where u is uptake rate (in micromoles per gram per hour), m is mass (in grams), and g is growth rate (in centimeters per year). Growth rate was divided by the maximum growth rate (10 cm · y−1) such that highest growth rates resulted in highest uptake rates. By scaling uptake rate with growth, we approximate metabolic scaling, resulting in a decline in uptake rate by a factor of 3.7 over the range of tubeworm sizes in this study [12]. The amount of sulfate that could be excreted by each individual was determined from the amount generated by sulfide oxidation carried out by the internal chemoautotrophic symbionts assuming constant internal sulfate concentration, thereby accounting for changes in body volume. We do not account for the binding of sulfur by free amino acids, as this is believed to relatively minor compared the flux rates of sulfate and sulfide, and is reversible [37]. Hydrogen ions are also generated in the oxidation of sulfide by the tubeworm symbionts. Hydrogen ion elimination rate was determined in the model in the same fashion as sulfide uptake, with growth rate determining the variability in this metabolic flux according to laboratory-measured ion fluxes (mean, 10.96 μmol · g−1 · h−1; standard deviation, 1.88 μmol · g−1 · h−1) [38]. Simple diffusion of hydrogen ions across the root surface was included in the model, though the exact mode of proton flux has not yet been determined experimentally for L. luymesi [38]. As diffusion across the roots accounts for a relatively small proportion of total proton flux (less than 10% in large individuals), additional pathways are likely and require further investigation.