Sheldon Spectrum and the Plankton Paradox: Two Sides of the Same Coin. A trait-based plankton size-spectrum model

TL;DR

This paper presents a trait-based, scale-invariant size-spectrum model for unicellular plankton that explains the Sheldon spectrum and resolves the Paradox of the Plankton by demonstrating species coexistence through allometric scaling of physiological rates.

Contribution

It introduces a novel species-resolved size-spectrum model incorporating trait variation and allometric scaling, providing analytic solutions and explaining plankton diversity and biomass distribution.

Findings

The model reproduces the Sheldon spectrum in unicellular plankton.

Coexistence of many species is facilitated by allometric scaling of physiological rates.

Analytic steady-state solutions describe size distributions and species abundances.

Abstract

The Sheldon spectrum describes a remarkable regularity in aquatic ecosystems: the biomass density as a function of logarithmic body mass is approximately constant over many orders of magnitude. While size-spectrum models have explained this phenomenon for assemblages of multicellular organisms, this paper introduces a species-resolved size-spectrum model to explain the phenomenon in unicellular plankton. A Sheldon spectrum spanning the cell-size range of unicellular plankton necessarily consists of a large number of coexisting species covering a wide range of characteristic sizes. The coexistence of many phytoplankton species feeding on a small number of resources is known as the Paradox of the Plankton. Our model resolves the paradox by showing that coexistence is facilitated by the allometric scaling of four physiological rates. Two of the allometries have empirical support, the remaining two emerge from predator-prey interactions exactly when the abundances follow a Sheldon spectrum. Our plankton model is a scale-invariant trait-based size-spectrum model: it describes the abundance of phyto- and zooplankton cells as a function of both size and species trait (the maximal size before cell division). It incorporates growth due to resource consumption and predation on smaller cells, death due to predation, and a flexible cell division process. We give analytic solutions at steady state for both the within-species size distributions and the relative abundances across species.