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

Examination of the allometric scaling of resting and maximum metabolic rate with gill surface area suggests that gill-oxygen uptake meets metabolic demand in the California Horn Shark,

where RMR, MMR, and gill surface area were each estimated in separate animals and studies (Muir and Hughes, 1969;Graham and Laurs, 1982;Hughes, 1984). In contrast, other studies have shown that gill area can scale in between that of MMR and RMR or even closer to RMR (Luo et al., 2020;Somo et al., 2023).
Understanding the intricacies of how the scaling of gill surface area, RMR, and MMR relate has become more critical in light of changes in organismal oxygen demands associated with climate warming and ocean deoxygenation (Lefevre et al., 2021). Indeed, the supply of oxygen delivered to the tissues appears tightly coupled to temperature performance curves in ectothermic animals and may ultimately limit MMR and hence aerobic scope at higher temperatures (Pörtner and Knust, 2007;Pörtner and Farrell, 2008;Rubalcaba et al., 2020).
While the acquisition of environmental oxygen at the gills represents only the first step in the "oxygen cascade" as oxygen is transferred from the environment through the blood and into the tissues where it is ultimately utilized, the gill has received renewed attention due to the Gill Oxygen Limitation Theory (GOLT). The GOLT focuses on this first step and argues that oxygen uptake at the gills may ultimately limit metabolism and the energy available for growth and other life-sustaining processes (Pauly, 2010(Pauly, , 2021Pauly and Cheung, 2017). This theory has been used to predict ecological patterns and processes, particularly with regard to how species will respond to a changing climate. For example, Cheung et al. (2013) used this framework to predict that fish maximum body sizes will decline by around 7-12% from 2000 to 2050 due to increased constraints of oxygen acquisition at the gills under warmer temperatures.
The GOLT centers on the scaling of relative oxygen supply, or oxygen obtained at the gill surface and used for metabolism. Specifically, the GOLT argues that a two-dimensional gill surface area cannot increase at the same rate as the three-dimensional body mass it must supply with oxygen and, in turn, this mismatch limits metabolism and dependent processes as an organism grows (Pauly 2010(Pauly , 2021. This supposition results in two testable predictions associated with the scaling of gill surface area and metabolic rate. First, the GOLT argues that gill surface area cannot scale with body mass with an allometric slope at or above b = 1.0 due to geometric limitations on the scaling of surface areas (e.g., geometric isometry would predict a surface area to volume increase of b = 0.67, and while the GOLT recognizes that gill surface area can Journal of Experimental Biology • Accepted manuscript scale higher than 0.67 it argues it cannot scale with an allometric slope of b ≥ 1.0; Pauly 2010, 2021). A second way this theory can be viewed is that gill surface area would scale with a lower allometric slope than metabolic rate (i.e., the ratio of gill surface area to metabolic rate should decrease with size; Scheuffele et al., 2021).
The GOLT perspective that gill surface area limits metabolic rate is in direct contradiction to the widely accepted physiological view that gill surface area is adapted to match metabolic demand over a range of body sizes (Lefevre et al., 2017(Lefevre et al., , 2018. While gills are indeed a surface, that surface is highly folded to increase the area available for gas exchange and gill surface area can indeed scale close to b = 1.0 if required by metabolic demand (Wegner, 2011;Lefevre et al., 2017, 2018, Wegner andFarrell, in press). While gill surface area does generally scale less than b = 1.0 as predicted by geometric isometry and the GOLT, there are robust datasets showing species-specific scaling of gill surface area close to or even exceeding b = 1.0, which would argue against the GOLT (Holeton, 1976;Wegner et al., 2010a;Bigman et al., 2018). Likewise, limited comparisons of the scaling of gill surface area and metabolic rate in the same species has shown that the ratio of gill surface area to metabolic rate does not necessarily decrease with growth (Scheuffele et al., 2021;Somo et al., 2023). However, most of the work to date that examines the links among oxygen, metabolic rate, and gill surface area are across species (Gillooly et al., 2016;Bigman et al., 2021Bigman et al., , 2023a. There are few studies that examine the scaling of gill surface area and metabolic rate for the same species (De Jager and Dekkers, 1975;Gillooly et al., 2016, Bigman et al., 2021 and even fewer studies that estimate gill surface area and metabolic rate in the same individual animals (Li et al., 2018;Luo et al., 2020;Somo et al., 2023). One of the key issues in comparing the allometry of traits, such as gill surface area or metabolic rate, is that the traits are often not measured in individuals of an overlapping bodysize range, and when they do overlap, it is often only for a small fraction of the species size range (Bigman et al., 2021;Scheuffele et al., 2021). As a consequence, comparing allometric slope estimates may be confounded by Jensen's inequality resulting from averaging non-linear (power law) relationships, particularly of partially non-overlapping size ranges (Denny, 2017;Bigman et al., 2023a,b).

