Lemna_Schmitt | R Documentation |
The model is a mechanistic combined toxicokinetic-toxicodynamic (TK/TD) and growth model for the aquatic macrophytes Lemna spp. The model simulates the development of Lemna biomass under laboratory and environmental conditions and was developed by Schmitt et al. (2013). Growth of the Lemna population is simulated on basis of photosynthesis and respiration rates which are functions of environmental conditions. The toxicodynamic sub-model describes the effects of growth-inhibiting substances by a respective reduction in the photosynthesis rate based on internal concentrations. This is the historical version of the Lemna model. For current uses, we recommend the Lemna (SETAC) model, which is a more recent version of the Schmitt model.
Lemna_Schmitt(param, init)
Lemna_SchmittThold(param, init)
param |
optional named |
init |
optional named numeric |
Constructors to ease creation of scenarios based on the Lemna model by
Schmitt et al. (2013).
A variant of this Lemna model, Lemna_SchmittThold()
, provides an additional
cumulative exposure threshold parameter. The Lemna biomass stops growing
if the integral of exposure over time exceeds the threshold. The integral
of exposure is internally accounted for by an additional state variable
AUC
(Area Under Curve).
an S4 object of type LemnaSchmittScenario
Lemna_SchmittThold()
: model variant with cumulative exposure threshold
The following list describes the default names and standard units of the model's state variables:
BM, g_dw/m2, dry weight biomass per square meter
E, -, effect [0,1]
M_int, ug, internal toxicant mass
AUC, ug/L, cumulative exposure (only for LemnaThreshold
model)
Biomass (BM) and internal toxicant mass (M_int) are initialized to zero by
default. See set_init()
on how to set the initial states.
The following model parameters are required:
Fate and biomass
k_phot_fix
, logical, TRUE then k_phot_max is not changed by environmental factors, else FALSE
k_phot_max
, 1/d, maximum photosynthesis rate
k_resp
, 1/d, respiration rate
k_loss
, 1/d, rate of loss (e.g. flow rate)
mass_per_frond
, g_dw/frond, dry weight per frond
BMw2BMd
, g_fw/g_dw, Fresh weight/dry weight
Effect
Emax
, -, maximum effect [0,1]
EC50
, ug/L, midpoint of effect curve
b
, -, slope of effect curve
Toxicokinetics
P_up
, cm/d, Permeability for uptake
AperBM
, cm2/g_dw, A_leaf / d_leaf = 1/d_leaf (for circular disc, d=0.05 cm)
Kbm
, -, Biomass(fw) : water partition coefficient
P_Temp
, logical, TRUE to enable temperature dependence of cuticle permeability, else FALSE
MolWeight
, g/mol, Molmass of molecule (determines Q10_permeability)
Temperature dependence
Tmin
, deg C, minimum temperature for growth
Tmax
, deg C, maximum temperature for growth
Topt
, deg C, optimal temperature for growth
t_ref
, deg C, reference temperature for respiration rate
Q10
, -, temperature dependence factor for respiration rate
Light dependence
k_0
, 1/d, light dependence: intercept of linear part
a_k
, (1/d)/(kJ/m2.d), light dependence: slope of linear part
Phosphorus dependence (Hill like dep.)
C_P
, mg/L, phosphorus concentration in water
CP50
, mg/L, phosphorus conc. where growth rate is halfed
a_p
, -, Hill coefficient
KiP
, mg/L, p-inhibition constant for very high p-conc.
Nitrogen dependence (Hill like dep.)
C_N
, mg/L, nitrogen concentration in water
CN50
, mg/L, n-conc. where growth rate is halfed
a_N
, -, Hill coefficient
KiN
, mg/L, n-inhibition constant for very high p-conc.
Density dependence
BM50
, g_dw/m2, cut off BM
The Lemna_SchmittThold
model requires the following additional parameter:
threshold
, ug/L, cumulative exposure threshold
Besides exposure, the Lemna model requires two environmental properties as
time-series input: global radiation (rad
, kJ/m2.d) and temperature (temp
, 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.
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.
Supported effect endpoints include BM (biomass) and r (average growth rate during simulation). The effect on biomass is calculated from the last state of a simulation. Be aware that endpoint r is incompatible with frond transfers.
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.
Simulation results will contain two additional columns besides state variables:
C_int
, ug/L, internal concentration of toxicant
FrondNo
, -, number of fronds
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()
, see examples below. nout=1
enables reporting of internal concentration (C_int), nout=14
enables all
additional outputs, and nout=0
will disable additional outputs.
The available output levels are as follows:
nout=1
C_int
, internal concentration (ug/L)
nout=2
FrondNo
, number of fronds (-)
nout=3
C_int_u
, unbound internal concentration (ug/l)
nout=8
, growth and TK/TD
BM_fresh
, fresh weight biomass (g_fw/m2)
k_photo_eff
, current photosynthesis rate (1/d)
k_resp_eff
, current respiration rate (1/d)
f_Eff
, toxic effect factor (-)
P_up_eff
, current permeability for uptake (cm/d)
nout=11
, environmental factors
actConc
, current toxicant concentration in surrounding medium (ug/L)
actTemp
, current environmental temperature (deg C)
actRad
, current environmental radiation (kJ/m2.d)
nout=14
, derivatives
d BM/dt
, current change in state variable BM
d E/dt
, current change in effect
d M_int/dt
, current change in internal toxicant mass
Models supporting biomass transfer can be instructed to move a fixed amount of biomass to a new medium after a period of time. This feature replicates a procedure occurring in e.g. Lemna effect studies and may be necessary to recreate study results.
The biomass transfer feature assumes that always a fixed amount of
biomass is transferred. Transfers can occur at any fixed point in time or
in regular intervals. During a transfer, the biomass is reset to the
transferred amount and additional compartments can be scaled 1:1 accordingly,
to e.g. reflect the change in internal toxicant mass when biomass is modified.
Transfer settings can be modified using set_transfer()
.
Any transfer time point must also be an output time point. If a transfer occurs, simulation results of that time point will report the model state before the transfer. Be aware that in order to use transfers at regular intervals, the simulation must start at time point zero.
Schmitt W., Bruns E., Dollinger M., and Sowig P., 2013: Mechanistic TK/TD-model simulating the effect of growth inhibitors on Lemna populations. Ecol Model 255, pp. 1-10. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.ecolmodel.2013.01.017")}
Lemna-models, Macrophyte-models, Transferable, Scenarios
Other Lemna models:
Lemna-models
,
Lemna_SETAC()
Other macrophyte models:
Lemna_SETAC()
,
Macrophyte-models
,
Myrio()
,
Myrio_log()
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