2016/07/14 by José A. Cuesta, Gustav W. Delius, Richard Law
Biochemistry, Genetics and Molecular Biology · Earth and Planetary Sciences · Environmental Science · Mathematics · Physics and Astronomy · #Abundance (ecology) #Allometry #Biology #Biomass (ecology) #Cell size #Ecology #Ecosystem #Fish Ecology and Management Studies #Marine and coastal ecosystems #Mathematics #Nutrient #Physics #Physiological and biochemical adaptations #Phytoplankton #Plankton #Predation #Range (aeronautics) #Scaling #Statistical physics #Zooplankton #msc:92C37 #msc:92D25 #msc:92D40 #physics.bio-ph #q-bio.PE
paper · pdf · doi:10.1007/s00285-017-1132-7
published as J. Math. Biol. (2017) 1--30 · 26 pages, 1 figure, needs Springer class file svjour3.cls
arxiv created 2016/07/14 · openalex publication_date 2017/05/25 · arxiv updated 2017/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.