Statistical analyses of variation in network metrics
We computed network metrics using the R package bipartite(Dormann et al. 2008). We considered the number of links per species, calculated as the total number of links divided by the total number of species. The generality index, which estimates the mean number of plant species per orthopteran species weighted by the marginal counts (Bersier et al. 2002) and is calculated from presences and absences of interactions instead of their intensities. The robustness of the networks (Dunne et al. 2002), which involves calculating the cumulative proportion of secondary extinctions caused by the sequential removal of plant species until all insect species are extinct. As implemented in bipartite , the function uses a quantitative estimation of the robustness introduced by Burgos et al. (2007). It measures the area under the attack tolerance curve (ATC), which describes the relationship between the proportion of species removed and the proportion of surviving insect species, until all species are extinct. The sequential species removal was done randomly for 100 replicates, excluding plant taxa that were not ingested. We finally computed the weighted nestedness following Galeano et al. (2009), as it has been associated to network robustness (Bascompte et al.2003). Relationships between mean summer temperature and the observed network metrics were tested using linear mixed effects models including transect identity as a random factor (packages lme4 Bateset al. 2008 and lmerTest Kuznetsova et al. 2017). We used a null model approach to discriminate the effect of the non-random interactions on the metric from the influence of inherent bias of network metric calculation (e.g. network size). We generated 999 random metawebs, where interactions were fully randomized and impossible links excluded. Individual random networks were then reconstructed for each study site according to their species composition. We further measured network properties for each network and metric variation along the gradient, following the same procedure as applied for the observed networks. Statistical significance of the metric variation was confirmed if the observed slope of the relationship between the temperature and the network metric fell outside the 2.5–97.5% quantile interval of the slopes obtained for the randomized network of interactions. We also calculated the standardized effect size (SES) to quantify the difference between the observed relationships and the null models. The approach we used here does not suppress the metrics’ sensitivity to sampling effects, but slope values outside the 2.5–97.5% quantile interval of the slopes obtained from random networks (and large values of SES) indicate that the interactions of empirical networks contribute more to the metric variation along the gradient than expected by chance.