Resource limitation alters the 3/4 size scaling of metabolic rates in phytoplankton

Under optimal growth conditions, many metabolic rates scale to the 3/4 power of mass. We show that resource limitation can alter this size scaling of metabolic rates if resource acquisition depends on organism size. A prime example of size-dependent resource acquisition is light harvesting by phytoplankton. The size-dependence of light acquisition causes a deviation in the 3/4 size scaling of growth and photosynthetic rates under growth-limiting irradiance. The degree of deviation from the 3/4 size-scaling exponent depends on the size-dependence of physiological acclimation in response to resource limitation. Phytoplankton acclimate to light limitation by changes in pigment concentration. We calculate the pigment concentration required to maximize photosynthetic rate, and predict that the light-limited photosynthetic rate must scale to the 2/3 power of cell volume. These theoretical results are consistent with the size scaling of pigment concentration and photosynthetic rate of phytoplankton cultures. Our results suggest that deviation from the 3/4 size-scaling exponent for metabolic rate under resource-limiting conditions is the consequence of the size-dependence of both resource acquisition and physiological acclimation to resource availability.