Journal of Experimental Biology • Accepted manuscript
Here, we examined the allometric scaling between oxygen supply (gill surface area) and

Animal acquisition and husbandry
We used a total of 20 California Horn Shark individuals ranging in size from 0.

Respirometry and experimental setup
We measured oxygen consumption rate (M O 2 in mgO 2 h -1 ) for each individual using respirometers consisting of a holding chamber proportional to the size of the shark and a short recirculation loop containing a fiber optic oxygen sensor and temperature probe connected to either a Fibox 3 or Fibox 4 oxygen meter (Presens, Regensburg, Germany) (Clark et al., 2013;Svendsen et al., 2016;Skelton et al., 2023). We used seven separate respirometer chambers of increasing width and length to accommodate the wide size range of individuals used in this study. The six larger chambers were commercially-available acrylic cylinders (Loligo Systems, Journal of Experimental Biology • Accepted manuscript Denmark) and varied in size resulting in a total respirometer volume of 5.8 to 52.5 L. The smallest respirometer (2.6 L) was constructed from a 28.1 x 19.3 x 7.9 cm rectangular Tupperware outfitted with a recirculating loop like the cylindrical chambers to accommodate the three smallest individuals. The chamber-to-fish volume ratio varied from 11.8:1 to 66.4:1.
During trials, we placed the respirometer in a large water bath to maintain a consistent experimental temperature (target 18.0 °C, mean 18.2°C [SD ± 0.2]) and to allow the system to be flushed with aerated seawater between oxygen depletion measurements through inlet / outlet one-way check valves on opposing ends of the chamber. Water entering the chamber from both the recirculating loop (constantly flowing) and inlet valve (opened during flush periods) was forced against a splitter or a wide plate to aid in water mixing within the chamber.
To reduce bacterial growth, water baths were constantly supplied with fresh, UV-sterilized aerated seawater (salinity 33.5‰, oxygen 100% air saturation) at a rate to fully exchange the bath water every 30-60 min, and we washed the systems with freshwater and detergent or sterilized with ethanol between experiments.

Estimation of resting metabolic rate
We estimated RMR for each individual using automated intermittent flow respirometry (Svendsen et al., 2015;Chabot et al., 2016). One at a time, we moved sharks from their holding tank to individual respirometer chambers set up within the water bath. Black plastic sheets were draped over the chambers to prevent visual disturbance. When time and space allowed, we ran two individuals at the same time within the water bath but in individual respirometers separated by a black plastic divider so they could not see each other. Based on preliminary trials, we allowed individuals to acclimate in the respirometer overnight for 12 hours to reduce any stress associated with handling and chamber acclimation. We then measured the resting oxygen consumption rate during the first daylight hours of the morning in which sharks were found to be most calm. California Horn Sharks are nocturnal and relatively inactive, preferring to hide in rock crevices during the day to avoid predators (Meese and Lowe, 2020), and thus showed little to no activity inside the respirometer while at rest.

Journal of Experimental Biology • Accepted manuscript
We used an automated intermittent flow respirometry protocol made up of repeated cycles, each consisting of a closed (10 min) and flush period (5-10 min depending on chamber size).
During the closed periods, the automated flush pump turned off and the inflow and outflow check valves sealed the chamber for measurement of oxygen depletion. During the open period, the flush pump turned on to allow fresh, oxygenated seawater to be pumped into the chamber to fully exchange and oxygenate the respirometer water. We began the cycles as soon as we placed the individual within the respirometer chamber and measured oxygen concentration within the recirculating loop once every five seconds.
Within the closed periods, we calculated the rate of oxygen consumption (M O 2 ) using the equation: where V r is the respirometer chamber volume in liters, V f is the fish volume (assumed to be equivalent to the fish mass, M f ), and  O 2 is the rate of oxygen depletion in the respirometer over time. For each closed period, we removed the first three minutes of oxygen depletion to allow for any measurement lag associated with water cycling through the system, and then used the following seven minutes to estimate M O 2 . Following the 12-hour acclimation period, we used the mean of the lowest three M O 2 measurements occurring during the remaining five to nine hours the individual was in the chamber as the RMR estimate for that individual. We

