Effects on biomass

Description

Two endpoints are calculated which describe the effects on biomass:

• BM, percent effect on biomass at the last time step of the simulation

• r, percent effect on the average growth rate of biomass

Usage

effect(...)

## Default S3 method:
effect(init, times, param, envir, duration, ...)

## S3 method for class 'lemna_scenario'
effect(x, init, times, param, envir, duration, ...)

Arguments

Value

numeric, effect on biomass in percent (%) [0,100]

Methods (by class)

• effect(default): All scenario parameters supplied as arguments

• effect(lemna_scenario): Scenario parameters supplied as a lemna_scenario object

Examples

# effects in sample scenario
effect(metsulfuron)

# effects with modified environmental data
myenvir <- metsulfuron$envir
myenvir$tmp <- 20   # increase to 20°C
myenvir$conc <- 0.3  # constant exposure of 0.3 ug/L
effect(metsulfuron, envir=myenvir)

# calculate effects for the first seven days
effect(metsulfuron, duration=7)

A Lemna scenario using FOCUS D1 Ditch environmental conditions

Description

The dataset consists of a named list which contains vectors describing initial state, parameters, output times, and environmental variables of the Lemna model. The scenario represents conditions of the FOCUS D1 Ditch exposure scenario.

Usage

focusd1

Format

An object of class lemna_scenario of length 4.

Details

The scenario will simulate a period of 365 days with hourly outputs, 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.

References

Hommen U., Schmitt W., Heine S., Brock Theo C.M., 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

Examples

# Simulate the example scenario
lemna(focusd1)

A Lemna scenario using FOCUS D2 Ditch environmental conditions

Description

The dataset consists of a named list which contains vectors describing initial state, parameters, output times, and environmental variables of the Lemna model. The scenario represents conditions of the FOCUS D2 Ditch exposure scenario.

Usage

focusd2

Format

An object of class lemna_scenario of length 4.

Details

The scenario will simulate a period of 365 days with hourly outputs, a start population of 100 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.

References

Hommen U., Schmitt W., Heine S., Brock Theo C.M., 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

Examples

# Simulate the example scenario
lemna(focusd2)

A Lemna scenario using FOCUS R3 Stream environmental conditions

Description

The dataset consists of a named list which contains vectors describing initial state, parameters, output times, and environmental variables of the Lemna model. The scenario represents conditions of the FOCUS R3 Stream exposure scenario.

Usage

focusr3

Format

An object of class lemna_scenario of length 4.

Details

The scenario will simulate a period of 365 days with hourly outputs, a start population of 100 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.

References

Hommen U., Schmitt W., Heine S., Brock Theo C.M., 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

Examples

# Simulate the example scenario
lemna(focusr3)

Observed frond numbers reported by Hommen et al. (2015)

Description

The data consists of observed frond numbers from experimental studies for various time points and exposure concentrations. The Lemna population was exposed to constant concentrations of metsulfuron-methyl for two days, followed by twelve days of recovery.

Usage

hommen212

Format

An object of class tbl_df (inherits from tbl, data.frame) with 25 rows and 3 columns.

Details

The dataset was presented in Hommen et al. (2015)], cf. Figure 3, and was included in this package by courtesy of the authors.

References

Hommen U., Schmitt W., Heine S., Brock Theo C.M., 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

Simulate a Lemna scenario

Description

The function numerically integrates the Lemna model using the supplied parameters, environmental factor time series, output time points, and other settings. Numerical integration is handled by deSolve::lsoda() by default which is well suited to handle stiff and non-stiff numerical problems.

Usage

lemna(...)

## Default S3 method:
lemna(
  init = c(BM = 0, M_int = 0),
  times,
  param,
  envir,
  ode_mode = c("r", "c"),
  nout = 2,
  hmax = 0.01,
  ...
)

## S3 method for class 'lemna_scenario'
lemna(x, init, times, param, envir, ...)

Arguments

Value

data.frame with simulation results

Methods (by class)

• lemna(default): All scenario parameters supplied as arguments

• lemna(lemna_scenario): Scenario parameters supplied as a lemna_scenario object

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)

Output times

The function will only return results for the requested time points. The solver may make additional time steps which are not returned, depending on the solver settings such as numerical tolerance. The number of output times and the distance between them can have influence on the numerical precision of results. Please refer to the manual of the deSolve package for more information on that topic.

Parameters

The list of available model parameters, their units, and suggested default values is documented in param_defaults().

