6. Models for primary producers
6.1. The pelagic microalgae model
6.1.1.
Documentation, testing and implementation of the formal model
Here the description of theflow-through-system model of Weber et al. (2012) is the only given, as this is the only published algae model where variable exposures are possible to implement. In addition, this system mimics the ecological situation of algae being removed from the system by either grazing or sedimentation, or by dilution with incoming water from rain, drain or ground water sources. As already mentioned in chapter 2, the algae model by Weber et al. (2012), does not contain a TK compartment, but uses the external concentration as a direct proxy for internal concentrations assuming instantaneous equilibrium between external and internal concentrations. Hence, external pesticide concentrations, phosphorous (P), irradiance (Irr) and temperature (T) affect relative growth rates (RGR) directly through different functions. In addition, also the dilution rate of the algae and the death rate of the algae will affect the population density over time. A diagram of the model is given in Figure 31.
Contrary to the GUTS model, where only effects of survival are assessed, in plant models, the toxicant affects plant growth. All models of plants and algae therefore include a growth model giving the factors affecting growth.
In the model presented in Weber et al. (2012), the parameters describing nutrient availability (Q and P) have different units depending on the equation they are used in. For a better understanding of the model, the units of the model parameters and the environmental variables (Q; P and R0) were harmonised in order to keep the same unit for one parameter throughout the different equations of the model.
6.1.1.1. The growth model for algae
The growth model described in Weber et al. (2012) depends on environmental parameters such as the temperature T (°C), irradiance I (lE/m2 per s), nutrient availability Q (mg P/L), and the dilution rate of the media D (day1) as represented in Figure 31. In addition, the concentration of the chemical stressor C (lg/L) is also affecting growth directly, describing the toxicodynamics, as toxicokinetics are ignored in this model. The parameters are implemented in the following differential equation, where A (mg fresh wt/L) represent the algae population biomass,lmax(day1) is the maximum relative growth
rate and mmax(day1) the maximum mortality rate.
dA
dt ¼ ðlmaxf(T) f(I) f(Q) f(C) mmax D)A (31)
To describe the temperature effect on algae growth rate a skewed normal distribution is used, where Tmin, Tmax, and Toptare the minimum, maximum and optimal temperature for algal growth, respectively (°C).
f(T) = e h 2;3 TTopt TxTopt 2i (32) Figure 31: Schematic representation of the algae model presented in Weber et al. (2012). External factors affecting chemical uptake or growth are given in blue and the different rate constants affecting biomass growth rates of the algae (green box) are given with grey arrows and described in Section 6.1.1.1. The flow and effect of the toxic substance is given by black arrows and the TD-model is described in Section6.1.1.2
With Tx¼
Tmin; T [ Topt
Tmax; T Topt
The effect of irradiance on algal growth rate is given by the following equation describing a saturation curve, where Iopt(lE/m2per s is the optimum irradiance for the algal growth rate:
f(I)¼ I Iopt e 1 I Iopt (33) In estimating the effect of nutrient availability to algal growth rate only phosphorous is considered by Weber et al. (2012) as a limiting nutrient, even though nitrogen and carbon availability can also limit growth. In this equation qmin (mg P/mg fresh/wt) is the minimum concentration of P in the cells
to allow any cell division, while Q (mg P/L) is the internal concentration of P.
f(Q)¼ 1 e(ln 2(qmin:AQ 1)) (34)
The internal concentration of P, Q (mg P/L), is given by the following differential equation, where vmax (mg P/mg fresh wt per day) describes the maximum uptake rate, A, mmax and D is the algal concentration (mg fresh wt/L), maximal death (day1) rate and dilution rate (day1), respectively.
dQ
dt ¼ vmaxf(Q, P) A ðmmaxþ DÞQ (35)
The uptake of P by the algae is limited by the internal concentration of P in algae represented by f(Q, P) below. In this function qmaxand qmin are the maximum and minimum internal concentration for
P, respectively, (mg P/L) and ks(mg P/L) is the half-saturated constant for extracellular P.
f(Q, P)¼ qmax:A Q ðqmax qminÞA
P kSþ P
(36) The external concentration of P is as follows with R0(mg P/L) being the concentration of P entering
the system.
dP
dt ¼ DR0 DP þ Qmmax ðvmaxf(Q, P)AÞ (37)
6.1.1.2. The TD model for algae
The algal growth rate is affected by the toxicant as a function of the concentration of the chemical in the system C (lg/L) and the concentration of the toxicant causing 50% effect EC50 (lg/L), where
b is the slope of the log-logistic function.
f(C)¼ 1
1þ C EC50
b (38)
The actual concentration of the chemical in the system is equivalent to the concentration of the chemical entering the system Cin(lg/L) while the degradation rate of toxicant in aquatic environments
k (1 day) and the toxicant eliminated by dilution are taken into account. This relationship is given by the next differential equation:
dC
6.1.1.3. Model application
The following section describes the flow-through-system model of Weber et al. (2012), as this is the only algae model where variable exposures are possible to implement.
