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ABSTRACT 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. 

Abstract Life history theory suggests that maximum size and growth evolve to maximize fitness. In contrast, the Gill Oxygen Limitation Theory (GOLT) suggests that growth and maximum size in fishes and other aquatic, water‐breathing organisms is constrained by the body mass‐scaling of gill surface area. Here, we use new data and a novel phylogenetic Bayesian multilevel modelling framework to test this idea by asking the three questions posed by the GOLT regarding maximum size, growth and gills. Across fishes, we ask whether the body mass‐scaling of gill surface area explains (1) variation in the von Bertalanffy growth coefficient (k) above and beyond that explained by asymptomatic size (W_∞), (2) variation in growth performance (a trait that integrates the tradeoff betweenkandW_∞) and (3) more variation in growth performance compared to activity (as approximated by caudal fin aspect ratio). Overall, we find that there is only a weak relationship among maximum size, growth and gill surface area across species. Indeed, the body mass‐scaling of gill surface area does not explain much variation ink(especially for those species that reach the sameW_∞) or growth performance. Activity explained three to five times more variation in growth performance compared to gill surface area. Our results suggest that in fishes, gill surface area is not the only factor that explains variation in maximum size and growth, and that other covariates (e.g. activity) are likely important in understanding how growth, maximum size and other life history traits vary across species.