Environmental variables

The model requires a time series for each of the five environmental variables For ease of use, a time series can be represented by either a constant numeric value, a data.frame containing a time series, a character string with a path to a CSV file containing a time series, or a function returning a value for a certain time point.

The five environmental variables are as follows:

• conc, Exposure concentration (mass per volume, e.g ug L-1)

• tmp, Temperature (deg C)

• irr, Irradiance (kJ m-2 d-1)

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

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

A data.frame containing a time series must consist of exactly two columns: The first column contains the time in days, the second column the environmental factor in question. The data.frame must contain at least one row. Time points are not required to coincide with the solver's output times but the user should take care that the solver's time step length is sufficiently small so that it can consider the relevant dynamics of the time series. This problem can be avoided by calling the model ODEs implemented in C, see argument ode_mode.

If a string is passed as an environmental factor, the function will interpret the string as a file path and will try to load the contents of a CSV file. The same requirements as for a data.frame apply to a time series loaded from a file.

When using the pure R code ODE, it is also possible to pass a function as an environmental factor. The function must accept exactly one argument which represents time and must return a single scalar value. Using a function in combination with the compiled code solver will raise an error.

R vs. compiled code

The model can be simulated using pure R code (the default) or an implementation that uses the compiled code feature of deSolve. Compiled code is almost always significantly faster than pure R. The solver for compiled ODEs also handles environmental variables better than the pure R version. For optimal performance, the time series of environmental variables should always be as short as possible and as long as needed.

To use the compiled code feature, set the argument ode_mode = "c".

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 compiled code model can return up to 18 additional variables which represent intermediary variables, environmental variables, and derivatives calculated within the model equations. Please refer to the model description of Klein et al. for more information on these variables and how they influence model behavior.

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)

References

Klein J., Cedergreen N., Heine S., Kehrein N., Reichenberger S., Rendal C., Schmitt W., Hommen U., 2022: Refined description of the Lemna TKTD growth model based on Schmitt et al. (2013) – equation system and default parameters, implementation in R. Report of the working group Lemna of the SETAC Europe Interest Group Effect Modeling. Version 1.1, uploaded on 09 May 2022. https://www.setac.org/group/effect-modeling.html

Examples

# Simulate the metsulfuron example scenario
lemna(metsulfuron)

# Create a simple plot of the number of fronds
lemna(metsulfuron) -> result
plot(result$time, result$FrondNo)

# Create a nicer plot using a dedicated plotting routine
plot(result)

# Simulate the example scenario for a period of 30 days
lemna(metsulfuron, times=0:30) -> result30
plot(result30)

##
## Create a custom Lemna scenario from scratch
##

# Initial state: 12 fronds, no toxicant mass
myinit <- c(BM=0.0012, M_int=0)

# Output times: simulate 7 days with a ~2 hour time step
mytime <- seq(0, 7, 0.1)

# Default model parameters + TKTD parameters of a hypothetical substance
myparam <- param_defaults(list(
  EC50_int = 0.1, # 50% effect level (ug L-1)
  b = 0.7,        # slope parameter (-)
  P = 0.01        # permeability (cm d-1)
))

# Custom environmental variables
myenvir <- list(
  # exposure step function:
  # 3 days no exposure, followed by 4 days of 10 ug L-1
  conc = data.frame(t=c(0,3,4,7), conc=c(0,0,10,10)),
  tmp = 18,    # constant temperature of 18 °C
  irr = 15000, # constant irradiance of 15,000 kJ m-2 d-1
  N = 0.6,     # constant Nitrogen concentration of 0.6 mg L-1
  P = 0.3      # constant Phosphorus concentration of 0.3 mg L-1
)

# Simulate the custom scenario and plot results
lemna(init=myinit, times=mytime, param=myparam, envir=myenvir) -> result_custom
plot(result_custom)

# Simulate again, forcing the solver to use smaller time steps of hmax=0.001.
# The resulting curves are almost identical for this example.
lemna(init=myinit, times=mytime, param=myparam, envir=myenvir, hmax=0.001) -> result_custom2
library(ggplot2)
ggplot(result_custom, aes(time, FrondNo)) +
  geom_line() +
  geom_line(data=result_custom2, color="red", style="dashed")

# Combine all settings into a scenario object and simulate it
scenario <- new_lemna_scenario(
 init = myinit,
 param = myparam,
 times = mytime,
 envir = myenvir
)
lemna(scenario)

Access to the ODE solver

Description

This function can be used by external packages to access the ODE implemented in C without the surrounding sanity checks and data loading procedures. All parameters will be passed on to the solver.

