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)
Algae_Weber()an S4 object of type AlgaeWeber
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)
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)
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 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 model derivatives dA and dQ. Set nout=0 to disable
additional outputs (default).
The available output levels are as follows:
Derivatives
nout >= 1: dA, biomass derivative (µg)
nout >= 2: dQ, internal phosphorous derivative (mg P/ug fresh wt)
nout >= 3: dP, external phosphorous derivative (mg P L-1)
nout >= 4: dC, external concentration derivative (ug L-1)
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.
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.
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. 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. tools:::Rd_expr_doi("10.2903/j.efsa.2018.5377")
Scenarios, Transferable
Other algae models:
Algae-models,
Algae_Simple(),
Algae_TKTD()