Ontogenetic shifts in body form in the bull shark Carcharhinus leucas

Recent studies have uncovered mosaic patterns of allometric and isometric growth underlying ontogenetic shifts in the body form of elasmobranch species (shark and rays). It is thought that shifts in trophic and spatial ecology through ontogeny drive these morphological changes; however, additional hypotheses relating to developmental constraints have also been posed. The bull shark (Carcharhinus leucas) is a large‐bodied coastal shark that exhibits strong ontogenetic shifts in trophic and spatial ecology. In this study, we utilise a large data set covering a large number of morphological structures to reveal ontogenetic shifts in the body form of C. leucas, stratifying analyses by sex and size classes to provide fine‐scale, more ecomorphologically relevant results. Our results indicate shifts in functional demands across the body through ontogeny, driven by selective pressures relating to trophic and spatial ecology driving the evolution of allometry. We also find significant differences in scaling trends between life stages, and between the sexes, highlighting the importance of utilising large, diverse datasets that can be stratified in this way to improve our understanding of elasmobranch morphological evolution. Ultimately, we discuss the implications of these results for existing ecomorphological hypotheses regarding the evolution of specific morphological structures, and pose novel hypotheses where relevant.


| INTRODUCTION
Body form, or external morphology, is a fundamental component of phenotype, mediating locomotion, survival and reproductive success (Bock, 1994;Wainwright, 1991).As such, body form is likely to be under relatively strong selection, providing the rationale for a host of ecomorphological studies seeking to understand why organisms display certain morphological phenotypes (e.g., Feilich, 2016;Sternes & Shimada, 2020;Streelman et al., 2002;Wainwright et al., 2002).It has long been recognised that adaptive differences in morphology are not restricted to the species level but may also be present between different developmental stages (Pélabon et al., 2013(Pélabon et al., , 2014)).Ontogenetic shifts in body form may result from developmental constraints associated with an increase in body size, or functional adaptation of traits associated with ontogenetic shifts in ecology (Voje et al., 2014).
Despite recent advances, relatively little is known about ontogenetic scaling trends in Elasmobranchii-both in terms of their manifestation and the factors underlying their evolution.This clade consists of more than 1000 species (Weigmann, 2016) and existing studies cover only a minute fraction of this diversity.Given the range of morphological and ecological specialisations exhibited within Elasmobranchii, there is little reason to suggest that results obtained from a small subset of extant species would be representative of those exhibited across elasmobranch diversity.
The bull shark (Carcharhinus leucas) is a large-bodied coastal shark distributed across tropical, subtropical and temperate waters (Compagno, 1984).This species is of high ecological importance as an apex predator capable of traversing freshwater, estuarine and marine environments (Matich et al., 2011;Smoothey et al., 2019).Although existing studies have addressed growth rates and maturation in multiple populations as well as ontogenetic shifts in specific morphological/physiological characters (Goodman et al., 2022;Habegger et al., 2012;Hoarau et al., 2021;Matich et al., 2019;Natanson et al., 2014), the presence and nature of any such shifts in body form remain unstudied.There are several key facets of C. leucas's ecology that make it a fascinating case study through which to examine ontogenetic morphometry.The well-documented use of nursery areas by juveniles (as opposed to speculation as with other species) should allow for more robust ecomorphological inferences regarding functional/selective explanations for scaling coefficients observed over individual life stages (Froeschke et al., 2010;Heupel & Simpfendorfer, 2011).Moreover, there are known sexual differences in spatial ecology and habitat, with females exhibiting philopatry and reduced dispersal compared to males (Devloo-Delva et al., 2023).For this reason, we expect to detect sexual dimorphism in scaling coefficients, as recovered in recent studies of other shark species (Gayford, Godfrey, et al., 2023).Although one previous study has addressed ontogenetic scaling in bull sharks (Irschick & Hammerschlag, 2015), the sample size used in this study was small (N = 29), and may not reflect true scaling trends observed across size classes and sexes.
In this study, we present ontogenetic body form scaling coefficients from a large, novel data set covering a range of life stages.We include an unprecedented number of measurements covering the caudal, pectoral, pelvic, dorsal and anal fins, as well as various aspects of trunk and head morphology.We also stratify results by life stage and by sex, providing finer-scale results that are easier to interpret using standard ecomorphological theory and existing studies of trophic/spatial ecology.

