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 interference competition in spatially structured populations. We show that this results not from spatial structure, but instead from the assumption that a small difference in mortality translates into a large difference in competitive ability. We present graphical criteria for recognizing functions that support one, two, or more species. High levels of coexistence in models of this form depend on a steep slope or a discontinuous second derivative of the function relating mortality to competitiveness. These criteria are identical to those in models of interference competition that lack explicit spatial structure.