Nothing
Introduction to the Lemna package
In lemna: Lemna Ecotox Effect Model
knitr::opts_chunk$set(
collapse = TRUE,
comment = "#>",
fig.width = 7.2,
fig.height = 5,
fig.align = "center"
)
# do not build vignette on package checks
is_check <- ("CheckExEnv" %in% search()) || any(c("_R_CHECK_TIMINGS_",
"_R_CHECK_LICENSE_") %in% names(Sys.getenv()))
knitr::opts_chunk$set(eval = !is_check)
The lemna package provides model equations and some useful helpers to
simulate the growth of Lemna (duckweed) aquatic plant populations.
Lemna is a standard test macrophyte used in ecotox effect studies. The
model was described and published by the SETAC Europe Interest Group Effect
Modeling (Klein et al. 2022).
The model's main state variable is biomass, or BM for short, of the simulated
Lemna population. Growth of Lemna is influenced by environmental variables
such as temperature, irradiation, nutrient concentrations, population density,
and toxicant concentration in the surrounding medium. To consider the influence
of toxicants on the plants, a one-compartment model was assumed by the authors for the
mass-balance of internal toxicant mass. The total amount of internal toxicant
mass is represented by state-variable M_int. The
combination of state variables BM and M_int fully describe the state of the
model system at any point in time.
To simulate a Lemna population, one has to define a scenario that consists
of the following data:
- Initial system state
- A time period to simulate
- Model parameters
- Environmental variables
How these scenario elements are represented and which values are chosen depends
on what one would like to achieve. Simulating the growth of Lemna in a controlled
lab environment will likely require different inputs than Lemna growing in an outdoor
water body, for example.
Core functions
To make functions and sample datasets of the lemna package available in your
R workspace, load the library first:
library(lemna)
The package function param_defaults() provides a list with all suggested
default parameters. Some parameter values will be missing, i.e.
set to NA, because they are substance specific and default values would not
be meaningful for these:
# get list of default parameters
params <- param_defaults()
params$k_photo_max
params$EC50_int # substance specific
# get default parameters and set a custom parameter value
myparam <- param_defaults(c(EC50_int = 42))
myparam$EC50_int
The growth of a Lemna population is simulated using the lemna() function.
The required scenario data are either supplied individually on function call
or are passed as a pre-defined scenario object, such as the metsulfuron sample
scenario:
lemna(metsulfuron)
lemna() returns a table which describes the change of state variables over time.
In addition, some supporting derived variables such as internal toxicant concentration
(C_int) and the number of fronds (FrondNo) will be returned by default.
A visual description of the simulated scenario and its results can be created
by running the plot() function. The plot() function requires a simulation result
as its first argument:
plot(lemna(metsulfuron))
The effect of the toxicant on the Lemna population can be calculated using
the effect() function. It requires scenario data the same way as lemna()
does. For the sample metsulfuron scenario, the effects of the toxicant
are as follows:
effect(metsulfuron)
In this scenario, exposure to the toxicant resulted in an 93% decrease of
population size (BM) and a 46% decrease in average growth rate (r) until the
end of the simulation. Effects are always calculated relative to an identical
control scenario which contains no toxicant exposure.
