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).