Input data
The model was calibrated for two microalgae species: Desmodesmus subspicatus and Raphidocelis subcapitata (formerly known as Pseudokirscheriella subcapitata). The 10 parameters used to describe algal growth capacity and growth dependence on temperature, irradiance and P-availability were archived through the authors own experiments combined with literature reviews on standard toxicity tests and are presented in Table C in the Supplementary Information of Weber et al. (2012) for both species. Background and further details on model development and the raw data for the calibration is given in the PhD thesis of Weber (2009) (https://publications.rwth-aachen.de/record/211799/). Calibrated parameters for the susceptibility of the algae to the herbicide isoproturon (PSII inhibitor) were obtained through standard chronic tests (OECD, 2011a), performed by the authors, with isoproturon concentration effects on growth rates being described by the Hill equation (equation 38) (Weber et al., 2012).
To validate the calibrated model, an exposure concentration profile was tested in the flow-through- system. The profile was based on a FOCUS D2 drainage scenario with a ditch as water body and autumn application of isoproturon of 1.5 kg a.i./ha. A time-window of 40 days of the most critical exposure pattern was selected and the exposure profile was modified to make it applicable in the flow- through system (Weber et al., 2012; Supplementary Information, Figure 1), keeping a focus on maintaining maximal concentration and duration of the peaks. As relatively little effects were seen for thefirst pulse in the experiment, pulse exposure concentrations were first doubled for the second peak and finally raised 10-fold for the last peak, compared to the FOCUS predictions, to study recovery from a very high pulse (850lg/L).
6.1.1.4. Model implementation
The model was implemented in Matlab version 2007b. No optimisation of parameters was performed, but model outputs were compared to the results from the flow-through-system employed. Model codes are not published.
6.1.1.5. Modelling results
The results of the model validation are shown as model predictions together with experimental data in Figures 32and 33directly copied from Weber et al. (2012).
Figure 32: The results of the model validation for the algae Desmodesmus subspicatus showing the exposure concentrations of isoproturon in black squares (right y-axis), and the corresponding algal biomass in black triangles (replicate A) and black circles (replicate B) (left y-axis) together with the model prediction and its 95% confidence limits (Weber, 2009)
6.1.1.6. Summary and discussion of the application
From a visual assessment of the model together with data, the model was able to predict both the level of growth inhibition and the rate of recovery of the population well, confirming that toxicity data
A
B
Figure 33: The results of the model validation for the algae Raphidocelis subcapitata (formerly known as Pseudokirscheriella subcapitata) showing the exposure concentrations of isoproturon in black squares (right y-axis), and the corresponding algal biomass in black circles (replicate A, Panel A) and black triangles (replicate B, Panel B) (left y-axis) together with the model prediction and its 95% confidence limits (Weber, 2009)
from standard toxicity tests can be used to parameterise a dynamic model. The focus of the study was to predict high and damaging exposures to the algal population; hence, P-availability, temperature and irradiance were kept constant and at close to optimal levels. It is therefore not known how well the model can also predict herbicide effects under variable growth conditions, possibly reaching extreme values in terms of P-availability, temperature and irradiance and whether it can be equally well parameterised for other species.
The uncertainties in terms of effects under more extreme growth conditions, species differences and species interactions are, however, the same as for the static tests presently used in risk assessment.
Contrary to the static tests, the dynamic model harbours the potential of implementing effects of dynamic growth conditions on algal populations. This potential is, however, not yet extensively tested. The largest drawback for implementing the models in pesticide risk assessment is that the flow through setup used in the existing example and needed to simulate long term variable exposures of pesticides to fast growing populations of algae has not yet been standardised, nor has the robustness of the setup been ring tested. Hence, presently the setup and the models are considered as important research tools but probably not yet mature enough to use for risk assessment purposes.
In principle, dynamic conditions are also recorded in normal static/semi-static tests whenever the test substance has a short half-life in water. Such feature, which is normally perceived as a problem by risk assessors, since standard tests aim at maintaining constant conditions, may become an asset if the data could be used to calibrate and/or validate a TKTD model. Nevertheless, the present model has never been tested under such conditions (i.e. static tests with fast-dissipating substances) and therefore, also in this case, its use for the risk assessment cannot be recommended at the present stage.