For more information on the metsulfuron sample scenario, please refer to the
help files:
?metsulfuron
Tutorial
Simulate the Lemna growth model
To simulate a Lemna population, one has to pass the four mandatory scenario
elements to the lemna() function:
# initial state of the model system: 1.0 g dw biomass, 0.0 ug/m2 internal toxicant
myinit <- c(BM=1, M_int=0)
# simulated period and output time points: each day for 7 days
mytimes <- 0:7
# default model parameters + substance specific values
myparam <- param_defaults(c(
EC50_int = 4.16,
b = 0.3,
P = 0.0054
))
# constant environmental conditions, including exposure
myenvir <- list(
tmp = 18, # 18 °C ambient temperature
irr = 15000, # 15,000 kJ m-2 d-1 irradiance
P = 0.3, # 0.3 mg L-1 Phosphorus concentration
N = 0.6, # 0.6 mg L-1 Nitrogen concentration
conc = 1 # 1 ug/L toxicant concentration
)
lemna(
init = myinit,
times = mytimes,
param = myparam,
envir = myenvir
)
The init argument controls at which system state the simulation starts. The
times argument defines the length of the simulated period and for which
time points results are returned. The temporal resolution of results can be increased
by specifying additional output times:
simresult <- lemna(
init = myinit,
times = seq(0, 7, 0.1), # a step length of 0.1 days = ~2 hours
param = myparam,
envir = myenvir
)
tail(simresult)
The resulting table now contains ten times as much rows because we decreased the
step length by a factor of ten but simulated the same period, i.e. seven days.
It can be observed that the state-variables differ slightly at the end of the
simulation although the scenarios were otherwise identical. The differences
originate from small numerical errors introduced by the solver of the model's
Ordinary Differential Equations (ODE). The step-length in time can have influence on
the precision of simulation results. To decrease the solver's step length
without increasing the number of result time points, make use of the optional
argument hmax. The smaller hmax, the more precise the results:
# hmax=0.01 forces a maximum step length of 0.01 days = ~15 minutes
lemna(myinit, mytimes, myparam, myenvir, hmax = 0.01)
By default, simulation results contain supporting variables such as
internal toxicant concentration and total frond number. These are calculated
from simulation results and model parameters for reasons of convenience. If these
variables are not required, they can be disabled by setting the optional argument
nout = 0:
lemna(myinit, mytimes, myparam, myenvir, nout = 0)
Using environmental time-series
The previous examples mostly assumed that environmental variables stay constant in time.
To simulate a scenario with changing environmental variables, such as a temperature
curve or exposure pattern, one has to define or load a data time-series. The model
accepts time-series for all environmental variables, i.e. exposure concentration,
temperature, irradiation, phosphorus concentration, and nitrogen concentration.
Within the scope of this package, time-series are represented by a
data.frame containing exactly two numerical columns: the first column for time, the second
for the variable's value. The column names are irrelevant but sensible names may
help documenting the data. As an example, the metsulfuron sample scenario
contains a step-function as its exposure time-series: seven days of
1 ug/L metsulfuron-methyl starting at time point zero (0.0), followed
by seven days of recovery (no exposure).
metsulfuron$envir$conc
Time points of the time-series and time points processed by the ODE solver
may not always match. To derive environmental variable values which are not
explicitly part of the time-series, variable values are interpolated with a linear
function.
If the time-series does not cover the full simulation period, the closest
value from the time-series is used. In the case of the metsulfuron sample
scenario, the step function will effectively extend to infinity, i.e. any time
point before day 7.0 will have 1 ug/L of exposure and any time point after
7.01 will have no exposure.
As an example, we will modify the metsulfuron sample scenario to use an
exposure time-series that declines linearly between start and day seven:
# define start and end points for the exposure series, the values
# in between will be interpolated
myexpo <- data.frame(time=c(0, 7), conc=c(1, 0))
# modify the sample scenario's exposure series
myenvir <- metsulfuron$envir
myenvir$conc <- myexpo
# simulate the sample scenario with modified environmental variables
plot(lemna(metsulfuron, envir=myenvir))
Time-series and data.frame objects can be stored conveniently as .csv files
which can be created and edited by common spreadsheet programs such as Microsoft
Excel. Be aware that the separator character used by R and your spreadsheet
program may differ depending on your computer's locale settings.