Estimation of maximum metabolic rate
Immediately following estimation of RMR for each shark, we estimated MMR using one of two methods: chase alone or chase with air exposure, hereafter termed "chase" and "chase + air", respectively. Following a two-day recovery period from the first MMR trial, we used the other MMR method on that individual. We randomly assigned the order of MMR methods for each individual. For either the chase or the chase + air methods, the protocol began by removing the individual from the respirometer chamber following the RMR trial and placing it in a large circular chase tank filled with aerated seawater siphoned from the holding tank. We then exercised the individual to exhaustion by grabbing and pinching at its tail and by turning it over with gloved hands. We deemed it exhausted once it stopped bursting away and began resting on the bottom of the chase tank between stimuli (usually after 4-7 minutes of chasing). If undergoing the chase method, we then immediately transferred the individual to the respirometer chamber for measurement of post-exercise oxygen consumption, where we recorded oxygen concentration once every second until the oxygen concentration within the chamber reached 80% saturation (Reidy et al., 1995;Prinzing et al., 2021). Transfer time from the chase tank to the start of oxygen depletion measurements was typically less than 30 s. In the chase + air method, after being chased to exhaustion, we placed the individual in a holding bin without water for ten minutes with a wet cloth draped over the eyes and gill slits before transferring it to the respirometer. Due to their small body size, we separated each MMR trial (chase, chase + air) for the three smallest individuals by at least four days to allow the shark to fully recover and feed between trials.
We estimated MMR using a rolling regression model following Prinzing et al. (2021)

Estimation of gill surface area
Following respirometry trials, we sacrificed the individual with an overdose of the anesthetic MS-222 for estimation of total gill surface area. We patted the shark dry for mass measurement, following which we removed the head posterior to the last gill arch and fixed it in seawater-buffered 10% formalin for a minimum of two weeks for tissue fixation before beginning gill dissections.
We estimated gill surface area for each shark as: where L fil is the total length of all gill filaments on both sides of the head, n lam is the lamellar frequency (i.e., the mean number of lamellae per unit length on one side of a filament, multiplied by two to account for lamellae on both sides of the filament), and A lam is the mean bilateral surface area of a lamellae (Wegner, 2011;Wegner, 2016). To determine these dimensions, we removed all five gill arches from the right side of the head and counted all filaments on all nine hemibranchs. We divided each hemibranch evenly into eight bins of filaments. We took a magnified photo of the median filament in each bin, which we assumed to be representative of all filaments in that bin (Meiji Techno America EMZ-8TR microscope with Moticam 5+ camera, San Jose, USA). We measured the length of this filament, including the section beneath the gill arch branchial canopy (Wegner et al., 2010b; Wegner 2016), using ImageJ imaging software (National Institutes of Health, USA, Java 1.8.0_172). We calculated the total length of all filaments on all hemibranchs on the right side of the head by multiplying the length of the median filament in each bin by the total number of filaments in that bin, then summing the length of all filaments in all bins. We then doubled this length to account for the length of filaments on the left side of the head, which were not measured.

Journal of Experimental Biology • Accepted manuscript
Following filament measurements, we removed the median filament from each bin for lamellar measurements. We turned each excised filament on its side to show the lamellae and took a magnified photo at the base, middle, and tip sections for estimation of lamellar frequency (number of lamellae per mm) using ImageJ software. We then made a cross section at each of these three locations on the filament to take magnified photographs of the extended lamellae on both sides of the filament. We estimated lamellar surface area in mm 2 using ImageJ software by tracing the outline of a lamella on one side of the filament, then doubling it to calculate the bilateral surface area of the lamella. We estimated mean lamellar frequency (mm -1 ) by averaging lamellar frequency measurements taken at each of the base, middle, and tip of each median filament, multiplying this mean by the total length of all filaments in that bin to give the total number of lamellae per bin, summing the total number of lamellae in all bins, then dividing this by the total length of all filaments. We estimated average lamellar surface area (mm 2 ) by taking the mean of lamellar surface area measurements taken at the same three locations as lamellar frequency on each filament, multiplying this mean by the total number of lamellae in that bin to give a total lamellar area per bin, summing the total lamellar area for all bins, then dividing by the total number of lamellae. We measured lamellar frequency and surface area on all median filaments from all nine hemibranchs on one side of the head on the first dissected individual. These measurements showed that the posterior hemibranch on the second gill arch was most representative of the gills as a whole, and thus for subsequent sharks, we based lamellar frequency and mean lamellar surface area measurements solely on this hemibranch (Wegner, 2011).

