Integrating nested spatial scales] implications for the coexistence of competitors on a patchy resource

0[ Intraspeci_c aggregation at a single spatial scale can promote the coexistence of competitors[ This paper demonstrates how this same mechanism can be applied to the many systems that are patchy at two scales\ with patches nested within {superpatches|[ 1[ Data are presented from a _eld study showing that insects living in rotting fruits have aggregated distributions in the fruits under a single tree\ and that the mean density and degree of aggregation varies signi_cantly among trees[ Observations in this system motivate the following models[ 2[ A model of competition has been developed between two species which explicitly represents spatial variation at two scales[ By integrating the probability distributions for each scale\ the marginal distributions of competitors over all patches can be found and used to calculate coexistence criteria[ This model assumes global movement of the competitors[ 3[ Although spatial variation at a single scale may not be su.cient for coexistence\ the total variation over all patches can allow coexistence[ Variation in mean densities among superpatches and variation in the degree of aggregation among superpatches both promote coexistence\ but act in di}erent ways[ 4[ A second model of competition between two species is described which incorporates the e}ects of limited movement among superpatches[ Limited movement among superpatches generally promotes coexistence\ and also leads to correlations among aggregation and the mean densities of competitors[