Simulation models

In the USA the evolution of computer simulation models occurred concurrently with the evolving concept of IPM (Logan, 1989). This coincidence provided the IPM researcher with a tool that could help deal with the complexity of IPM. Simulation methodology also provides an unequalled ability for producing realistic models of systems behaviour for a reasonable investment of time and money (McKinion, 1989). These models can also be readily used by non-mathematicians because they do not necessarily require a high degree of mathematical sophistication to implement (Getz and Gutierrez, 1982). The real advantage of a simulation model is, however, that it permits study of the real system without actual modification of that system. This means that a system simulated on the computer can be subjected to a series of alternative modifications in a controlled and systematic manner and the consequences of these modifications studied (McKinion, 1989). These attributes and the common claim that simulation models are a preeminently useful research tool because they help identify gaps in our knowledge (Conway, 1984a) has made the technique highly acceptable as an approach consistent with IPM and IPM needs and objectives.

The technique does, however, have a number of recognized pitfalls (Getz and

Gutierrez, 1982). A lack of awareness of certain important processes may lead to their omission from the model. By their very nature it may not be readily apparent what impact such omissions will have on the model, but eventually such models will fail. There is also the problem that sometimes the construction of the complete model becomes an end in itself.

It is not possible to relate here the techniques used in simulation models (see Rabbinge et al., 1989; Holt and Norton, 1993; Holt and Cheke, 1997) but a brief description of the principles involved may provide some understanding of the type of relations and processes that drive such models. Simulation models should all start as a relational diagram (Fig. 9.12). Relational diagrams are qualitative models that contain the most important elements and relationships of the system. They make use of a special form of notation and convention, developed to depict industrial systems (Forrester, 1961). An understanding of this notation (Table 9.7) means that the relational diagrams and the general functioning of the model can be understood. The modelling approach using this notation has gained wide acceptance and is known as the state variable approach. State variables are quantities such as number of species, or number of individuals or biomass and each state variable is associated with a rate variable. Rate variables characterize the rate of change of a state variable over a given length of time and they include such variables as development rate, mortality rate and reproductive rate. The value of a state variable will change over time according to the rate variable which in turn can influence the value of the rate variable. In this way positive or negative feedback loops are developed. The form the loop takes will determine whether a state variable continues to increase, decrease or reaches a steady state. A positive feedback loop is characterized by a positive relation between the rate and state variable which will lead to the rate enhancing the state and vice versa so that both continue to increase, e.g. exponential growth. In a negative feedback loop the rate may be either positive or negative but will decrease as a function of the state variable (Leffelaar and Ferrari, 1989). Unlike the positive feedback loop, negative feedback causes the system to approach some goal. Such an equilibrium state is stable since any departure will cause a return to the equilibrium position. The state variables and the rate variables can be influenced by driving variables which tend to characterize the effect of the environment on the system, e.g. temperature, rainfall, but they can also be immigration and emigration or sex ratio. A simulation model is constructed using state variables, rate variables and driving variables (also parameters, see Table 9.7, Fig. 9.12). These variables are all related in a model with the use of difference equations.

Although the use of simulation modelling is most often associated with research, they provide an excellent means of testing and developing management strategies and for providing a basis for pest management advice (Holt and Norton, 1993). The ability of simulation models to predict means they can be used to either derive general rules or in real time operation, and given appropriate field inputs, they can provide short term tactical advice.

Simulation models have now been produced for a range of pest species and systems, e.g. cereal aphids (Carter and Rabbinge, 1980; Rabbinge et al., 1979), larch moths (van den Bos and Rabbinge, 1976), planthoppers in rice (Cheng and Holt, 1990), spider mites in fruit trees (Rabbinge, 1989), potato leafhopper in alfalfa (Onstad et al., 1984) and Helicoverpa amigera in pigeonpea (Holt et al., 1990). They are used in tactical models to predict pest outbreaks in tandem with management models (Cheng and Holt, 1990) or to determine optimum insecticide spray timing (Baumgaertner and Zahner, 1984; Cheng et al., 1990; Holt et al., 1990) while in strategic models they have been used to simulate plant growth and pest damage (Boote et al., 1983; Gutierrez et al., 1988a,b; see also Rabbinge et al., 1989) and strategies for

Fig. 9.12. A relational diagram for the grey larch bud moth (Zieraphera diniaria) (after van den Bos and Rabbinge, 1976).

Table 9.7. The basic elements of relational diagrams, the symbols of Forrester (1961) notation (Leffelaar and Ferrari, 1989).

Symbol

Meaning

A state variable, or integral of the flow; the final result of what has happened

Flow direction of an action by which an amount, or state variable is changed. These flows always begin or end at a state variable, and may connect two state variables

Flow and direction of information derived from the state of the system. Dotted arrows always point to rate variables, never to state variables. The use of information does not affect the information source itself. Information may be delayed and as such be a part of the process itself

Valve in a flow, indicating calculation of a rate variable takes place; the lines of incoming information indicate the factors upon which the rate depends

Source and sink of quantities in whose content one is not interested. This symbol is often omitted

A constant or parameter

Auxiliary or intermediate variable in the flow of material or of information

Sometimes placed next to a flow of information, to indicate whether a loop involves a positive or negative feedback

insecticide use (Holt et al., 1992) and biological control (Hearn et al., 1994).

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