Statistical analysis
We conducted all data processing and analyses in R version 4.2.1 (R Core Team, 2020).
We estimated the allometric scaling coefficients of RMR (mgO 2 h -1 ), MMR (mgO 2 h -1 ), aerobic scope (mgO 2 h -1 ), and gill surface area (cm 2 ) as a function of body mass (kg) using ordinary least squares (OLS) regression. We log 10 -transformed the data prior to fitting the model [see White and Kearney, 2011; Bigman et al., 2018 for discussion on fitting power laws with linear Journal of Experimental Biology • Accepted manuscript regression (our approach) vs. nonlinear regression)]. We then checked the residuals for normality and homoscedasticity. The gill surface area and body mass relationship appeared to have a breakpoint. We fit a broken stick regression with log 10 total gill surface area as a function of log 10 body mass using the selgmented function from the package segmented (version 1.6-0, Muggeo, 2022), and used AIC to compare this model to the equivalent OLS model.
We tested for a difference between the allometric slopes of RMR and MMR by fitting a linear mixed-effects model, where the log 10 metabolic rate estimate was a function of log 10 body mass with metabolic rate type as an interaction term and individual as a random effect. We then used the emtrends function from the package emmeans to compare allometric slope estimates from our linear mixed-effects model (version 1.8.1-1, Lenth et al., 2020). This analysis is similar to an ANCOVA but accounts for the influence of the random effect of individual in our model.
Using just the 17 largest shark individuals, we examined the ratio of gill surface area to metabolic rate, calculated as total gill surface area (cm 2 ) divided by either RMR or MMR (mgO 2 h -1 ) for each individual and then log 10 transformed (Scheuffele et al., 2021). We excluded the three smallest individuals from this analysis as their gill surface areas appeared to deviate from that of the larger sharks as seen through an inflection point at the fourth smallest shark (see Results). We then estimated the allometric slope of the ratio estimates for each of log 10 gill surface area to resting metabolic rate (GSA/RMR) and log 10 GSA/MMR against log 10 body mass.
Finally, we examined the allometric slopes of each gill surface area component to understand how California Horn Shark increase gill surface area as they grow. We examined the scaling of each gill surface area component including log 10 total filament length (cm), log 10 average lamellar frequency (mm -1 ), and log 10 mean bilateral lamellar surface area (mm 2 ) as a function of log 10 body mass, using OLS regression. Similar to gill surface area, there appeared to be an inflection point in the relationship between log 10 lamellar surface area and log 10 body mass, and we also fit a broken stick regression to these data and compared this to the equivalent OLS models using AIC (version 1.6-0, Muggeo, 2022).
The higher allometric slope for MMR in relation to RMR led to an allometric slope greater than 1.0 for absolute aerobic scope (b = 1.098 ± 0.022; Table 1, Fig. 1b). When the allometric scaling of gill surface area was examined using a broken stick regression, this model estimated an inflection point at the fourth smallest individual (0.203 kg body mass) and produced slope estimates of b = 0.564 ± 0.261 for individuals smaller than 0.203 kg and b = 1.012 ± 0.113 for individuals larger than 0.203 kg (Table 1, Fig. 1c). When modeled across the full sample size of California Horn Shark using OLS regression, the allometric slope of gill surface area was b = 0.877 ± 0.067 (Table 1, Fig. 1c). Comparing these models using AIC revealed that the broken stick regression model was a better fit to the gill surface area data relative to the OLS regression (Table 1).
When we examined the allometric slope of the ratio of gill surface area (cm 2 ) to metabolic rate (mg O 2 h -1 ) for the 17 largest individuals, we found that the amount of gill surface area per unit RMR remained effectively constant (b = 0.040 ± 0.188), while the amount of gill surface area per unit MMR decreased slightly but not significantly (the 95% confidence interval crossed zero; b = -0.102 ± 0.122; Fig. 2).