| Data collection
The shark control programme was implemented in 2012 on the west coast of Reunion Island (where most nautical activities occur) after a series of fatal human-shark interactions mostly attributed to the bull shark (Guyomard et al., 2019(Guyomard et al., , 2020;;Werbrouck et al., 2014).Reunion Island (−21°08′; 55°32′) is an oceanic island of volcanic origin located in the Western Indian Ocean, 800 km east of Madagascar.The fish fauna is diverse (Fricke et al., 2009), including elasmobranchs (Jaquemet et al., 2023).All individual sharks targeted by the shark control programme were conserved in a fish factory at 4°C until further analyses.Less than 36 h after catches, necropsies were conducted on all specimens to improve the knowledge of the biology and ecology of the species in relation to risk management.For this purpose, a series of 23 body measurements were collected prior to the opening of the general cavity (Figure 1; Table 1).In addition, the wet mass of the liver was recorded.A total of 185 bull sharks were caught and analysed between November 2012 and May 2023, with 48% representing males and 46% representing juveniles.Pelvic fin measurements did not include the claspers, enabling direct comparison between males and females.The necropsy protocol, including taking measurements, was designed by SJ in collaboration with other local scientists and authorities.The data set is owned by SJ.
Simple linear regression analyses were conducted by fitting linear models using the R function lm (R Core Team, 2023).All measurements except TL, PL and LM were regressed against PL with output from these analyses tested against a null model of isometry with a scaling coefficient of 1.00.Liver mass was regressed against PL with output tested against a null model of isometry with a scaling coefficient of 3.00 (as LM is a volume rather than a linear measurement).Five separate analyses were conducted: one using the full data set, two using male-only and female-only datasets, respectively, and two more using adult-only and juvenile-only datasets.Separate analyses were conducted in this way to provide greater resolution regarding the ontogenetic expression of scaling trends and reveal and sex-based morphological differences differences (Gayford, Godfrey, et al., 2023).

| Total data set
Regression of 23 morphological measurements against PL using the total data set uncovered 14 cases of allometric growth and nine cases of isometric growth (Table 2; Figure 2).The proportion of variance explained by the regression line (R 2 ) ranged from 0.6773 (EYD, Table 2) to 0.9708 (RPL, Table 2).Six of the 14 allometric relationships were positive (HW, EH, MO, RPL, PW and LM), whereas the other eight (CK, EYD, DW1, DH2, DW2, UL, AH and PH) were negative (Table 2; Figure 2).Some of the scaling coefficients that differed significantly from isometry were nonetheless close to 1.00.

| Male-only data set
Regression of 23 morphological measurements against PL using the male-only data set uncovered 11 cases of allometric growth and 12 cases of isometric growth (Table 2; Figure 3).The proportion of variance explained by the regression line (R 2 ) ranged from 0.6412 (EYD, Table 3) to 0.9560 (RPL, Table 3).Four of the 11 allometric relationships were positive (MO, RPL, PW and LM), whereas the other seven (FS, CK, EYD, DW1, DW2, AH and PH) were negative (Table 3; Figure 3).Some of the scaling coefficients that differed significantly from isometry were nonetheless close to 1.00.

| Female-only data set
Regression of 23 morphological measurements against PL using the female-only data set uncovered 14 cases of allometric growth and nine cases of isometric growth (Table 4; Figure 4).The proportion of variance explained by the regression line (R 2 ) ranged from 0.7478 (EYD, Table 4) to 0.9820 (RPL, Table 4).Seven of the 14 allometric relationships were positive (LS, FS, HW, EH, MO, RPL and LM), whereas the other seven (CK, EYD, DW1, DH2, DW2, UL and AH) were negative (Table 4; Figure 4).Some of the scaling coefficients that differed significantly from isometry were nonetheless close to 1.00.

| Adult-only data set
Regression of 23 morphological measurements against PL using the adult-only data set uncovered 16 cases of allometric growth and seven cases of isometric growth (Table 5; Figure 5).The proportion of variance explained by the regression line (R 2 ) ranged from 0.04019 (MO, Table 5) to 0.7001 (LS, Table 5).Six of the 16 allometric relationships were positive (LS, FS, PS, SF, HW and LM), whereas the other 10 (CK, EYD, DH1, DW1, DH2, DW2, UL, LL, AH and AW) were negative (Table 5; Figure 5).Some of the scaling coefficients that differed significantly from isometry were nonetheless close to 1.00.

