Is space necessary? Interference competition and limits to biodiversity

A single trade-off between competitive ability and mortality has been shown to support an arbitrarily large number of species in models of interferenc e competition in spatially structured populations. We show that this result s not from spatial structure, but instead from the assumption that a small difference in mortality translates into a large difference in competitive a bility. We present graphical criteria for recognizing functions that suppor t one, two, or more species. High levels of coexistence in models of this f orm depend on a steep slope or a discontinuous second derivative of the fun ction relating mortality to competitiveness. These criteria are identical t o those in models of interference competition chat lack explicit spatial st ructure.