Discussion
Our results suggest that the scaling of oxygen supply and demand, as measured by gill surface area and metabolic rate, are closely matched in the California Horn Shark. When viewed across a nearly complete body size range, the allometric slope of RMR was b = 0.966 and that of MMR was significantly greater at b = 1.073; as such, aerobic scope increased with body mass (b = 1.098). Surprisingly, we found that the relationship between gill surface area and body mass was best explained by a broken stick regression model in which small sharks showed a shallower allometric slope, while the gill surface area of larger individuals scaled at b = 1.012, in between that of RMR and MMR. The findings that gill surface area scales near b = 1.0 and that neither the ratio of GSA/RMR or GSA/MMR shows a significant negative relationship are inconsistent with predictions of the GOLT and suggest aerobic metabolism is not limited by gill surface area in this species. In the following, we first discuss the allometric scaling of metabolic rate and compare the slope of RMR to MMR. Second, we compare the scaling of metabolic rate to that of gill surface area and then discuss how our findings fit into the larger framework of metabolic scaling in the context of oxygen supply and demand. Finally, we discuss the potential physiological underpinnings of the allometric scaling of gill surface area.
Across a body size range representing the near-complete ontogeny of the California Horn Shark, our results showed that the mean allometric slopes of RMR and MMR were around b = 1.0. This pattern is consistent with the metabolic level boundaries hypothesis, which predicts that relatively inactive species are less likely influenced by surface area limits on fluxes of resources and wastes and, thus, can have metabolic rate slopes nearer to 1.0, while more active species may be more constrained by surface area to volume ratios and generally exhibit relatively shallower metabolic allometric slopes (Glazier, 2005;Killen et al., 2010). Killen et al. (2010) showed that this activity-scaling pattern holds across 89 fish species binned into one of four ecological lifestyle categories (pelagic, benthopelagic, benthic, and bathyal) or four swimming modes (thunniform, carangiform, subcarangiform, and anguilliform), and suggested these factors may be partly responsible for the variation in allometric slope estimates observed across species.

