Plankton: the paradox and the power law

TL;DR

This paper demonstrates through a numerical model that allometric scaling of growth and mortality rates explains the high biodiversity and power-law abundance distribution observed in plankton communities, highlighting the importance of species richness.

Contribution

It introduces a size-structured multispecies model showing how allometric scalings lead to coexistence and power-law distributions in plankton assemblages, a novel explanation for observed patterns.

Findings

Power-law abundance distributions emerge with many species.

Allometric scalings support coexistence in large species pools.

Species exclusion is slow near the power law.

Abstract

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 species-richness 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.