set.seed(23)
# define a random time-series, values will be uniformly distributed between
# the values 0.1 and 3.0, e.g to represent an exposure time-series
myexpo <- data.frame(time = 0:14,
conc = round(runif(15, 0.1, 3.0), 1))
# plot the time-series
plot(myexpo, main="Random exposure time-series")
lines(myexpo)
# write data to .csv file in working directory
write.csv(myexpo, file="random_series.csv", row.names=FALSE)
# write data using semicolons as separating character
write.csv2(myexpo, file="random_series2.csv", row.names=FALSE)
# read file from working directory
myimport <- read.csv(file="random_series.csv")
# check that written and read data are identical
myexpo$conc == myimport$conc
Time-series can be imported manually as in the previous example or they can be
imported automatically by the lemna() function for convenience. If an
environmental variable is set to a string, it will be interpreted as a file path
and lemna() will try to import the time-series using read.csv():
# automatically load the exposure time-series from a file
myenvir <- metsulfuron$envir
myenvir$conc <- "random_series.csv"
# simulate the sample scenario with the exposure series loaded from a .csv file
plot(lemna(metsulfuron, envir=myenvir), legend=FALSE)
# clean up vignette directory
file.remove("random_series.csv")
file.remove("random_series2.csv")
For a more complex scenario that uses hourly and daily time-series of
exposure and temperature/irradiance, respectively, please have a look at
e.g. the focusd1 scenario:
myenvir <- focusd1$envir
myenvir$conc
myenvir$tmp
myenvir$irr
Using simulation results
Simulation results are returned as a table, i.e. a data.frame object. The table
will contain the state variables biomass (BM) and internal toxicant mass (M_int)
for each requested output time point. The table may also contain additional
columns for other supporting variables. The
data can be processed like any other dataset in R to e.g. create plots, derive
other values, or to perform statistical tests:
myresult <- lemna(focusd1)
head(myresult)
To get an initial impression of a scenario and its results, simply pass the
simulation result to the plot() function:
plot(myresult)
As an example, we will analyze if and how the internal toxicant concentration
(C_int) correlates with the internal toxicant mass (M_int):
summary(lm(C_int ~ M_int, myresult))
The linear model indicates a strong correlation of internal toxicant mass
and concentration which intuitively makes sense. The correlation is not a
100% because biomass is a confounding factor in the model equations.
Derive effect endpoints
To quantify the influence a toxicant exerts on a Lemna population, use the
effect() function. It works similar to lemna() and accepts the same
arguments in order to specify a scenario:
# calculate effects on biomass in sample scenario
effect(metsulfuron)
The return values describe the effect in percent (%) on the respective effect
endpoint. Effects are calculated relative to a control scenario which exhibits
no exposure. By default, the effect refers to the reduction in biomass (BM) or
average growth rate (r) at the end of the simulation. In the example above,
biomass was reduced by 93% and the growth rate was reduced by 46% in the Lemna
population due to exposure to the toxicant.
If a scenario covers a long time period but effects are desired for an earlier
time point, the scenario can be cut short by using the duration argument.
If duration is set, the scenario will be clipped to the time period from t0
to t0 + duration:
# calculate effects on biomass after 7 days, instead of 14
effect(metsulfuron, duration=7)
In this example, the effect on biomass is smaller after 7 days compared to the
effects after 14 days. However, the average growth rate experienced a strong decrease
from 46 to 71%.
Create scenario objects
A Lemna growth scenario consists of the following four mandatory scenario
elements: model parameters, environmental variables, initial state, and output times.
