Phytoplankton size scaling with nutrient concentration

Phytoplankton, the autotrophic component of the plankton community, is a key factor in oceanic ecosystems and in biogeochemical cycling. Over much of the ocean, phytoplankton growth is limited by nitrogen uptake (as nitrate), which is commonly described in ecosystem modelling by the Michaelis-Menten equation: V = V-max S/(K + S). Previous phytoplankton data compilations have shown that the maximum uptake rate, V-max, and the half-saturation constant, K, increase with organism size. Independent studies have also reported that K increases with nitrate concentration, S. Here, we assume that this K increase with S is due to an increase in the dominant organism size in the phytoplankton community with increasing nutrient concentration. Previous studies support this assumption, showing that nitrate abundance is the main factor determining dominant organism size. Based on this assumption and on previously published experimental observations for K, we show that phytoplankton dominant size, r, scales approximately with S-0.85. This increase in dominant size can also entail size-related changes in traits (such as the number of porters) that impact K and V-max. Furthermore, by combining a trait-based uptake model with the experimental results of K and V-max, we derive scaling relations for the number of porters and the handling time in terms of r. Our results indicate that handling time decreases approximately with r(-0.90) while porter number increases approximately with r(1.56). These results may be useful in characterizing size-dependent nutrient uptake in marine ecosystems and biogeochemical cycling models.