Magma: Magma model (Witt et al., submitted)

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

Magma model (Witt et al., submitted)

Description

The Magma model interprets the Tier 2C version of the Lemna model by Klein et al. (2021), as a generic macrophyte model. It is mathematically equivalent to the Tier 2C version of the model by Klein et al. (2021) with the recommended Tier 2C settings k_photo_fixed=TRUE and k_resp=0.

Usage

Magma(growth = c("exp", "log"))

Myrio()

Myrio_log()

Arguments

growth

character, growth model to simulate: "exp" for exponential growth or "log" for logistic growth. Default is "exp".

Details

In particular, the growth model is a simple exponential growth model, which is considered to be the typical situation for a laboratory macrophyte study. Instead of frond numbers as for Lemna, the biomass is also returned as total shoot length (TSL) in simulation results. Consequently, the model has the additional parameter r_DW_TSL (dry weight per total shoot length ratio) instead of r_DW_FN (dry weight per frond number ratio). A model variant with an option for logistic growth is provided as well.

Value

an S4 object of type Magma

State variables

The model has two state variables:

• BM, Biomass (g dw)

• M_int, Mass of toxicant in plant population (ng)

Model parameters

The growth model can either simulate exponential growth (the default) or logistic growth. For logistic growth, an additional parameter D_L describing the limit density or carrying capacity needs to be provided.

• Growth model

  • mu_control, Maximum photosynthesis rate (d-1), default: 0.47

  • (optional) D_L, Limit density (g dw)

• Concentration response (Toxicodynamics)

  • EC50_int, Internal concentration resulting in 50% effect (ug L-1)

  • E_max, Maximum inhibition (-), default: 1

  • b, Slope parameter (-)

• Internal concentration (Toxicokinetics)

  • P, Permeability (cm d-1)

  • r_A_DW, Area per dry-weight ratio (cm2 g-1), default: 1000

  • r_FW_DW, Fresh weight per dry weight ratio (-), default: 16.7

  • r_FW_V, Fresh weight density (g cm-3), default: 1

  • r_DW_TSL, Dry weight per total shoot length ratio (g dw cm-1)

  • K_pw, Partitioning coefficient plant:water (-), default: 1

  • k_met, Metabolisation rate (d-1), default: 0

Environmental factors

None.

Parameter boundaries

Default values for parameter boundaries are set for all parameters by expert judgement, for calibration purposes. Values can be modified using set_bounds().

Simulation output

Simulation results will contain the state variables biomass (BM) and mass of internal toxicant (M_int).

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(). As an example, set nout=2 to enable reporting of total shoot length (TSL) and internal concentration (C_int). Set nout=0 to disable additional outputs. The default is nout=1.

The available output levels are as follows:

• nout >= 1: TSL, total shoot length (cm)

• nout >= 2: C_int, internal concentration (ug L-1)

• nout >= 3: f_photo, photosynthesis dependency function (-)

• nout >= 4: C_int_unb, unbound internal concentration (ug L-1)

• nout >= 5: C_ext, external concentration (ug L-1)

• nout >= 6: dBM, biomass derivative (g dw d-1)

• nout >= 7: dM_int, mass of toxicant in plants derivative (ng d-1)

Solver settings

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.

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.

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().

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.

References

Witt et al., submitted

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 1.1, uploaded on 09 May 2022. https://www.setac.org/group/effect-modeling.html

See Also

Macrophyte-models, Lemna-models, Transferable, Scenarios

Other macrophyte models: Lemna_SETAC(), Lemna_Schmitt(), Macrophyte-models

cvasi documentation built on Sept. 11, 2025, 5:11 p.m.