Significance of spatial patterns against the null models for analysis 2 and 3
In order to determine whether the observed summary functions indicating spatial associations between congeners (g 12(r )) and the spatial distribution of size between congeners (κm 1.(r )) differed from the expected values under the appropriate null models, we first performed 199 Monte Carlo simulations of the point processes underlying the null models. Then we created global simulation envelopes for the 1-50 m distance interval, considering the critical α value as calculated in the Z test statistics. The global envelopes have the convenient property that the null model can be rejected with the prescribed significance level α if the observed summary function falls at least at one distance bin outside the envelopes (Wiegand et al. , 2016).