The Model

A detailed description of the model applied to test our hypothesis (Gottschalk et al. 2003) and to rate the impact of global change on the viability of P. albopunctata can be found in Griebeler and Gottschalk (2000a). The following is a short summary of this individual-based day-degree model.

We distinguish three life stages in this model: eggs, larvae and adults. We assume an equal sex ratio. The model is based on the idea that eggs and larvae accumulate temperatures on a daily basis during their development. Both stages need minimum temperatures for daily development (T0egg = 7.5°C, Ingrisch 1986;

T0Jma=9.6°C) and a total temperature input (TSegg = 808.5°C days, Ingrisch 1986; TSlarva=381.9°C days) to enter the next life stage. The model considers a fixed diapause D for eggs between 1st November and 31st March of the following year (Ingrisch 1986). Eggs do not accumulate daily temperatures within these winter months. The model assumes a constant mortality rate for the egg stage (megg=60%) and for the larva stage (mlarva=90%), which summarize all mortalities during the respective life stage. These two rates that determine the final transition of a life stage to the next are randomly applied to each individual before it enters the next life stage. Each adult individual, however, has a constant daily mortality risk (mimago=5.1%) that is independent of its age. The daily oviposition rate of adults depends on temperature (Eggs(T) = 0.1 x (10.1 x T - 66.1), T daily temperature, Waltert et al. 1999) and egg laying requires temperatures higher than T0 egg. The total reproductive output of an individual is limited (maxegg = 100) and adults start reproduction at a minimal age (Amn = 14 days).

The quality of the area inhabited by the population is modelled by two entities: (1) a constant carrying capacity K that mimics food availability and limits the daily number of adults in the population; and (2) a temperature profile that affects all life stages on each simulated day. For density regulation of the population we assume a ceiling model. Surplus adults die if an overflow in capacity occurs. They are randomly removed from the population. We use a long-term meteorological data record from the weather station "Bamberg" to model the effects of daily temperatures on population development (Griebeler and Gottschalk 2000a). This weather station is located in a distance of about 25 km from both study areas. At each simulated day, a temperature value is sequentially taken from a database that contains the daily mean temperatures registered for this meteorological station.

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