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(1)
where Q i (t) stands for the proportion of individuals in age class i at time t. The parameter
r(t) is the transition rate from age class i to age class i + 1 and corresponds to the
developmental rate that is quantified with the according function describing development
as function of temperature. Individuals leaving the last age class are entering the next
implemented developmental stage (Fig. 3).
The algorithms implementing the time-varying distributed delay models were originally
written in Pascal and later implemented with the program Delphi 6.0 (Borland, Cupertino,
CA and Atlanta, GA, USA) in a MS Windows application (cf. below).
Life stages in Codling moth model
Time-varying distributed delays allow for fully overlapping life stages
Late Larvae+
Pupae
(Postdiapause)
Embryo
(Egg)
Adult moths
Reproduction Mortality
Larvae
Pupae
Hibernating
Generation
Age of female
Age
Temperature
1 st following
Generation
Day length
Temperature
Temperature
Temperature
Age of female
Age
2 nd following
Generation
Diapause,
Hibernation
Temperature
Temperature
Fig. 3. Life stages implemented in the Codling moth model and schematic relationship
between temperature and process rates (development rate, reproduction rate, mortality rate)
for the respective stages of the life cycle. Age is always transferred to physiological time
above the developmental thermal threshold to account for the temperature effect.
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