Non-uniform scaling in phytoplankton growth rate due to intracellular light and CO2 decline

Scaling laws are central to relate ecological and physiological traits in unicellular autotrophs. Classical uniform scaling applied to phytoplankton maximum growth rate (mmax), however, meets several theoretical and empirical limitations. As an alternative model, I propose a non-uniform size dependency of mmax by considering how the geometry of unicells determines photosynthetic capacity. The model starts from physical laws of absorption and diffusion and uses known biochemical or biophysical coefficients. Calculated intracellular light and CO2 levels decline from the membrane to the cell centre, which may depress photosynthesis even under optimal growth conditions. Combination of the depletion model with a mechanistically motivated scaling rule for respiration generates a uni-modal size function for mmax. The function greatly improves predictions of classical allometries, in particular, for small cells and across taxonomic groups. Uni-modality in mmax has various implications for phytoplankton eco-physiology and morphology, correctly describing the absence of very small diatoms or giant green algae. For larger size classes, an increased benefit of non-spherical forms or of elevated pCO2 is calculated, whereas the advantage of carbon concentrating mechanisms turns out to be maximal for intermediate sizes. The model also points to a high degree of co-adaptation in different uptake systems.