Algae_Simple: Algae model with exponential growth but without additional...

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

Algae model with exponential growth but without additional forcings

Description

The model is a mechanistic combined toxicokinetic-toxicodynamic (TK/TD) and growth model for algae. It follows the concept of a simplified algae model described in Rendal et al. (2023). The model simulates the development of algal biomass. The growth of the algae population is simulated on the basis of growth rates, which are, in contrast to the Weber model, independent on environmental conditions which are usually optimal in laboratory effect studies. The toxicodynamic sub-model describes the effects of growth-inhibiting substances through a corresponding reduction in the photosynthesis rate on the basis of either external or internal concentrations (depending on user choice of 'scaled' parameter setting).

Usage

Algae_Simple()

Value

an S4 object of type AlgaeSimpleScenario

State variables

The model has two state variables:

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

• Dw, only used if scaled = 1

Model parameters

• Growth model

  • mu_max, Maximum growth rate (d-1)

• Concentration response (Toxicodynamics)

  • EC_50, Effect concentration of 50% inhibition of growth rate (ug L-1)

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

  • dose_response, shape of the dose response curve (0 = logit, 1 = probit)

• External concentration (Toxicokinetics)

  • kD, dominant rate constant of toxicant in aquatic environments (d-1)

  • scaled, 0 = no internal scaled damage / 1 = yes (-)

Forcings

Simplified model without additional forcings for e.g. irradiation or temperature as implemented in Algae_Weber. A constant growth over time is assumed. In case that growth is time dependent, a forcing variable (f_growth) can be set. Forcing time-series are represented by data.frame objects consisting of two columns. The first for time and the second for a scaling factor of mu_max. The input format for all forcings is a list of the data frames. If f_growth is not set, a default scaling factor of 1 is used.

Parameter boundaries

Upper and lower parameter boundaries are set by default for each parameter. This, to avoid extreme values during calibration (particularly likelihood profiling)

Simulation output

Simulation results will contain the state variables biomass (A) and in case of scaled damage the damage concentration (Dw). The derivatives are also available as additional output.

• nout >= 2

  • dA, biomass derivative (µg)

  • dDw, damage concentration derivative (ug L-1)

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")}

See Also

Scenarios, Transferable

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

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