electronic supplementary material Appendix B Detailed results for small-scale interactions at BCI Results of analysis 2 based on the summary statistics K12 and D12
The goodness-of-fit test based on the summary statistics K12 and D12detected for the BCI data in 3.2% of all cases (121 species pairs) significant departures from the heterogeneous Poisson null model at scales 0-30m. This result is similar to the 4.0% found at Sinharaja (83 pairs), but quite different from the 15% found at the CBS forest (31 pairs).
The results of the BCI forest are qualitatively similar to that obtained at Sinharaja (figure A3a and b): negative small-scale associations were more common than positive small-scale associations but they disappeared at the BCI forest at smaller distances (i.e., r < 20m) while a certain proportion of negative association were maintained at the Sinharaja plot for distances > 30m. The latter is an effect of the cumulative nature of the K-functions where strong associations at small distances influence the result at larger distances (Wiegand and Moloney ). The larger range of negative associations found at the Sinharaja plot could be a result of the stronger topographic habitat heterogeneity with some sharp habitat boundaries (Gunatilleke et al. ). The temperate CBS forest yielded a substantially higher proportion of negative small-scale associations that disappeared, similarly to the BCI plot, at distances of r < 20m (figure A3c). Comparing across the three forests shows in accordance with specific hypothesis H2 that the proportion of non-significant small-scale interactions increased with increasing species richness although no differences were found for the two species-richer tropical forests.
Detailed results for small-scale interactions at BCI captured with the pair correlation function
Three species (Eugenia coloradoensis, Swartzia simplex_var.ochnacea, and Trichilia pallida,) did not show any significant interaction to any other species as depicted by the goodness-of-fit test. On the other extreme, the two species Oenocarpus mapora and Trichilia tuberculata showed significant interactions to 28 other species, followed by the species Cecropia insignis and Hirtella triandra with 21 and 16 significant interactions, respectively. All other species maintained less than 14 significant interactions with other species. The shade-tolerant canopy species T. tuberculata is the most abundant species in our analysis (1681 stems with dbh > 10cm) and has escaped dispersal limitation . In most cases it showed negative small-scale associations to other species. O. mapora, a common subcanopy clonal palm, showed in most cases significant negative interactions to other species. C. insignis, a common canopy tree that regenerates in gaps showed mostly positive interactions to other species.
Distribution function of the number of significant interactions per species
It seems that O. mapora and T. tuberculata may interact with more other species than expected by a random allocation of species interactions. To explore if the significant interactions found among species pairs were randomly distributed among species or if some species such as O. mapora and T. tuberculata may have more (or less) interactions with other species than expected by chance we used a randomization approach. In analysis 2 we analyzed all n × (n - 1) bivariate patterns that are possible for the n species included in the analysis (n = 62, 46, 15 from BCI, Sinharaja, and CBS, respectively). This yields a n × n interaction matrix M(k, l) with value 1 if the goodness-of-fit test indicated a significant departure from the null, a value 0 if the goodness-of-fit test could not detect a significant departure from the null, but the diagonal (k = l) which would correspond to univariate analyses was excluded. In this matrix we counted the sum for each row and column which yields the number of significant interactions where the species was focal species and second species, respectively. The total number of significant interactions for each species was the sum of both values.
For our analysis we used the cumulative distribution function that gives the proportion of species which have less than x significant second-order interactions to other species as summary statistic (figure A4). To find out if the observed distribution function was compatible with random allocation of significant associations (as opposed to some species having more or less significant associations as expected by chance) we randomized the interaction matrix M(k, l) by randomly shuffling the values of the associations over all elements of the matrix except diagonal elements. We thus randomized the observed associations in a way that each species pair had the same chance of having a significant association. We repeated the randomization procedure 199 times and calculated for each realization of the null model the corresponding distribution function and the fifth lowest and highest values of the simulated distribution function as simulation envelopes.
We found that species interactions at the BCI forest are not randomly distributed among species. There were some species with considerably more interactions as expected by chance and many species with fewer interactions as expected (figure A4). For example, there were 19 species with 2 or less interactions observed, but only a maximum of 5 was expected by chance (the upper simulation envelope in figure A4a). The maximal number of interactions expected by chance was 15, but there were 5 species with as much as 16, 18, 21, and 28 significant interactions. The species Oenocarpus mapora and Trichilia tuberculata that showed the highest number of (mostly negative) interactions to other species did not reach local dominance since their average relative stem densities yielded only 5.5% (O. mapora) and 16.3% (T. tuberculata). Additionally, the 28 significant interactions of O. mapora and T. tuberculata included 9 and 10 symmetric interactions (e.g., O. mapora - T. tuberculata as well as T. tuberculata - O. mapora were significant), respectively. Thus, even these two species with the most pronounced interspecific interactions maintained significant small-scale relationships with less than 25% of the analyzed species.
We also reanalyzed the data of the Sinharaja forest in Sri Lanka (Wiegand et al. ) and found a surprising accordance between both forests. The cumulative distribution functions were almost identical (cf. figure A4a and figure A4b). Similar results were also found at the CBS forest (figure A4c) where three species showed many interactions (17, and 18).