Fick’s Diffusion Laws and Scaling of the Gill Surface Area and Oxygen Uptake in Fish

The oxygen consumption of adult fish (Q) is proportional to their body weight (W) raised to a power, estimated as the slope (dQ) of a linear regression of log(Q) vs. log(W). Similarly, the gill surface area of adult fish (GSA) is proportional to W raised to the power dG, as also estimated via a log-log linear proportional to their surface area. Moreover, because of Fick’s laws of diffusion, dQ should be at least similar to dG. Recently, the claim has been made that non-zero differences between dQ and dG invalidate the Gill-Oxygen Limitation Theory (GOLT), which suggests that the O2 supplied by gills growing with dG <1 limits the growth of older and larger fish. We show here, based on 33 pairs of dG and dQ in 33 fish species and other information that (i) while individual differences between dQ and dG are observed in several cases, there is no significant overall difference across the 33 estimates and (ii) large differences between dQ and dG are primarily due to ontogenetic changes in scaling (OCS), likely ontogenetic changes in gills’ water–blood (or ‘diffusion’) distance and, as well, multiple sources of experimental variability and potential errors, leading to outliers and random differences.