Lemna_Schmitt {cvasi}

Lemna model (Schmitt et al. 2013)

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

param

optional named list or vector of model parameters

init

optional named numeric vector of initial state values

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.

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()