Fig. 3.

a Elemental ratios for an entire ecosystem given a cell size distribution characterized by $\mathcal{F}\propto V_c^{-\alpha }$ where $\mathcal{F}$ is frequency and $V_c$ is cell size. The dashed lined is the standard Redfield N:P ratio of 16:1. The black curve is for gram-negative bacteria and gray is for gram-positive bacteria. For reference, b gives a measured size spectrum from Cavender-Bares et al. (2001) with a fitted exponent of $\alpha =-1.07\pm 0.05$. Here the size bin is defined by $i\le {log}_{10}{V}_c<i+\mathrm{\Delta }$ with i taken in steps of $\mathrm{\Delta }=0.10$. The comprehensive data from Cavender-Bares et al. (2001) show exponents that vary between $\alpha =-0.95$ and −1.35. In a we used a discrete logarithmic summation to obtain total N and P concentrations.