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 veg etation is often clustered, appearing as 'islands'. If 'independent' specie s, usually colonizers, can be distinguished from species which are 'depende nt' on the presence of the colonizing species for successful establishment and/or persistence, the type of spatial pattern of the association - isotro pic (spatially symmetric) or anisotropic (spatially asymmetric)- can give i nformation on the underlying environmental factors driving the process of a ssociation. Modified spatial pattern analysis based on Ripley's K-function can be applied to bivariate clustered patterns by cardinal direction in ord er to detect possible anisotropy in the pattern of association. The method was applied to mapped distribution patterns of two types of semi-arid shrub land in southeastern Spain. In shrubland of Retama sphaerocarpa, low shrubs of Artemisia barrelieri were significantly clustered under the canopy of t he Retama shrubs in all four cardinal directions, suggesting an isotropic f acilitation effect. In low shrubland dominated by Anthyllis cytisoides and Artemisia barrelieri, Anthyllis shrubs occurred more frequently than expect ed on the eastern side (and downslope) of Artemisia shrub. The possible env ironmental factors driving the two association patterns are discussed and r ecommendations for further applications of the analytical method are given.