTS-RED-models. The equations were described by EFSA (2018).

Value

a data.frame containing simulation results

References

EFSA PPR Panel (EFSA Panel on Plant Protection Products and their Residues), Ockleford C, Adriaanse P, Berny P, et al., 2018: Scientific Opinion on the state of the art of Toxicokinetic/Toxicodynamic (TKTD) effect models for regulatory risk assessment of pesticides for aquatic organisms. EFSA Journal 2018; 16(8):5377, 188 pp. doi:10.2903/j.efsa.2018.5377

See Also

GUTS-RED-models

Examples

# calculate survival rate
minnow_it %>% survival()

# plot survival over time based on a random exposure profile
minnow_sd %>%
  set_exposure(data.frame(t=1:100, c=runif(100)*10)) %>%
  survival() -> df
plot(df$time, df$survival, "l")

Description

By inheriting from class Transferable, a scenario's behavior can be extended to support transfer and reset of biomass at dedicated points during simulation.

Slots

transfer.times

numeric, vector of time points at which transfers occur, e.g. c(7,10,14)

transfer.interval

numeric, interval length until frond transfer to new medium

transfer.biomass

numeric, amount of biomass transferred to new medium

transfer.comp.biomass

character state variable which describes biomass

transfer.comp.scaled

character vector of state variable which will be scaled 1:1 when biomass is modified, e.g. internal toxicant mass

Biomass transfer

Models supporting biomass transfer can be instructed to move a fixed amount of biomass to a new medium after a period of time. This feature replicates a procedure occurring in e.g. Lemna effect studies and may be necessary to recreate study results.

The biomass transfer feature assumes that always a fixed amount of biomass is transferred. Transfers can occur at any fixed point in time or in regular intervals. During a transfer, the biomass is reset to the transferred amount and additional compartments can be scaled 1:1 accordingly, to e.g. reflect the change in internal toxicant mass when biomass is modified. Transfer settings can be modified using set_transfer().

Any transfer time point must also be an output time point. If a transfer occurs, simulation results of that time point will report the model state before the transfer. Be aware that in order to use transfers at regular intervals, the simulation must start at time point zero.

See Also

set_transfer()

Other scenarios: Algae-models, DEB-models, GUTS-RED-models, Lemna-models, Macrophyte-models, Myriophyllum-models, Scenarios