Algae_Weber: Algae model, _SAM-X_ (Weber et al. 2012)

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

Algae model, SAM-X (Weber et al. 2012)

Description

The model is a mechanistic combined toxicokinetic-toxicodynamic (TK/TD) and growth model for algae. The model simulates the development of algal biomass under laboratory and environmental conditions and was developed by Weber et al. (2012) as cited in EFSA TKTD opinion (2018). The growth of the algae population is simulated on the basis of growth rates, which are dependent on environmental conditions (radiation, temperature, and phosphorus). The toxicodynamic sub-model describes the effects of growth-inhibiting substances through a corresponding reduction in the photosynthesis rate on the basis of internal concentrations.

Usage

Algae_Weber()

SamX()

Details

Deviating from the equations described by Weber et al., this model implementation uses a user-defined time-series to represent (environmental) concentrations. Therefore, state-variable C and its differential equation was removed and model output C is identical to the exposure time-series. The implementation of Weber et al. (2012) was followed where units differ from EFSA (2018).

Value

an S4 object of type AlgaeWeber

Functions

• SamX(): Alias using original model name.

State variables

The model has three state variables:

• A, Biomass (µg fresh wt/mL, cells/mL *10^4)

• Q, Mass of phosphorous internal (mg P/L, or µg P/mL)

• P, Mass of phosphorous external (mg P/L, or µg P/mL)

The original model by Weber et al. contains an additional state variable C which models the external stressor concentration. However, the model implementation in this packages uses a user-defined time-series to represent environmental concentrations. Therefore, state variable C and accompanying parameters are not present here.

Model parameters

• Growth model

  • mu_max, Maximum growth rate (d-1)

  • Q_min, Minimum intracellular P (µg P/µg fresh wt)

  • Q_max, Maximum intracellular P (µg P/µg fresh wt)

  • v_max, Maximum P-uptake rate at non-limited growth (µg P/µg fresh wt/d)

  • k_s, Half-saturation constant for extracellular P (mg P/L)

  • m_max, Natural mortality rate (1/d)

  • I_opt, Optimum light intensity for growth (uE/m²/s)

  • T_opt, Optimum temperature for growth (°C)

  • T_max, Maximum temperature for growth (°C)

  • T_min, Minimum temperature for growth (°C)

  • D, Dilution rate (1/d)

  • R_0, Influx concentration of P (mg P/L)

• Concentration response (Toxicodynamics)

  • EC_50, Effect concentration of 50% inhibition of growth rate (µg/L)

  • b, slope of concentration effect curve at EC_50 (-)

Forcings

The Weber model requires two environmental properties as time-series input:

• T_act, temperature (°C), and

• I, irradiance (uE/m²/s).

The following constant default values are used for these properties:

• T_act = 23 °C

• I = 100 uE/m²/s

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.

Simulation output

Simulation results will contain the state variables Biomass (A), mass of internal phosphorous (Q), mass of external phosphorous (P) and the external concentration (C).

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 external concentration and model derivative dA. Set nout=0 to disable additional outputs. The default is nout=1.

The available output levels are as follows:

• nout >= 1: C, external concentration (µg/L)

• nout >= 2: f(T), temperature dependence (-)

• nout >= 3: f(I), light dependence (-)

• nout >= 4: f(Q), nutrient dependence (-)

• nout >= 5: f(Q, P), uptake flow reduction (-)

• nout >= 6: f(C), effect of chemical stressor (-)

• nout >= 7: dA, biomass derivative (µg)

• nout >= 8: dQ, internal phosphorous derivative (mg P/µg fresh wt)

• nout >= 9: dP, external phosphorous derivative (mg P L-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.

Parameter boundaries

Default values for parameter boundaries are set for all parameters by expert judgement, for calibration purposes. Values can be access from the object, and defaults overwritten.

Model history and changes

• cvasi v1.5.0

  • Unused state variable C and parameter k removed from documentation and code. External concentration C added to simulation output by means of optional output level nout=1.

References

Weber D, Schaefer D, Dorgerloh M, Bruns E, Goerlitz G, Hammel K, Preuss TG and Ratte HT, 2012. Combination of a higher-tier flow-through system and population modeling to assess the effects of time-variable exposure of isoproturon on the green algae Desmodesmus subspictatus and Pseudokirchneriella subcapitata. Environmental Toxicology and Chemistry, 31(4), 899-908. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1002/etc.1765")}

EFSA PPR Panel (EFSA Panel on Plant Protection Products and their Residues), Ockleford C, Adriaanse P, Berny P, Brock T, Duquesne S, Grilli S, Hernandez-Jerez AF, Bennekou SH,Klein M, Kuhl T, Laskowski R, Machera K, Pelkonen O, Pieper S, Smith RH, Stemmer M, Sundh I, Tiktak A,Topping CJ, Wolterink G, Cedergreen N, Charles S, Focks A, Reed M, Arena M, Ippolito A, Byers H andTeodorovic I, 2018. Scientific Opinion on the state of the art of Toxicokinetic/Toxicodynamic (TKTD)effect models for regulatory risk assessment of pesticides for aquatic organisms. EFSA Journal, 16(8), 5377. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.2903/j.efsa.2018.5377")}

See Also

Scenarios, Transferable

Other algae models: Algae-models, Algae_Simple(), Algae_TKTD()

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