The elements can be passed to lemna() and effect() separately or they can be
combined to a compact scenario object. All sample scenarios which were
used in this tutorial are scenario objects:
# list properties of the sample scenario object
metsulfuron
Scenario objects are basically just a base R list object with some additional
metadata. If correctly defined, scenario objects fully describe a scenario and
can be passed to e.g. lemna() without additional arguments. It is, however,
possible to override a scenario object's data by passing an alternative
dataset:
# custom output times and time period:
# four days with a 12 hour time step
mytimes <- seq(0, 4, 0.5)
# simulate sample scenario with custom output times & period
lemna(metsulfuron, times=mytimes)
A custom scenario object can be created by passing the scenario elements to
new_lemna_scenario():
myscenario <- new_lemna_scenario(
init = c(BM=1, M_int=0),
times = 0:7,
param = param_defaults(c(EC50_int = 4.16, b = 0.3, P = 0.0054)),
envir = list(
tmp = 18, # 18 °C ambient temperature
irr = 15000, # 15,000 kJ m-2 d-1 irradiance
P = 0.3, # 0.3 mg L-1 Phosphorus concentration
N = 0.6, # 0.6 mg L-1 Nitrogen concentration
conc = 1 # 1 ug/L toxicant concentration
)
)
lemna(myscenario)
Speed up simulations with compiled code
The Lemna growth model is simulated by default using model equations
implemented in pure R. In case many simulations have to be conducted
or the time required to get results becomes an issue, the compiled code
feature can be used. The lemna package provides an alternative implementation
of the Klein et al. model equations using C code. The C code
executes significantly faster than the pure R alternative.
# use model implemented in pure R
tail(lemna(metsulfuron, ode_mode="r"), n = 1)
# use model implemented in C
tail(lemna(metsulfuron, ode_mode="c"), n = 1)
Simulation results of R and C code will be identical as far as numerical
precision allows. The speed increase of using C will range from a factor
of 3 to 5 for short scenarios and up to 50+ for longer scenarios:
# Benchmark the shorter metsulfuron scenario
microbenchmark::microbenchmark(
lemna(metsulfuron, ode_mode="r"),
lemna(metsulfuron, ode_mode="c")
)
# Benchmark the more complex and longer focusd1 scenario
microbenchmark::microbenchmark(
lemna(focusd1, ode_mode="r"),
lemna(focusd1, ode_mode="c"),
times = 10
)
There is however a small disadvantage to using the C model: if there are
any issues stemming from, for example, invalid parameters, the error messages
raised by the C code might be less descriptive than those from R.
On the other hand, the C code can output on demand almost all intermediary model
variables which can support debugging and model understanding:
# simulate and request all additional output variables
lemna(metsulfuron, ode_mode="c", nout=18)
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
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knitr::opts_chunk$set( collapse = TRUE, comment = "#>", fig.width = 7.2, fig.height = 5, fig.align = "center" ) # do not build vignette on package checks is_check <- ("CheckExEnv" %in% search()) || any(c("_R_CHECK_TIMINGS_", "_R_CHECK_LICENSE_") %in% names(Sys.getenv())) knitr::opts_chunk$set(eval = !is_check)
The lemna package provides model equations and some useful helpers to simulate the growth of Lemna (duckweed) aquatic plant populations. Lemna is a standard test macrophyte used in ecotox effect studies. The model was described and published by the SETAC Europe Interest Group Effect Modeling (Klein et al. 2022).
The model's main state variable is biomass, or BM for short, of the simulated
Lemna population. Growth of Lemna is influenced by environmental variables
such as temperature, irradiation, nutrient concentrations, population density,
and toxicant concentration in the surrounding medium. To consider the influence
of toxicants on the plants, a one-compartment model was assumed by the authors for the
mass-balance of internal toxicant mass. The total amount of internal toxicant
mass is represented by state-variable M_int. The
combination of state variables BM and M_int fully describe the state of the
model system at any point in time.
To simulate a Lemna population, one has to define a scenario that consists of the following data:
- Initial system state
- A time period to simulate
- Model parameters
- Environmental variables
How these scenario elements are represented and which values are chosen depends on what one would like to achieve. Simulating the growth of Lemna in a controlled lab environment will likely require different inputs than Lemna growing in an outdoor water body, for example.
