Table 1.
Description of variables.
Table 2.
Allometric, stoichiometric and ammonium transport characteristics for 3 phytoplankton species.
More detailed explanations of the variables are given in Table 1. The data have been compiled from [29–34] for the coccolithophorid Emiliania huxleyi, raphidophyte Heterosigma carterae and the diatom Thalassiosira weissflogii.
Table 3.
Alternatives to Table 2 computed using an allometric scaling function.
More detailed explanations of the variables are given in Table 1 and legend of Table 2.
Fig 1.
Plots of the potential growth rate for cells of different size against bulk nutrient concentration.
In all instances the maximum growth rate is set at Gmax = 0.693 d-1 (one doubling per day, assuming a constant rate of N-transport over the day). Organism configurations shown represent cells with a cellular carbon density which is fixed (C150), which accords with a generic protist phytoplankton (Cprot) or with a diatom (Cdiat). More details are given in Table 1. TRDmax = 0.4 pgN μm-2 d-1. The dashed horizontal line indicates G = Gmax/2 = G0.5; the corresponding value of DIN is KG.
Fig 2.
Relationship between cell size and the resultant value of KG.
Organism configurations are shown representing a cellular carbon density that is fixed (C150), and accords with a generic protist phytoplankton (Cprot), or with a diatom (Cdiat). More details are given in Table 1. The green layer is for non-motile (non-swimming or non-sedimenting) cells; the pink layer is for motile (non-diatom protist; Eq 12 in Methods), or sedimenting (diatoms; Eq 13 in Methods) cells. Note that the KG scale is logarithmic.
Fig 3.
ESD vs μmax and their resultant values of Gmax/KG.
Developed from Fig 2, this plot shows organism configurations representing a cellular carbon density that is fixed (C150), accords with a generic protist phytoplankton (Cprot), or with a diatom (Cdiat). More details are given in Table 1 and in the legend for Fig 2.
Fig 4.
Developed from Fig 3, this plot shows ESD vs Gmax/KG.
Table 4 shows the power-regression for best fit through these data. See legend for Fig 2 for further information.
Table 4.
Power-regression for (Gmax/KG = a * ESDb) best fit through the data shown in Fig 4.
Further explanations regarding the organism configuration and motility scaling are provided in Table 1.
Fig 5.
Relationship between the minimum N:C quota, cell size, and the DIN concentration required to support G0.5.
Gmax = 0.693 d-1 for motile and non-motile protists alike. The green layer is for DIN at the cell surface (S0), and is the same in both plots; the red layers are for DIN in the bulk medium (S∞), and thus is the value of KG. In all instances, NCmax = 0.18.
Fig 6.
Relationship between N-status (N:C) and Tmax for cells of different size.
Calculations were undertaken using Eqs 5, 6 and 7. Here Gmax = 0.693 d-1, KTcon = 0.1, maximum and minimum N:C at 0.18 and 0.05, respectively; the cellular carbon density was assumed to be fixed at 150gC (cell L)-1 (i.e., C150); the maximum transporter rate density was set at TRDmax = 0.4 pgN μm-2 d-1.
Fig 7.
Relationship between ammonium or nitrate concentration and growth rate for Emiliania or Heterosigma.
The response curves relating Tmax to nutrient status, and nutrient status to growth rate were as in S2 Fig. The grey curve indicates the relationship at the plasma-membrane surface; this relationship would also apply if diffusion limitation was zero (i.e., ignored). The solid red curve is the relationship with the bulk nutrient concentration. The dashed black curve is the rectangular hyperbolic type 2 (RHt2) fit through the data describing the red curves with unconstrained fitted values of Tmax and KG. Note the different x-axis ranges.
Fig 8.
Relationship between Gmax, cell size, and TRDGmax.
Maximum N:C (at G = Gmax) was assumed as 0.18 gN gC-1.The required value for TRDGmax in Cdiat is less than that for Cprot because diatoms, being more vacuolated with a lower gC (cell L)-1, have a decreased demand for N across a given area of cell plasma-membrane. The absolute maximum value of TRD (TRDmax) is expected to be ca. 0.4 pgN μm-2 d-1; large fast-growing protists approach the limit of TRDGmax = TRDmax.
Fig 9.
Relationship between Tmax N-status (N:C) and cell size (ESD).
This is shown for cells as protists or diatoms of different size (as equivalent spherical diameter, ESD), defined using Eqs 5, 6 and 7 with KTcon = 0.1. The green layer shows the transport need to support growth; the difference between this green layer and the potential transport rate Tmax indicates the potential over-capacity for transport (see S2 Fig). The maximum growth rate was assumed as 0.693 d-1; at higher Gmax the green layer is elevated there thus being less difference between Tmax and the transport required to meet demand. Maximum and minimum N:C were assumed at 0.18 and 0.05 gN gC-1, respectively; the cellular carbon density was set via the allometric relationships for Cprot and Cdiat [9]; the maximum transporter rate density was set at TRDmax = 0.4 pgN μm-2 d-1.