Can isotropy vs. anisotropy in the spatial association of plant species reveal physical vs. biotic facilitation?

In dryland ecosystems and other harsh environments, a large part of the vegetation is often clustered, appearing as 'islands'. If 'independent' species, usually colonizers, can be distinguished from species which are 'dependent' on the presence of the colonizing species for successful establishment and/or persistence, the type of spatial pattern of the association - isotropic (spatially symmetric) or anisotropic (spatially asymmetric)- can give information on the underlying environmental factors driving the process of association. Modified spatial pattern analysis based on Ripley's K-function can be applied to bivariate clustered patterns by cardinal direction in order to detect possible anisotropy in the pattern of association. The method was applied to mapped distribution patterns of two types of semi-arid shrubland in southeastern Spain. In shrubland of Retama sphaerocarpa, low shrubs of Artemisia barrelieri were significantly clustered under the canopy of the Retama shrubs in all four cardinal directions, suggesting an isotropic facilitation effect. In low shrubland dominated by Anthyllis cytisoides and Artemisia barrelieri, Anthyllis shrubs occurred more frequently than expected on the eastern side (and downslope) of Artemisia shrub. The possible environmental factors driving the two association patterns are discussed and recommendations for further applications of the analytical method are given.