Nutrient cycling in terrestrial ecosystems involves not only the vertical recycling of nutrients at specific locations in space, but also biologically driven horizontal fluxes between different areas of the landscape. This latter process can result in net accumulation of nutrients in some places and net losses in others. We examined the effects of such nutrient-concentrating fluxes on the R* rule, which predicts that the species that can survive in steady state at the lowest level of limiting resource, R*, can exclude all competing species. To study the R* rule in this context, we used a literature model of plant growth and nutrient cycling in which both nutrients and light may limit growth, with plants allocating carbon and nutrients between foliage and roots according to different strategies. We incorporated the assumption that biological processes may concentrate nutrients in some parts of the landscape. We assumed further that these processes draw nutrients from outside the zone of local recycling at a rate proportional to the local biomass density. Analysis showed that at sites where there is a sufficient biomass-dependent accumulation of nutrients, the plant species with the highest biomass production rates (roughly corresponding to the best competitors) do not reduce locally available nutrients to a minimum concentration level (that is, minimum R*), as expected from the R* rule, but instead maximize local nutrient concentration. These new results require broadening of our understanding of the relationships between nutrients and vegetation competition on the landscape level. The R* rule is replaced by a more complex criterion that varies across a landscape and reduces to the R* rule only under certain limiting conditions.