Core functions
To make functions and sample datasets of the lemna package available in your R workspace, load the library first:
library(lemna)
The package function param_defaults() provides a list with all suggested
default parameters. Some parameter values will be missing, i.e.
set to NA, because they are substance specific and default values would not
be meaningful for these:
# get list of default parameters params <- param_defaults() params$k_photo_max params$EC50_int # substance specific # get default parameters and set a custom parameter value myparam <- param_defaults(c(EC50_int = 42)) myparam$EC50_int
The growth of a Lemna population is simulated using the lemna() function.
The required scenario data are either supplied individually on function call
or are passed as a pre-defined scenario object, such as the metsulfuron sample
scenario:
lemna(metsulfuron)
lemna() returns a table which describes the change of state variables over time.
In addition, some supporting derived variables such as internal toxicant concentration
(C_int) and the number of fronds (FrondNo) will be returned by default.
A visual description of the simulated scenario and its results can be created
by running the plot() function. The plot() function requires a simulation result
as its first argument:
plot(lemna(metsulfuron))
The effect of the toxicant on the Lemna population can be calculated using
the effect() function. It requires scenario data the same way as lemna()
does. For the sample metsulfuron scenario, the effects of the toxicant
are as follows:
effect(metsulfuron)
In this scenario, exposure to the toxicant resulted in an 93% decrease of
population size (BM) and a 46% decrease in average growth rate (r) until the
end of the simulation. Effects are always calculated relative to an identical
control scenario which contains no toxicant exposure.
For more information on the metsulfuron sample scenario, please refer to the
help files:
?metsulfuron
Tutorial
Simulate the Lemna growth model
To simulate a Lemna population, one has to pass the four mandatory scenario
elements to the lemna() function:
# initial state of the model system: 1.0 g dw biomass, 0.0 ug/m2 internal toxicant myinit <- c(BM=1, M_int=0) # simulated period and output time points: each day for 7 days mytimes <- 0:7 # default model parameters + substance specific values myparam <- param_defaults(c( EC50_int = 4.16, b = 0.3, P = 0.0054 )) # constant environmental conditions, including exposure myenvir <- list( tmp = 18, # 18 °C ambient temperature irr = 15000, # 15,000 kJ m-2 d-1 irradiance P = 0.3, # 0.3 mg L-1 Phosphorus concentration N = 0.6, # 0.6 mg L-1 Nitrogen concentration conc = 1 # 1 ug/L toxicant concentration ) lemna( init = myinit, times = mytimes, param = myparam, envir = myenvir )
The init argument controls at which system state the simulation starts. The
times argument defines the length of the simulated period and for which
time points results are returned. The temporal resolution of results can be increased
by specifying additional output times:
simresult <- lemna( init = myinit, times = seq(0, 7, 0.1), # a step length of 0.1 days = ~2 hours param = myparam, envir = myenvir ) tail(simresult)
The resulting table now contains ten times as much rows because we decreased the
step length by a factor of ten but simulated the same period, i.e. seven days.
It can be observed that the state-variables differ slightly at the end of the
simulation although the scenarios were otherwise identical. The differences
originate from small numerical errors introduced by the solver of the model's
Ordinary Differential Equations (ODE). The step-length in time can have influence on
the precision of simulation results. To decrease the solver's step length
without increasing the number of result time points, make use of the optional
argument hmax. The smaller hmax, the more precise the results:
# hmax=0.01 forces a maximum step length of 0.01 days = ~15 minutes lemna(myinit, mytimes, myparam, myenvir, hmax = 0.01)
By default, simulation results contain supporting variables such as
internal toxicant concentration and total frond number. These are calculated
from simulation results and model parameters for reasons of convenience. If these
variables are not required, they can be disabled by setting the optional argument
nout = 0:
lemna(myinit, mytimes, myparam, myenvir, nout = 0)
Using environmental time-series
The previous examples mostly assumed that environmental variables stay constant in time. To simulate a scenario with changing environmental variables, such as a temperature curve or exposure pattern, one has to define or load a data time-series. The model accepts time-series for all environmental variables, i.e. exposure concentration, temperature, irradiation, phosphorus concentration, and nitrogen concentration.