| Juvenile-only data set
Regression of 23 morphological measurements against PL using the juvenile-only data set uncovered nine cases of allometric growth and 14 cases of isometric growth (Table 6; Figure 6).The proportion of variance explained by the regression line (R 2 ) ranged from 0.6740 (EYD, Table 6) to 0.9702 (RPL, Table 6).Seven of the nine allometric relationships were positive (HH, EH, MO, RPL, RPW, DH1 and PW), whereas the other two (CK and EYD) were negative (Table 6; Figure 6).Some of the scaling coefficients that differed significantly from isometry were nonetheless close to 1.00.

| DISCUSSION
The purpose of this study was to test for allometric growth in a range of morphological structures in C. leucas, so that we might better understand relationships between morphology, ecology and body size in sharks.In the total data set, and data sets sorted by sex and maturity, there are multiple aspects of morphology that scale allometrically with body size, but others that scale isometrically (Tables 2-6).This is consistent with scaling coefficients reported for other shark species (Bellodi et al., 2023;Gayford, Whitehead, et al., 2023;Irschick et al., 2017).We also note the presence of unambiguous differences in morphometric scaling between the sexes and between size classes (Tables 3-6).Notably, allometry in the caudal fin is found in females only (Figure 4; Table 4) and liver allometry is not found in juveniles (Figure 6; Table 6), amongst other differences.In the following sections, we address the significance of these results for our understanding of morphometric scaling and morphological evolution in sharks.We must however urge some caution: whilst other studies have stratified morphometric data between more than two size classes (Gayford, Whitehead, et al., 2023), we restricted our analyses to two size classes (adult and juvenile).This was done to maximise the strength of ecomorphological inference that we can extract from our results, as most ecological information about this C. leucas population describes only two broad size classes (e.g., Blaison et al., 2015;Niella et al., 2021).
Moreover, some of the scaling coefficients that we recovered as allometric are relatively close to isometric predictions, despite statistical significance.It is possible that these results are not of biological significance.Nevertheless, our results have several implications in light of existing literature on shark allometry.

