Web-Based Decision Support for Sustainable Pest Management in Fruit Orchards: Development of the Swiss System SOPRA - Efficient Decision Support Systems: Practice and Challenges from Current to Future - page 376

Insect body temperatures in the models of SOPRA are based on studies of habitat selection
of relevant developmental stages and according simulations using the driving variables and
structural orchard features.
On base of local weather data, age structure of the pest populations is simulated and, based
on the simulated phenology, crucial events for management activities are predicted by the
SOPRA system.
Through the web-interface, the phenology is directly linked to the decision process of the
fruit farmers throughout the season. Thereby SOPRA serves as decision support system for
the major insect pests of fruit orchards on local and regional scale and has a wide range of
possible applications in the alpine valleys and north of the Alps.
2. Single-species phenology models in SOPRA
2.1 Time-varying distributed delays
The flow of entities with variable transit times through a given process, as applicable for
insect development, can be easily simulated by time-varying distributed delay models
(Manetsch, 1976; Severini et al., 1990; Gutierrez, 1996).
This approach makes use of an Erlang density function to generate the frequency
distribution of the individual development times, and is parameterized with the thermal
constant of the specific developmental stage and its variance. An algorithm originally
written by Abkin & Wolf (1976) was adapted to compute the process of aging within the
different developmental stages and to continuously keep track of the age structure of the
population. The changes in the age structure of the pest populations are continuously
recorded by a balance of input and output from the state variables i.e. the developmental
stages implemented for the single species.
In a poikilothermic development process, the mean transit time in calendar time units and
its variance vary dramatically depending on temperature as exemplified here for the Smaller
fruit tortrix (Fig. 2 A). Within the rate-enhancing phase of temperature, high temperatures
lead to faster development, i.e. higher development rates. Low temperatures slow down
biological processes until development nearly stops at the so-called developmental thermal
threshold (Fig. 2 B). The relationship of process rate and temperature rises until the so-called
optimum temperature is reached and decreases above this optimum due to rate-reducing or
destructive effects (cf. Fig. 2), mostly at first as reversible structural damage of the enzyme
systems (Somero, 1995; Willmer et al., 2000).
In order to account for these effects of temperature on biological processes, developmental
time and variance are not considered as constants in the present modelling approach but as
variables that are updated for each simulation step (i.e. for every hour of the season) on the
basis of relationships between temperature and process rates (see below). These
relationships are kept as simple as possible, which means that linear rate functions are
applied wherever they give appropriate approximations (cf. Fig. 2).
Thereby, for a single delay, the ratio between the square of the mean transit time in
physiological time units (i.e., the simplifying so-called thermal constant in day-degrees) and
its variance specifies the order (k) of the delay and hence the number of first order
differential equations required to generate the observed variability. Each of these k first
order differential equations represents an age class within the simulated stage and describes
the daily changes in this age class as