Lemna_SETAC: Lemna model (Klein et al. 2021)

In cvasi: Calibration, Validation, and Simulation of TKTD Models

Lemna model (Klein et al. 2021)

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. \Sexpr[results=rd]{tools:::Rd_expr_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()

cvasi documentation built on Sept. 23, 2024, 9:08 a.m.