Within the scope of this package, time-series are represented by a
data.frame containing exactly two numerical columns: the first column for time, the second
for the variable's value. The column names are irrelevant but sensible names may
help documenting the data. As an example, the metsulfuron sample scenario
contains a step-function as its exposure time-series: seven days of
1 ug/L metsulfuron-methyl starting at time point zero (0.0), followed
by seven days of recovery (no exposure).
metsulfuron$envir$conc
Time points of the time-series and time points processed by the ODE solver
may not always match. To derive environmental variable values which are not
explicitly part of the time-series, variable values are interpolated with a linear
function.
If the time-series does not cover the full simulation period, the closest
value from the time-series is used. In the case of the metsulfuron sample
scenario, the step function will effectively extend to infinity, i.e. any time
point before day 7.0 will have 1 ug/L of exposure and any time point after
7.01 will have no exposure.
As an example, we will modify the metsulfuron sample scenario to use an
exposure time-series that declines linearly between start and day seven:
# define start and end points for the exposure series, the values # in between will be interpolated myexpo <- data.frame(time=c(0, 7), conc=c(1, 0)) # modify the sample scenario's exposure series myenvir <- metsulfuron$envir myenvir$conc <- myexpo # simulate the sample scenario with modified environmental variables plot(lemna(metsulfuron, envir=myenvir))
Time-series and data.frame objects can be stored conveniently as .csv files
which can be created and edited by common spreadsheet programs such as Microsoft
Excel. Be aware that the separator character used by R and your spreadsheet
program may differ depending on your computer's locale settings.
set.seed(23) # define a random time-series, values will be uniformly distributed between # the values 0.1 and 3.0, e.g to represent an exposure time-series myexpo <- data.frame(time = 0:14, conc = round(runif(15, 0.1, 3.0), 1)) # plot the time-series plot(myexpo, main="Random exposure time-series") lines(myexpo) # write data to .csv file in working directory write.csv(myexpo, file="random_series.csv", row.names=FALSE) # write data using semicolons as separating character write.csv2(myexpo, file="random_series2.csv", row.names=FALSE) # read file from working directory myimport <- read.csv(file="random_series.csv") # check that written and read data are identical myexpo$conc == myimport$conc
Time-series can be imported manually as in the previous example or they can be
imported automatically by the lemna() function for convenience. If an
environmental variable is set to a string, it will be interpreted as a file path
and lemna() will try to import the time-series using read.csv():
# automatically load the exposure time-series from a file myenvir <- metsulfuron$envir myenvir$conc <- "random_series.csv" # simulate the sample scenario with the exposure series loaded from a .csv file plot(lemna(metsulfuron, envir=myenvir), legend=FALSE)
# clean up vignette directory file.remove("random_series.csv") file.remove("random_series2.csv")
For a more complex scenario that uses hourly and daily time-series of
exposure and temperature/irradiance, respectively, please have a look at
e.g. the focusd1 scenario:
myenvir <- focusd1$envir myenvir$conc myenvir$tmp myenvir$irr
Using simulation results
Simulation results are returned as a table, i.e. a data.frame object. The table
will contain the state variables biomass (BM) and internal toxicant mass (M_int)
for each requested output time point. The table may also contain additional
columns for other supporting variables. The
data can be processed like any other dataset in R to e.g. create plots, derive
other values, or to perform statistical tests:
myresult <- lemna(focusd1) head(myresult)
To get an initial impression of a scenario and its results, simply pass the
simulation result to the plot() function:
plot(myresult)
As an example, we will analyze if and how the internal toxicant concentration
(C_int) correlates with the internal toxicant mass (M_int):
summary(lm(C_int ~ M_int, myresult))
The linear model indicates a strong correlation of internal toxicant mass and concentration which intuitively makes sense. The correlation is not a 100% because biomass is a confounding factor in the model equations.
