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Table 1 Nearest-neighbor based statistics and pattern analysis of fairy circles and Euphorbias in the three regions Giribes, Brandberg and Garub

From: Revisiting Theron’s hypothesis on the origin of fairy circles after four decades: Euphorbias are not the cause

Region Data name Number of points Mean NN distance (m) CV of NN distance Clark-Evans index R p-value General type of pattern
Giribes Gir-1 Fairy Circles 277 22.6 22.4 1.51 0.002 Regular
Giribes Gir-1 Euphorbias 130 19.8 60.7 0.90 0.006 Clustered
Giribes Gir-3 Fairy Circles 1143 12.0 18.8 1.62 0.002 Regular
Brandberg Bra-1 Fairy Circles 284 17.4 42.7 1.17 0.002 Regular
Brandberg Bra-1 Euphorbias 58 30.1 56.4 0.92 0.066 Random
Brandberg Bra-2 Fairy Circles 138 24.2 51.4 1.14 0.036 Regular
Brandberg Bra-2 Euphorbias 87 24.2 65.2 0.90 0.024 Clustered
Brandberg Bra-3 Fairy Circles 437 18.0 21.1 1.50 0.002 Regular
Garub Gar-1 Fairy Circles 113 26.6 38.9 1.10 0.32 Random
Garub Gar-1 Euphorbias 90 21.6 95.3 0.80 0.002 Clustered
Garub Gar-2 Fairy Circles 45 38.5 55.5 0.91 0.074 Random
Garub Gar-2 Euphorbias 358 14.5 52.0 0.97 0.082 Random
  1. NN = nearest neighbor, CV = coefficient of variation. Assessment of the spatial pattern was based on the Clark-Evans index R
  2. Significant deviations from random distributions towards clustered or regular patterns are indicated by p-values < 0.05. Note that there were no Euphorbias in Gir-3 and only nine Euphorbias were in Bra-3, hence these plots have not been analyzed for Euphorbias. The specific type of pattern of the Gir-3 plot was spatially periodic (cf. g-function in Fig. 5), which is a special form of a regular pattern with an extraordinary degree of ordering