Determining patch size

Abstract

Shrub encroachment, i.e. the increase in density of woody species, is threatening tree-grass coexistence in savannas worldwide (see e.g. Smit, 2004; Wiegand, Ward {\&} Saltz, 2005; Wiegand, Saltz {\&} Ward, 2006). In addition to ecological problems, shrub encroachment creates economic problems, because it reduces the extent of areas suitable for grazing of livestock. In recognition of the importance of spatial and temporal scales for savannas, Wiegand et al. (2005, 2006) proposed patch-dynamics as the driving mechanism of tree-grass coexistence in savannas including a naturally shrub encroached phase. In patch-dynamic landscapes, patches are asynchronously cycling between woody and grassy dominance. Evidence for patch-dynamic savannas is accumulating (e.g. Gillson, 2004; Wiegand et al., 2006), but simple methods for the determination of the spatial scale of patches are still lacking. In the present study, we propose a method for estimating patch sizes based on the canopy diameter and the spatial location of individuals and apply it to an example data set from a semi-arid savanna in South Africa.