Derive effect endpoints
To quantify the influence a toxicant exerts on a Lemna population, use the
effect() function. It works similar to lemna() and accepts the same
arguments in order to specify a scenario:
# calculate effects on biomass in sample scenario effect(metsulfuron)
The return values describe the effect in percent (%) on the respective effect
endpoint. Effects are calculated relative to a control scenario which exhibits
no exposure. By default, the effect refers to the reduction in biomass (BM) or
average growth rate (r) at the end of the simulation. In the example above,
biomass was reduced by 93% and the growth rate was reduced by 46% in the Lemna
population due to exposure to the toxicant.
If a scenario covers a long time period but effects are desired for an earlier
time point, the scenario can be cut short by using the duration argument.
If duration is set, the scenario will be clipped to the time period from t0
to t0 + duration:
# calculate effects on biomass after 7 days, instead of 14 effect(metsulfuron, duration=7)
In this example, the effect on biomass is smaller after 7 days compared to the effects after 14 days. However, the average growth rate experienced a strong decrease from 46 to 71%.
Create scenario objects
A Lemna growth scenario consists of the following four mandatory scenario
elements: model parameters, environmental variables, initial state, and output times.
The elements can be passed to lemna() and effect() separately or they can be
combined to a compact scenario object. All sample scenarios which were
used in this tutorial are scenario objects:
# list properties of the sample scenario object
metsulfuron
Scenario objects are basically just a base R list object with some additional
metadata. If correctly defined, scenario objects fully describe a scenario and
can be passed to e.g. lemna() without additional arguments. It is, however,
possible to override a scenario object's data by passing an alternative
dataset:
# custom output times and time period: # four days with a 12 hour time step mytimes <- seq(0, 4, 0.5) # simulate sample scenario with custom output times & period lemna(metsulfuron, times=mytimes)
A custom scenario object can be created by passing the scenario elements to
new_lemna_scenario():
myscenario <- new_lemna_scenario( init = c(BM=1, M_int=0), times = 0:7, param = param_defaults(c(EC50_int = 4.16, b = 0.3, P = 0.0054)), envir = list( tmp = 18, # 18 °C ambient temperature irr = 15000, # 15,000 kJ m-2 d-1 irradiance P = 0.3, # 0.3 mg L-1 Phosphorus concentration N = 0.6, # 0.6 mg L-1 Nitrogen concentration conc = 1 # 1 ug/L toxicant concentration ) ) lemna(myscenario)
Speed up simulations with compiled code
The Lemna growth model is simulated by default using model equations implemented in pure R. In case many simulations have to be conducted or the time required to get results becomes an issue, the compiled code feature can be used. The lemna package provides an alternative implementation of the Klein et al. model equations using C code. The C code executes significantly faster than the pure R alternative.
# use model implemented in pure R tail(lemna(metsulfuron, ode_mode="r"), n = 1) # use model implemented in C tail(lemna(metsulfuron, ode_mode="c"), n = 1)
Simulation results of R and C code will be identical as far as numerical precision allows. The speed increase of using C will range from a factor of 3 to 5 for short scenarios and up to 50+ for longer scenarios:
# Benchmark the shorter metsulfuron scenario microbenchmark::microbenchmark( lemna(metsulfuron, ode_mode="r"), lemna(metsulfuron, ode_mode="c") ) # Benchmark the more complex and longer focusd1 scenario microbenchmark::microbenchmark( lemna(focusd1, ode_mode="r"), lemna(focusd1, ode_mode="c"), times = 10 )
There is however a small disadvantage to using the C model: if there are any issues stemming from, for example, invalid parameters, the error messages raised by the C code might be less descriptive than those from R. On the other hand, the C code can output on demand almost all intermediary model variables which can support debugging and model understanding:
# simulate and request all additional output variables lemna(metsulfuron, ode_mode="c", nout=18)
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
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