Fig. 5

Differences between spatial distributions of fairy circles and Euphorbias, assessed with the g-function. The pattern is regular or aggregated at circular neighborhood distances if the red line of the g-function is either below the lower or above the upper grey lines of the simulation envelopes, respectively. Strong and significant fluctuations of the g-function far above and below the null-model envelopes, as shown for Gir-3, indicate a spatially periodic pattern. Null model envelopes were constructed using the 5th‐lowest and 5th‐highest value of 199 Monte Carlo simulations of the randomly distributed Poisson point process. The spatial patterns of the fairy circles and Euphorbias in the drone-mapped plots are shown above the g-functions for the Giribes (Gir-1, Gir-3), the Brandberg (Bra-1, Bra-2, Bra-3) and Garub (Gar-1, Gar-2). The g-function, also known as pair-correlation function, is a non-cumulative neighborhood-density function (see “Methods”)