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).
Algae_Simple()an S4 object of type AlgaeSimple
The model has two state variables:
A, Biomass (ug fresh wt/mL, cells/mL *10^4)
Dw, only used if scaled = 1
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 (-)
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.
Upper and lower parameter boundaries are set by default for each parameter. This, to avoid extreme values during calibration (particularly likelihood profiling)
Simulation results will contain the state variables biomass (A) and
scaled damage concentration (Dw).
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 (Cw) and growth scaling factor
(f_growth). Set nout=0 to disable additional outputs (default).
The available output levels are as follows:
nout >= 1: Cw external concentration (ug L-1)
nout >= 2: f_growth growth scaling factor (-)
nout >= 3: dA, biomass derivative (µg)
nout >= 4: dDw, damage 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 = 0.01
Maximum step length in time suitable for most simulations.
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")
Scenarios, Transferable
Other algae models:
Algae-models,
Algae_TKTD(),
Algae_Weber()