Journal of Experimental Biology • Accepted manuscript
The metabolic level boundaries hypothesis also predicts that the slope of MMR will generally scale steeper than the slope of RMR as metabolic rate during strenuous exercise should be influenced primarily by the volume-related scaling of muscle power, yielding an allometric slope nearer to 1.0, while lower, relatively sustainable metabolic rates should be more closely tied to surface area to volume ratios and scale with a shallower allometric slope (Glazier, 2005(Glazier, , 2009 (Zhang et al., 2014;Luo et al., 2015), which the authors conclude may be related to the low relative contribution of muscular energy expenditure to whole body metabolism in these inactive species. Thus, more paired measures of RMR and MMR across ontogeny in species from a wider range of activity levels are needed to help us better understand the interplay of oxygen uptake, oxygen demand, and activity level.
In contrast to the scaling of metabolic rate, we found that the scaling of gill surface area in the California Horn Shark was best estimated by a broken stick regression model, indicating a shift in gill growth and demand with ontogeny. The inflection point in the gill surface area-body mass relationship shows a steepening of the allometric slope near 30 cm total length, corresponding to the size at which California Horn Shark are thought to begin transitioning from their juvenile to adolescent life stage (35 cm) (Ebert et al., 2013). This inflection point is not seen in either the MMR nor RMR regressions and suggests a potential disconnect between oxygen demand and Journal of Experimental Biology • Accepted manuscript supply prior to the inflection point, at which point gill surface area appears to begin to track metabolism. Unlike most teleosts, oviparous elasmobranchs such as the California Horn Shark emerge from their egg cases resembling adults, covered in calcareous dermal denticles, and mainly respire across their gill tissue (Rodda and Seymour, 2008;Toulmond et al., 1982). Thus, at least at later stages of embryonic development within the egg case, they must rely on their gills as the sole gas exchange surface, possibly resulting in a relatively large gill surface area as an adaptation to protect against potential hypoxia in their surrounding environment or within the potentially diffusion-limited egg case itself (Di Santo et al., 2016). Further, embryonic metabolic rates may be relatively high in oviparous elasmobranchs because of the need for highly-active tail beating to ventilate the egg capsule and circulate water (Leonard et al., 1999).
It appears that California Horn Shark (and likely other oviparous elasmobranchs) may require a larger gill surface area as developing embryos than immediately post hatch. Thus, once hatched, California Horn Shark appear to possess excess gill surface area relative to their oxygen demand resulting in a lower gill surface area allometric slope during early life until faster gill growth is again needed to meet metabolic needs, at which point gill surface area scales similarly to metabolic rate with an allometric slope falling between that of RMR and MMR. This broken stick pattern in the allometry of gill surface area in juvenile California Horn Shark contrasts with the initially very steep scaling of gill surface area in larval teleost fishes that reflects rapid teleost gill development following initial reliance on cutaneous gas exchange during early larval stages (Oikawa and Itazawa, 1985;Rombough and Moroz, 1997). Future work should test if our findings for California Horn Shark apply across other oviparous elasmobranchs.
Comparison of the allometric slope of gill surface area with that of RMR and MMR can provide potential insight into factors influencing rates of oxygen uptake and demand and activity.
Previous work has suggested that the allometric slope of gill surface area should fall closer to that of MMR in order to supply the fish with sufficient oxygen for activity above rest (Hughes, 1972(Hughes, , 1984. This makes sense when we consider that the allometric slope of MMR is often steeper than that of RMR and that fish require sufficient gill surface area to meet maximum aerobic energy requirements (Hughes, 1984;Bishop, 1999;Killen et al., 2007 In addition to providing insight into California Horn Shark activity and life history, our results argue against suppositions made by the GOLT that posit that geometric constraints of gill surface area limit fish metabolism (Pauly, 2010(Pauly, , 2021Pauly and Cheung, 2017). Specifically, our results show that gill surface area scales at b = 1.012 in the California Horn Shark after the inflection point (0.203kg), which differs from the GOLT argument that gill surface area must scale less than b = 1.0 due to two-dimensional surface area constraints. Likewise, our results show that gill surface area in the California Horn Shark scales similar to the allometric slopes of both RMR and MMR and thus the scaling of both the GSA/RMR and GSA/MMR ratios do not differ significantly from zero. If either ratio showed a negative relationship it could indicate a potential mismatch in oxygen supply and demand (Scheuffele et al., 2021). In contrast, our data suggest there is not a mismatch in the allometric scaling of oxygen supply and demand in the California Horn Shark, and these results closely match recent work on the Tidepool Sculpin Journal of Experimental Biology • Accepted manuscript Oligocottus maculosus Girard, 1856 an inactive teleost species (Somo et al., 2023). Finally, an increase in aerobic scope (b = 1.098) and the high allometric slope of MMR (b = 1.073) over the entire ontogeny of California Horn Shark examined here shows that the capacity for aerobic performance (and hence oxygen consumption) actually disproportionately increases with growth, suggesting that oxygen uptake at the gills cannot be limiting, as suggested by the GOLT (which would predict a decline in aerobic scope with increasing body size, Pauly, 2010, 2021).
These findings are consistent with widely held physiological views that the gills are adapted to match metabolic needs, rather than metabolism being constrained by gill surface area (Wegner, 2011;Lefevre et al., 2017Lefevre et al., , 2018. Thus, the relatively low oxygen demands of this generally inactive species appear amply met by their available gill surface area. Examination of individual gill components, specifically filament length, lamellar frequency, and subsequently shift to faster growth to align gill surface area with metabolic demand at larger sizes. Such changes in lamellar size mirror those seen in fishes exposed to hypoxia or increased temperature in which a greater gill surface area is needed when the dissolved oxygen content of the water is low or metabolic demands are elevated (Sollid and Nilsson, 2006;Chapman, 2007;Wegner and Farrell, in press). Thus, lamellar surface area seems to be a highly plastic component of gill surface area that can be rapidly manipulated to meet changing oxygen demands across fish groups.
In summary, our findings are a thorough look at the allometric scaling patterns of RMR, MMR, aerobic scope, and gill surface area using paired estimates within the same individuals. This allows for more precise exploration of the relationship between metabolic rate and gill surface area by removing complications arising from comparing multiple data sets with contrasting body masses and species (Gillooly et al., 2016;Scheuffele et al., 2021;Bigman et al., 2021).
Taken together, our results show that for some species like the relatively inactive California Horn Shark, the allometric slope of metabolic rate and gill surface area can approach or even exceed b = 1.0. The unusually steep allometric slopes found here emphasize the need for more Table 1. Model parameter estimates of linear and segmented relationships between body mass (log 10 kg) and resting (RMR) and maximum (MMR) metabolic rate (log 10 mgO 2 h -1 ), absolute aerobic scope (log 10 mgO 2 h -1 ), and gill surface area (GSA, log 10 cm 2 ) at a mean temperature of 18.2 °C, in the California Horn Shark, Heterodontus francisci, using ordinary least squares (OLS) and broken stick (BS) regression (a = intercept, b = allometric slope). Allometric regression parameters for the equation log 10 Y = a + b log 10 M (a = scaling coefficient or intercept, b = allometric slope, M = mass (kg), Y = trait). 95% confidence intervals are given where available. ">0.203 kg" and "<0.203 kg" superscripts indicate estimates for each size range, respectively. For both gill surface area and lamellar area, AIC indicated that the broken stick regression model was a better fit relative to the OLS regression model. Ratio analyses were conducted excluding the three smallest sharks (see text).