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.
Lemna_SETAC()an S4 object of type LemnaSetac
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)
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)
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.
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.
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 (-)
Response functions
nout >= 3: f_loss, respiration dependency function (-)
nout >= 4: f_photo, photosynthesis dependency function (-)
nout >= 5: fT_photo, temperature response of photosynthesis (-)
nout >= 6: fI_photo, irradiance response of photosynthesis (-)
nout >= 7: fP_photo, phosphorus response of photosynthesis (-)
nout >= 8: fN_photo, nitrogen response of photosynthesis (-)
nout >= 9: fBM_photo, density response of photosynthesis (-)
nout >= 10: fCint_photo, concentration response of photosynthesis (-)
Environmental variables
nout >= 11: C_int_unb, unbound internal concentration (mass per volume)
nout >= 12: C_ext, external concentration (mass per volume)
nout >= 13: Tmp, temperature (deg C)
nout >= 14: Irr, irradiance (kJ m-2 d-1)
nout >= 15: Phs, Phosphorus concentration (mg P L-1)
nout >= 16: Ntr, Nitrogen concentration (mg N L-1)
Derivatives
nout >= 17: dBM, biomass derivative (g dw m-2 d-1)
nout >= 18: dM_int, mass of toxicant in plants derivative (mass per m2 d-1)
The arguments to ODE solver deSolve::ode() control how model equations
are numerically integrated. The settings influence stability of the numerical
integration scheme as well as numerical precision of model outputs. Generally, the
default settings as defined by deSolve are used, but all deSolve settings
can be modified in cvasi workflows by the user, if needed. Please refer
to e.g. simulate() on how to pass arguments to deSolve in cvasi
workflows.
Some default settings of deSolve were adapted for this model by expert judgement to enable precise, but also computationally efficient, simulations for most model parameters. These settings can be modified by the user, if needed:
hmax = 0.1
Maximum step length in time suitable for most simulations.
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().
If a transfer occurs, simulation results of that time point will report the model state
before the transfer. Be aware that if transfers are defined using the
interval argument, the transfers will always occur relative to time point
zero (t = 0). As an example, setting a regular transfer of seven days,
interval = 7, will result at transfers occurring at time points which are
integer multiplicates of seven, such as t=0, t=7, t=14 and so forth.
The starting and end times of a scenario do not influece when a regular
transfer occurs, only if it occurs.
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. tools:::Rd_expr_doi("10.1016/j.ecolmodel.2013.01.017")
Lemna-models, Macrophyte-models, Transferable, Scenarios
Other Lemna models:
Lemna-models,
Lemna_Schmitt()
Other macrophyte models:
Lemna_Schmitt(),
Macrophyte-models,
Myrio(),
Myrio_log()