The allometric scaling of oxygen supply and demand in the California horn shark, Heterodontus francisci.

The gill surface area of aquatic ectotherms is thought to be closely linked to the ontogenetic scaling of metabolic rate, a relationship that is often used to explain and predict ecological patterns across species. However, there are surprisingly few within-species tests of whether metabolic rate and gill area scale similarly. We examined the relationship between oxygen supply (gill area) and demand (metabolic rate) by making paired estimates of gill area with resting and maximum metabolic rates across ontogeny in the relatively inactive California horn shark, Heterodontus francisci. We found that the allometric slope of resting metabolic rate was 0.966±0.058 (±95% CI), whereas that of maximum metabolic rate was somewhat steeper (1.073±0.040). We also discovered that the scaling of gill area shifted with ontogeny: the allometric slope of gill area was shallower in individuals <0.203 kg in body mass (0.564±0.261), but increased to 1.012±0.113 later in life. This appears to reflect changes in demand for gill-oxygen uptake during egg case development and immediately post hatch, whereas for most of ontogeny, gill area scales in between that of resting and maximum metabolic rate. These relationships differ from predictions of the gill oxygen limitation theory, which argues that the allometric scaling of gill area constrains metabolic processes. Thus, for the California horn shark, metabolic rate does not appear limited by theoretical surface-area-to-volume ratio constraints of gill area. These results highlight the importance of data from paired and size-matched individuals when comparing physiological scaling relationships.