The structural organization of several antagonistic networks has been demonstrated to be largely conserved through time and space even when species beta-diversity is high. This might occur either because species are replaced by others that fulfill similar network roles, or because interaction probabilities are given by species relative abundances rather than by their functional traits. Alternatively, if species-specific traits are important drivers of realized interactions, any change in species composition should promote a certain degree of network structural dissimilarity. Here, we used a spatial-temporal system comprising asteraceous plants and flower head herbivores from remnants of Brazilian Cerrado to investigate whether the relationship between spatial beta-diversity of species and network structural dissimilarity changes over time. We measured species beta-diversity using Sørensen’s dissimilarity index (βsor) and its components of species replacement (β-3) and richness differences (βrich). Network structural dissimilarity was estimated using three different metrics: connectance, modularity and web asymmetry. We show that, in general, the effect of species beta-diversity on network structure was time-dependent: while some periods presented a positive relationship between spatial beta-diversity and network structural dissimilarity, others presented no significant relationship. This indicates that functionally similar species may present different turnover rates at distinct periods and different non-exclusive processes affect plant-herbivore network organization across time.

Asteraceae and endophagous herbivores were sampled in remnants of Cerrado vegetation in the state of São Paulo, southeastern Brazil, between April 2004 and February 2005 (Almeida-Neto et al., 2010, 2011). Originally, the plant-herbivore interaction data used in this study were recorded in 20 remnants of Brazilian Cerrado to investigate the influence of invasive grass cover on the diversity patterns of asteraceous plants and their herbivorous insects (Almeida-Neto et al., 2010, 2011). However, several studies relied on this same dataset (entirely or partially) to test other hypotheses about the ecological and evolutionary processes shaping plant-insect interactions (Bergamini, Lewinsohn, Jorge, & Almeida-Neto, 2017; Jorge, Prado, Almeida-Neto, & Lewinsohn, 2014; Nobre, Bergamini, Lewinsohn, Jorge, & Almeida-Neto, 2016; Martins, Medina, Lewinsohn, & Almeida‐Neto, 2019). In the present study, we chose the ten Cerrado remnants with lowest levels of invasive grass cover to minimize possible confounding effects among sites. Remnants ranged in area from 6 to 150 ha (mean area = 47.4) and the minimum and maximum distances between any two sites were 1.8 and 31.5 km, respectively (mean distance = 11.3 km).

Plant-herbivore networks were sampled during three periods in each site: April-May 2004, August-September 2004 and January-February 2005. These periods were chosen because they include the flowering peaks of the most common and speciose tribes of Asteraceae in the Brazilian Cerrado. The first period (April-May) includes the flowering peaks of the tribes Eupatorieae and Vernonieae. The second period (August-September) includes the flowering peaks of Mutisieae and Gochnatieae, and the third period (January-February) includes the flowering peak of Astereae. Sites were sampled within 35 days in each period. Every study site consisted of 15 transects of 30 x 5 m randomly allocated in relation to the edges of the site.  The local abundance of each plant species was estimated by counting the number of flowering or fruiting individuals within the transect. A maximum volume of 80 ml of flower heads per individual plant was randomly sampled from 20 up to 35 flowering individuals (when available) per species. Sampled flower heads were taken to the laboratory and the emergence of adult herbivores was monitored weekly for at least two months. Due to the lack of taxonomic information on Neotropical Cecidomyiidae (Diptera) and Apionidae (Coleoptera) species, these groups were identified to the genus level and then separated into morphospecies.

Herbivore's species names without epithet (e.g. Apion_sp.1) do not necessarily match the names in our Table S2. The reason is that the names in the original dataset (n = 20 sites) were changed for clarity in Table S2, as only herbivore species occuring in the ten Cerrado remnants with lowest levels of invasive grass cover were used in our analyses (please see Methods section). As such,  Apion species names are Apion_sp.1, Apion sp.2, Apion_sp.4, Apion_sp.5, Apion_sp.6, Apion_sp.9, Apion_sp.10 and Apion_sp.11 (n =8 Apion species) in the the local networks here presented, while the names in Table S2 ranges from Apion sp.1 to Apion sp.8. Notice that this pattern holds true for other herbivore genera including species without epithets, but this does not affect the reproducibility of our results. In fact, calling a species Apion_sp.11 or Apion sp.8 does not have any effects on the ecological patterns presented in the main paper.