The allometry of oxygen supply and demand in the California Horn Shark, Heterodontus francisci

The scaling relationship between metabolic rate and body mass is one of the most notable functional relationships in comparative physiology and macroecology. In aquatic ectotherms, the surface area of the gills is thought to be a major contributor to the allometric scaling patterns we see for metabolic rate, both within and across species. Here, I first examined the allometric relationship between oxygen supply (gill area) and consumption (metabolic rate) and found that the allometry of gill area was isometric and very similar to that of metabolic rate. Second, I tested the effects of three statistical analysis techniques for estimating maximum metabolic rate and found that a rolling regression model was the best candidate model across four fish species. Together, these results support the hypothesis that oxygen supply and demand are closely matched and suggest that a two-dimensional gill can overcome geometric constraints to increase at the same rate as the three-dimensional mass of an inactive organism. Additionally, they highlight the importance of statistical choices in producing comparable and reproducible estimates of metabolic rate across species.