In spite of wide spread use of territorial use rights fisheries (TURFs) as a management tool, efficient design of spatial property rights, particularly in context of communal ownership, remains poorly understood. We develop a spatially explicit game-theoretic model of a two-patch communally exploited TURF network to investigate spatial scale, species dispersal, and fisher interactions. We characterize biological networks and patch sizes conducive to fostering internally cooperative harvesting behaviors. We also characterize the magnitude and spatial distribution of cost of any defection from cooperative harvesting behaviors. We find when neighboring patches are each independently cooperative, profitability in presence of high larval-stage dispersal is higher than when species are immobile. Mutually non-cooperative behavior across TURFs produce outcomes under connectivity that are worse than when species are immobile. Our results demonstrate that joint accounting of species dispersal habits and behavioral organization of communities within spatial property rights are critical when demarcating property rights boundaries.