Mathematical modelling is an applied science. Analogues of real systems are mathematically simulated. The model itself as a theoretical construct and the simulation results are used in many areas for research and for practical applications. On the one hand models support the building of a theory; on the other hand models allow the analysis of measured data in a way that would not be possible without simulations. However, modelling of a real system is cer- tainly only a factual simplification of reality.
In most areas where models are used, they can help to explain complex issues. Certain dan- gerous processes in automobile development and crash testing can be predicted by simula- tions or partly substituted by models (Schmitt et al. 2002; Ibitoye et al. 2006). Model predic- tions for behavior of real systems (weather predictions, climate change or earthquake predic- tions) can provide helpful information. Without models, an assessment of hazard or a risk analysis is hardly possible in many cases.
Literature provides different approaches for the development of ecological models from the past to the present day (Jørgensen and Bendoricchio 2001). Twenty years ago, a trend was observable to develop large-scale and complex models that tend to reflect as many real pro- cesses and interactions as possible. These models attempted to mimic reality as close as possible with a general applicability for a broad range of different uses. Nowadays, more simple models are requested which can answer specific questions and can be applied in a more target-oriented way for a special scope of use. The concept to develop a model as simple and transparent as possible, but also as detailed and complex as necessary, should be a basic principle for each model developer.
The areas where ecological models play an important role and where experimental studies can be supported or partly substituted by models are increasing permanently. Models for environmental or ecological assessments are used at present in various areas e.g. fisheries (FAO 2007), water quality assessments (Kirchesch and Schöl 1999), eutrophication of lakes or rivers (Bowen and Hieronymus 2003), or geo-referenced data evaluation and forestry (DSE 2007). Ecological models in these areas are requested compulsorily by authorities. Simulation models are used with increasing frequency in the research and development area of Plant Protection Products. Lysimeter studies (Reinken 2004) as example, played a key role in leaching risk assessment and are nowadays almost completely substituted by math- ematical modelling. Mass transport and fate processes and corresponding environmental concentrations of pesticides are calculated using different fate models, e.g. the FOCUS
models (FOCUS 2003). The use of these models in the risk assessment of plant protection products is mandatory and widely accepted by the authorities. The results of the model simu- lations are used to assess the potential risk of pesticides for non-target organisms and the hazard in the endangered environment.
Since years, models of ecosystems or subsystems which can answer questions in the risk assessment of pesticides, are receiving increasing interest (Pastorok et al. 2002). So far, the regulatory requested experiments in this area are not substituted by ecological models. The high complexity and interactions in biological systems imply a high uncertainty of the simu- lated processes. Therefore, at present, the regulatory agencies did not clarify in detail in which cases or under which circumstances ecological modelling in the risk assessment of pesticides would be accepted. In many models the state of validation is not sufficient for the model’s purpose of application (Forbes et al. 2009). Many available ecological models are very complex and transparency and traceability of the simulated processes is not given. The sum of required input parameters needed for initialization of some models is high (Hipsey et
al. 2007; US EPA 2006 and 2008; Litchman et al. 2006); parameter values are not measura-
ble in many cases or are very difficult to be determined. Sometimes, only estimations of pa- rameter values are available or model parameters are mathematical constructs without eco- logical meaning. The complexity and opacity of many models makes a potential acceptance in the risk assessment from the regulatory side more difficult.
The demands for a “good modelling practice” during the development of a model are identi- cal for each type of model (Grimm et al. 2006). Models with the purpose to address issues in hazard assessment for the environment need to be validated sufficiently. The implemented processes should be clear and transparent and the model should not have a gratuitous com- plexity. The model should be well documented, should rely on a good data base and be in principle available for testing and peer review (Schäfer et al. 2009). Furthermore, the results need to be comprehensible, reproducible and the model should be properly validated.
There are various model types in the field of ecological modelling that deal with diverse ap- proaches to support the pesticide risk assessment. Different types of ecological models are
e.g. deterministic simulation models to describe populations, individual-based models which
simulate each individual with its own properties and mostly complex life cycles (Preuss et al. 2009b; Vanoverbeke 2008; Van den Brink et al. 2007), statistical models (Van den Brink et
al. 2002) or complex ecosystem models (US EPA 2008; Strauss 2009; Hipsey et al. 2007;
Rinke and Rothhaupt 2008) for simulations of multiple trophic levels and interactions. The type of model to be developed and applied strongly depends on the purpose of the model and the type of questions to be answered (whether the model should be able to provide reli- able predictions or should its main purpose only be the simulation of measured data).The
Higher-Tier Risk Assessments
Background 19
different types of models can be developed and deployed with the aim to address specific issues. Subjects of potential model applications are survival or recovery of individuals or populations after exposure to a chemical substance, re-colonization, uptake and elimination or bioaccumulation of pesticides (Ashauer et al. 2006a, 2006b, 2007a-c; Preuss et al. 2009b; Van den Brink et al. 2007). For instance, population models are commonly developed to simulate growth dynamics of populations influenced by external factors such as light, tem- perature and the availability of resources or space. Models which also consider the effects of external stressors on the growth of populations (e.g. algae populations exposed to a herbi- cide) can be used to predict the effects at population-level or recovery times (Weber 2006). Therefore, a verification and validation of such a model is necessary before an intended use in the regulatory risk assessments is adequate.
The use of ecological models is a possible way to extrapolate effects from individuals to communities (Ratte et al. 1992 and 1994a; Forbes et al. 2008). They can be deployed for the extrapolation of mesocosm results or as supportive tools prior to mesocosm experiments (for planning purposes, or in order to possibly avoid this expensive type of study). However, not only extrapolations can be made, but also predictions of ecotoxicological experiments are possible. Several case studies were described where models can help to extrapolate from mesocosm results and to assess effects of pesticides at community level (Ratte et al. 1994b; Hommen 1998). Naito et al. (2002) showed the application of a complex ecosystem model; Van den Brink et al. (2007) applied an individual-based metapopulation model and Sowig and Schäfer (2007) used a simple population model in the risk assessment of pesticides. At present, the successful application of ecological models to support the registration of plant protection products is only known in a few cases (Brock et al. 2007; Forbes et al. 2009). Anyway, ecological modelling is a subject of increasing importance and should be consid- ered as promising option in higher-tier risk assessments for pesticides. This, in turn, makes a more detailed research into the opportunities and limits necessary.