Algae_Weber: Algae model with exponential growth and forcings (I, T)

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

Algae model with exponential growth and forcings (I, T)

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. (the implementation of Weber et al. (2012) is followed where units differ with EFSA)

Usage

Algae_Weber()

Value

an S4 object of type AlgaeWeberScenario

State variables

The model has four state variables:

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

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

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

• C, external substance concentration (ug/L)

Model parameters

• Growth model

  • mu_max, Maximum growth rate (d-1)

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

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

  • v_max, Maximum P-uptake rate at non-limited growth (ug P/ug 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 (ug/L)

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

• External concentration (Toxicokinetics)

  • k, Degradation rate of toxicant in aquatic environments (d-1)

Forcings

Besides exposure events (C_in), the Algae model requires three environmental properties as time-series input: Irradiance (I, uE/m²/s) and temperature (T_act, 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. The input format for all forcings is a list of the data frames.

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). The derivatives are also available as additional output.

• nout >= 4

  • dA, biomass derivative (µg)

  • dQ, internal phosphorous derivative (mg P/ug fresh wt)

  • dP, external phosphorous derivative (mg P L-1)

  • dC, external concentration derivative (ug L-1)

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.

References

Weber D, Schaeffer 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, 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. 23, 2024, 9:08 a.m.