| Ecomorphology of caudal fin scaling
Ontogenetic shifts in caudal morphology are perhaps more studied in elasmobranchs than any other external morphological feature.
Observed scaling trends in all species for which studies exist are consistent with a trade-off between the manoeuvrability and agility afforded by relatively heterocercal caudal fins and energy efficiency, with less heterocercal caudal fins thought to be optimised for longdistance movements (Fu et al., 2016;Gayford, Whitehead, et al., 2023;Lauder, 2000;Sternes & Higham, 2022).This trade-off is reflected in our total data set results, in which we recovered evidence for negative allometry in the upper, but not lower caudal lobe, such that the caudal fin becomes less heterocercal through ontogeny (Figure 2; Table 2).This result is broadly consistent with results from Irschick  (Grubbs, 2010;Heupel & Simpfendorfer, 2011;Trystram et al., 2017).
Thus, whilst a caudal fin optimised for efficient cruising and lift generation would be favoured in later ontogenetic stages, a relatively heterocercal caudal fin would likely be favoured in juveniles to aid in the capture of relatively small agile prey and to avoid predation during the early stages of their life.Few studies have examined scaling trends separately between ontogenetic stages; however, the bull shark appears unique in that negative caudal allometry is displayed only in adults and not juveniles (Figures 5 and 6; Tables 5 and 6).Other species, such as Sphyrna lewini and Rhizoprionodon longurio, appear to consistently show negative caudal allometry across multiple ontogenetic stages (Gayford, Whitehead, et al., 2023).The reasons for this discrepancy are unclear, although it is possible that juvenile bull sharks simply remain in their shallow nearshore environments longer than these other species.Furthermore, there is little evidence to suggest usage of nursery areas to the same extent as C. leucas in either S. lewini or R. longurio (Gayford & Whitehead, 2023;Heupel et al., 2007).Alternatively, juvenile bull sharks may be subjected to greater predation pressure than juveniles of either S. lewini or R. longurio.Utilisation of nursery areas is thought to be adaptive as these areas are associated with lower predation pressure (Heupel & Simpfendorfer, 2011;Heupel et al., 2007).
However, unlike S. lewini or R. longurio, C. leucas is known to practice cannibalism (Werry et al., 2011(Werry et al., , 2012)).For this reason, selection may favour the retention of a relatively flexible heterocercal caudal fin (theoretically conveying increased escape potential) until individuals reach a sufficient size such that cannibalism is unlikely to present a significant threat.The differentiation between cannibalism and interspecific predation pressure is relevant here as conspecifics are likely to be present in freshwater and brackish nursery areas where other potential predators are absent (Werry et al., 2011(Werry et al., , 2012)).
When sorted by sex, negative caudal allometry is only recovered in females (Figure 4; Table 4), with males exhibiting isometric growth (Figure 3; Table 3).Male bull sharks are typically thought to have T A B L E 3 Linear regression results for the log10 transformed male data set.Note: Coefficients that differ significantly from isometry (p ≤ .05)are indicated in bold.In all cases other than liver mass (LM), coefficients greater than 1 denote positive allometry, and coefficients lower than 1 denote negative allometry.In the case of LM, coefficients that differ significantly from 3 denote allometry.
greater dispersal potential than females (Devloo-Delva et al., 2023), and thus, this result would appear to contradict the allometric niche shift hypothesis, as the sex exhibiting greater long-distance movements exhibits isometry (Gayford, Whitehead, et al., 2023).We might expect male bull sharks, with greater dispersal potential, to exhibit greater allometry as they will rely more upon the lift generated by a less-heterocercal tail for efficient long-distance locomotion.As female bull sharks reach a larger size than males, our results are consistent with developmental constraint-based hypotheses for allometry (Hoarau et al., 2021;Natanson et al., 2014;Voje et al., 2014).It should be noted however that our understanding of bull shark spatial ecology is far from complete, and that in some populations females have been recorded undertaking long-distance migrations across the open ocean (Espinoza et al., 2016;Lea et al., 2015).In Reunion Island, specifically, both sexes display significant seasonal variations in abundance and distribution along the coast (Blaison et al., 2015;Soria et al., 2019), suggesting that differences between male and female spatial ecology may be more subtle, in relation to the nature of the island and the geomorphology that leads to narrow coastal ecosystems (<200 m).For this reason, we suggest that additional ecological studies are required before this clear sexual dimorphism in caudal scaling can be fully interpreted.
Caudal keel circumference in C. leucas shows strong negative allometry across both sexes and size classes (Tables 2-6).In species that show pronounced caudal keels, this structure is thought to be associated with bursts of high-speed swimming, likely aiding in prey capture (Lingham-Soliar, 2005a;Zhang et al., 2020).Our results would thus suggest that generating bursts of acceleration becomes less important through ontogeny, broadly in line with the theory regarding differences in predation pressure and prey targeted between nursery areas and deeper coastal waters, as discussed previously.Negative caudal keel allometry was also recovered in adult scalloped hammerheads (Gayford, Whitehead, et al., 2023); however, other studies have recovered isometric or even positive allometric growth in this measurement (Gayford, Godfrey, et   leucas has a more anterior mass distribution than other shark species, and so the keel region may be less important for force redirection of the tail than in other species.However, there is no clear reason for why C. leucas should differ from these other species in this manor, and we suggest that data from additional species is required before differences in caudal keel scaling can be fully understood.

| Ecomorphology of girth scaling
Form-function relationships for girth measurements in elasmobranchs are poorly understood, and several hypotheses exist to explain observed trends.Liver allometry, conditioning related to migrations and pregnancy, and drag minimalization/streamlining have all been posited to explain observed scaling trends in various measurements of girth (Gayford, Whitehead, et al., 2023;Sternes & Higham, 2022).When considering the total data set, the anterior body exhibits isometric growth (Figure 2; Table 2), matching results obtained by Irschick and Hammerschlag (2015).However, when subsetting data by either sex or size class, a more complex trend is observed, where the anterior body exhibits negative allometric growth in males but positive allometric growth in females (Figures 3 and 4; Tables 3 and 4) and whilst adults appear to show strong positive allometry (Figure 5; Table 5) no allometry is recovered in juveniles (Figure 6; Table 6).These results would appear consistent with the notion that liver allometry is responsible for observed growth trends as no positive allometry was recovered either in girth measurements or liver mass in juveniles (Figure 6; Table 6).Comparison of liver allometry coefficients between males and females, and between juveniles and adults also suggests some correlation between liver allometry and body girth (Tables 3-6).It should also be pointed out that this correlation by no means implies that liver allometry is driving the evolution of girth trajectories, and it is equally, if not more plausible, that it is increased body size that is resulting in the evolution of liver allometry for the purposes of buoyancy T A B L E 5 Linear regression results for the log10 transformed adult data set.Note: Coefficients that differ significantly from isometry (p ≤ .05)are indicated in bold.In all cases other than liver mass (LM), coefficients greater than 1 denote positive allometry, and coefficients lower than 1 denote negative allometry.In the case of LM, coefficients that differ significantly from 3 denote allometry.
F I G U R E 5 Scaling relationships between log10 transformed values of precaudal length (PL) and lateral span (a), frontal span (b), proximal span (c), caudal keel circumference (d), snout to first dorsal fin length (e), head width (f), eye diameter (g), first dorsal fin height (h), first dorsal fin width (i), second dorsal fin height (j), second dorsal fin width (k), upper caudal length (i), lower caudal length (m), anal fin height (n), anal fin width (o) and liver mass (p) using the adult-only data set.The grey shaded area represents the 95% confidence interval for the scaling coefficient.Blue dashed lines representing isometry are not visible in these plots as the allometric coefficients in Table 5 differ too much from 1.00 to be visible in the plot frame.A miniaturised version of Figure 1 is provided to aid interpretation.
maintenance (Gleiss et al., 2017;Iosilevskii & Papastamatiou, 2016).The observed sexual dimorphism in anterior body scaling appears broadly consistent with existing literature regarding the spatial ecology of bull sharks, where selection would likely favour greater streamlining and drag reduction in adult males as a result of their increased dispersal potential relative to females and juveniles (Devloo-Delva et al., 2023), whereas this selective pressure may be comparatively weaker in adult females.Additionally, females may require greater energy stores than males due to the physiological and bioenergetic consequences of pregnancy (Hammerschlag et al., 2018).

