Appendix S1
Species richness is measured as the number of unique body sizes observed at a given time within the whole community or within discrete trophic levels. Trophic position is defined continuously as the weighted mean trophic position of a consumer’s prey plus one, where basal nutrients are given a trophic level of zero, as in Loeuille & Loreau
(2005). For within trophic level analyses a nominal classification is used whereby trophic level 1 contains species with trophic positions from 1-1.5, level 2 contains positions 1.5-
2.5, level 3 contains positions 2.5-3.5, and level 4 contains positions 3.5-4.5 (no trophic position above 4.5 was observed). Model simulations were run in the program R
(http://www.r-project.org/) for 10 million time steps. This was sufficient time for species richness to reach a dynamic equilibrium whereby richness did not change directionally.
To determine the robustness of simulation results partial replicate simulations were run across three periods of time. This provided a computationally efficient approach for quantifying variation in richness-temperature slopes through time. More specifically, for each parameter combination and each temperature, five replicates were run for 100,000 time steps. Replicates were initialized at time 0; 400,000; or 4,900,000 such that richness was measured at time 100,000; 500,000; or 5,000,000. Community structure in the original simulations was used as the initial conditions for replicate simulations. For each set of replicate simulations, for a single time period across temperature values, a richnesstemperature slope was quantified. Five replicate ‘sets’ of simulations therefore provided five slope values. In turn, the mean slope and its corresponding standard deviation were quantified for each time period and each parameter combination. The results of this replication analysis are presented in Fig. 4.
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