Usage

lemna_desolve(...)

Arguments

Value

result from deSolve::ode()

A Lemna scenario fitted to metsulfuron-methyl effect data

Description

The dataset consists of a named list which contains vectors describing initial state, parameters, output times, and environmental variables of the Lemna model.

Usage

metsulfuron

Format

An object of class lemna_scenario of length 4.

Details

The scenario will simulate a period of 14 days with daily outputs, a start population of 12 fronds, unlimited growth conditions, and an exposure pattern represented by a step-function.

The scenario setup was published by Schmitt et al. (2013). A mechanistic combined toxicokinetic-toxicodynamic (TK/TD) and growth model for the aquatic macrophytes Lemna spp. was parameterized by the authors based on literature data. TK/TD parameters were determined by calibrating the model using substance specific effect data of metsulfuron-methyl.

References

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

Examples

# Simulate the example scenario
lemna(metsulfuron)

# Simulate a longer time period of 21 days
lemna(metsulfuron, times=0:21)

# Print the scenario's exposure series
metsulfuron$envir$conc

# Print all environmental variables
metsulfuron$envir

Lemna scenario constructor

Description

Lemna scenario constructor

Usage

new_lemna_scenario(
  init = c(BM = 0, M_int = 0),
  times = c(),
  param = list(),
  envir = list()
)

Arguments

Value

a lemna_scenario object

Default parameters

Description

Returns the default Lemna model parameters as reported by Klein et al. (2022).

Usage

param_defaults(values)

param_new(values)

Arguments

Details

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_min, Threshold density for setting dBM/dt to zero (g dw m-2)

Temperature response of photosynthesis

• T_opt, Optimum growth temperature (deg C)

• T_min, Minimum growth temperature (deg C)

• T_max, Maximum growth temperature (deg 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 (mass per volume)

• 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)

Model changes

• lemna version 1.0.2 The default value of parameter beta is set to 0.25. This reflects the changes made to the (upcoming) SETAC working group report version 1.2.

Value

named list

Functions

• param_new(): A parameter set without default values

References

Klein J., Cedergreen N., Heine S., Kehrein N., Reichenberger S., Rendal C., Schmitt W., Hommen U., 2022: Refined description of the Lemna TKTD growth model based on Schmitt et al. (2013) – equation system and default parameters, implementation in R. Report of the working group Lemna of the SETAC Europe Interest Group Effect Modeling. Version 1.1, uploaded on 09 May 2022. https://www.setac.org/group/effect-modeling.html

Examples

# Returns default model parameters, some parameters are not defined (NA)
param_defaults()

# Overwrite one of the default parameters
param_defaults(list(k_photo_max = 0.42))

# Provide values for substance specific TKTD parameters
param_defaults(list(
  EC50_int = 23, # 50% effect level (mass per volume)
  b = 1,         # slope parameter (-)
  P = 0.42       # permeability (cm d-1)
))

# Returns a list of required model parameters with all values set to NA
param_new()

Plot a Lemna scenario result

Description

Creates up to four plots in a gridded layout depicting

1. Exposure (i.e. external) concentration, as well as damage (internal concentration, C_int) if available

2. Internal toxicant mass (M_int)

3. Population size as biomass (BM)

4. Population size as number of fronds (FrondNo) if available

Usage

## S3 method for class 'lemna_result'
plot(x, y, munit = "ug/m2", cunit = "ug/L", legend = TRUE, ...)

Arguments

Value

a gridded plot

Examples

# Simulate a sample scenario and plot results
result <- lemna(metsulfuron)
plot(result)

# Hide the legend of the concentration plot
plot(result, legend=FALSE)

# Simulate and plot a scenario with changing environmental conditions
plot(lemna(focusd1))

Observed frond numbers reported by Schmitt et al. (2013)

Description

The data consists of observed frond numbers from experimental studies for various time points and exposure concentrations. The Lemna population was exposed to constant concentrations of metsulfuron-methyl for seven days, followed by seven days of recovery.

Usage

schmitt77

Format

An object of class tbl_df (inherits from tbl, data.frame) with 49 rows and 3 columns.

Details

The dataset was presented in Schmitt et al. (2013), cf. Figure 2, and was included in this package by courtesy of the authors.

References

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