Computer Simulations

We performed three major simulation studies. In the first study, we tested whether differences in temperature conditions and food limitation account for the observed differences in population development between Prappach and Hammelburg. Therefore, by applying our model we generated population dynamics for each area over the field period between 1993 and 1999. Concerning temperature conditions, we directly applied the daily mean temperatures of the meteorological station Bamberg recorded between 1993 and 1999 for Prappach (Griebeler and Gottschalk 2000a). For Hammelburg, we added on each simulated day 4.8°C to the value obtained from this database reflecting the higher temperatures found in our field studies (Gottschalk et al. 2003). For food limitation, we assumed different carrying capacities. Capacities implementing different levels of food availability were 100, 200, 300, 400, 500, 750, 1,000, 2,000, 3,000, 4,000, 5,000, 7,500 and 10,000 adults per day. All simulations were randomly started for Prappach on 26th July 1993 with

1,218, 1,424, or 1,630 adults or for Hammelburg on 24th July 1993 with 598, 676, or 754 adults. These initial population sizes were chosen according to the population sizes estimated on these dates in the field and the respective estimation errors of sizes (Prappach: ±206, Hammelburg: ±78). For each of the capacities considered per study area, we repeated the Monte Carlo simulation of population size 3,000 (= 3 initial sizes x 1,000 simulations) times. In total, we investigated 26 (= 2 areas x 13 capacities) simulation scenarios. For each of these simulation scenarios, we annually recorded population sizes in each simulation run.

To derive a more general understanding of how thermal conditions and food availability affect populations of the grey bush cricket and to rate the impact of global warming on this species, we performed a second simulation study. With this study, we aimed to estimate the extinction risk of populations inhabiting areas of different food availability with different temperature profiles. Starting with temperature conditions as observed at Prappach, we added on each simulated day 2, 4, 4.8°C (Hammelburg), 6.8 or 8.8°C to the respective temperature value of the meteorological database. For all temperature profiles we considered 15 carrying capacities (100, 250, 500, 750, 1,000, 2,000, 3,000, 4,000, 5,000, 7,500, 10,000, 15,000, 20,000, 25,000 and 30,000) implementing food availability. All 90 simulation scenarios (= 6 temperature profiles x 15 capacities) were started on 1st July. The initial population consisted of adults and its size equalled the respective carrying capacity. For the annual temperature course, we applied mean daily temperatures of the meteorological station Bamberg from 1949 to 1985. For each simulation scenario, we estimated the extinction probability and the mean number of adults based on 1,000 Monte Carlo simulations over 35 years (Griebeler and Gottschalk 2000a). From these estimates, we derived minimum viable population sizes (MVP) for each temperature scenario according to Shaffer (1987). If we assume an extinction probability of 2% for a 35-year time span, this MVP definition conforms to Shaffer's (1987) limit of 5% in 100 years.

In the last simulation study (Table 1), we performed a standard sensitivity analysis for each of the mortalities assumed for life stages (m , m , m ) and j o \ egg larva adult'

the assumed end of egg diapause (Dend). We aimed to rate their individual impact on both the extinction probability and the mean annual number of adults over 35 years. Changes in habitat temperature conditions expected under global warming are likely to affect mortalities (e.g. by altering the probability at which the cricket is predated) or the termination of diapause (because eggs need no frost as stimulus for hatching and larvae hatch earlier at higher temperatures, Ingrisch 1985). Simulations were performed as in the second simulation study, with the exception that we considered only the temperature conditions of Prappach and Hammelburg. Initial population sizes and capacities were 30,000 adults for Prappach and 3,000 adults for Hammelburg, because we expected low extinction rates for these capacities and default values of mortalities and egg diapause (see Results, Table 1). Again for each simulation scenario, we estimated the extinction probability and the mean annual number of adults based on 1,000 Monte Carlo simulations over 35 years.

Table 1 Mortalities (me , mlalva, madult) and ends of egg diapause (Dend) studied in the third simulation study

Table 1 Mortalities (me , mlalva, madult) and ends of egg diapause (Dend) studied in the third simulation study

Parameter

m

{0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1}

m larva

{0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8. 0.9, 0.925, 0.95, 0.975, 1}

madult

{0, 0.01, 0.02, 0.03, 0.04, 0.051, 0.06, 0.07, 0.08, 0.09, 0.1, 0.15, 0.2}

Dend end

{0, 1, 2, 3, 4, 5, 6} weeks before 31st March

Bold values are defaults assumed in the model of Griebeler and Gottschalk (2000a)

Bold values are defaults assumed in the model of Griebeler and Gottschalk (2000a)

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