Plankton: the paradox and the power law

Two basic features of assemblages of unicellular plankton: (1) their high biodiversity and (2) the power-law structure of their abundance, can be explained by an allometric scaling of cell growth and mortality with respect to cell size. To show this, we describe a numerical study of a size-structured, multispecies, population-dynamic model; the model has a single resource, supporting an arbitrary number of phytoplankton and zooplankton species. If the number of plankton species is large enough, the death rate of prey and cell growth rate of predators have approximate allometric scalings with cell size. Together, these scalings give rise to an equilibrium distribution of abundance near the power law, on which many species can coexist. Scalings of this kind cannot be achieved if the number of species is small. This suggests that the conjunction of speciesrichness and power-law structures in plankton communities is more than a coincidence. Although the exact allometric scalings used here should not be expected in practice, exclusion of species should be relatively slow if they lie close to the power law. Thus the forces needed to achieve coexistence could be effective, even if they are relatively weak.