Forest edges increase pollinator network robustness to extinction with declining area

Plant-pollinator community structure and network architecture on islands might differ from the mainland reference sites both as a result of fragmentation processes and as a result of biases in sampling effort. The purpose of the null model is to determine whether variation in plant-pollinator community structure and network architecture on islands is significantly greater (or less) than expected from a simple ‘passive sampling effect’ from the continuous mainland reference pool. To do this, we compiled plant-pollinator interaction data from all sampling transects on the mainland edge and interior, respectively (16 transects in the mainland edge: 52 plant species, 266 pollinator species, and 1098 individual interactions; and 16 transects in the mainland interior: 19 plant species, 92 pollinator species, and 152 individual interactions), then used this as our expected 'reference' pools. From the edge and interior reference pools, we use two methods to simulate 'null communities' and 'null networks': (1) Null model Ⅰ (S1 code): a random draw of the same number of transects from the mainland as observed on each of the 41 sampled islands (i.e., constraining the number of sampling transects used to acquire a null estimate of floral resources, plant richness, pollinator richness and pollinator abundance); (2) Null model Ⅱ (S2 code): a random draw of the same number of pairwise interactions, while ensuring the same numbers of plant and pollinator species were selected as those observed on each of the 41 sampled islands (i.e., constraining both network abundance and network size). The re-sampling process was repeated 1000 times, generating 1000 simulated null networks for each island. We repeated this process separately for the edge and interior networks of each island. The detailed steps are as follows: Null model Ⅰ: constraining the same number of transects For each of the 41 islands, we conducted a random draw of the same number of transects as sampled on the island (across the 20 sampling intervals), and then calculated cumulative floral resources, plant richness, pollinator abundance, and pollinator richness. This process was repeated 1000 times, generating the null expected mean value (± 95% confidence limits) for each variable from 1,000 null draws. Null model Ⅱ: Constraining both network abundance and network size In null model II we constrained null draws by both network abundance and network size. The simplest and most intuitive approach to null model II was a fully-random process (S2 code: step of “A. Null model Ⅱ”) in which potential plant and pollinator species were drawn at random until the number of species was equal to the observed network, after which potential interactions were drawn at random until equal to the observed network. Following the random draws, the resulting null network was evaluated to determine whether it was equal in size to the observed network. However, the probability of the null network meeting both network abundance and size criteria was low and the fully-random process (S2 code: step of “B. Null model Ⅱ”) was computationally slow, except for networks that contained only a small number of plant and pollinator species but had a high network abundance. Therefore, a more computationally efficient constrained 'stepwise-random' process was developed. First, following the random draw of potential plant species (network rows), the randomly-drawn pollinator species (network columns) were constrained to only those with known potential links in the reference pool, in order to avoid null network column totals that intrinsically sum to zero. Second, prior to the random draw of potential interactions, the null network was 'auto-populated' with the minimum number of randomly-drawn interactions to avoid network row and column totals stochastically summing to zero. Finally, after null network size was constrained to equal the observed network size, additional potential interactions were drawn at random to equal observed network abundance. Therefore, the fully-random process (S2 code: step of “B. Null model Ⅱ”) we eventually used to complete the Null model Ⅱ.