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.