| Ecomorphology of the head and jaws
The head is clearly a functionally important structure, involved heavily in hydrodynamic performance and prey acquisition in sharks (Fu et al., 2016;Gaylord et al., 2020;Motta & Huber, 2004;Wilga et al., 2007;Wilga et al., 2012).We found that there is pervasive allometric growth in the head of C. leucas such that the lower jaw becomes disproportionately larger through ontogeny (Figures 2-6; Tables 2-6).In adult females (but no other groups), there is also a lateral expansion of the head such that it becomes broader through ontogeny (Figure 4; Table 4), in line with the positive allometric growth of the anterior body.Similar results have been recovered in the tiger shark (Galeocerdo cuvier), where ontogenetic shifts in diet and consequently jaw musculature (specifically hyptertrophication of adductor muscles in the jaws) are thought to underlie observed head allometry (Fu et al., 2016;Habegger et al., 2012).Like tiger sharks, bull sharks undergo an ontogenetic shift in diet to much larger and more diverse prey requiring larger gape and bite force to process (Goodman et al., 2022;TinHan & Wells, 2021;Trystram et al., 2017).
In fact, both tooth morphology and bite force have been shown to scale allometrically through ontogeny in bull sharks (Goodman et al., 2022;Habegger et al., 2012).Even more convincing, these T A B L E 6 Linear regression results for the log10 transformed juvenile data set.Note: Coefficients that differ significantly from isometry (p ≤ .05)are indicated in bold.In all cases other than liver mass (LM), coefficients greater than 1 denote positive allometry, and coefficients lower than 1 denote negative allometry.In the case of LM, coefficients that differ significantly from 3 denote allometry.
shifts in bite force and jaw size appear to be temporally linked, with both being more pronounced relatively early in ontogeny (Tables 5 and 6; Habegger et al., 2012).As for why these shifts would be concentrated during early ontogeny, it has been hypothesised that such a 'performance increase' would enable juvenile bull sharks to target a greater range of prey items (Habegger et al., 2012).
It should also be noted however that changes in the proportion of the head also have significant hydrodynamic consequences-with relatively conical heads reducing drag relative to broad heads (Fu et al., 2016).This may explain why in all groups except adult females changes in head morphology are associated with height and not width of the head, and why relative head height appears to continue to increase even in adults.In juveniles (escaping predation and targeting more agile prey) and males (travelling greater distances in the open ocean), the need to minimise drag and maximise hydrodynamic efficiency may be greater than in adult females.
Nevertheless, additional experimental studies will be required to determine the specific hydrodynamic consequences of observed ontogenetic head shape variation in C. leucas.

| Ecomorphology of the dorsal fins
There appears to be taxonomic variation in the functional role of the first dorsal fin amongst sharks, such that some species rely on the structure predominantly for thrust generation, whilst in others, it performs a stabilising function (Lingham-Soliar, 2005b;Maia & Wilga, 2013;Maia et al., 2017).Despite this dichotomy, it appears that there is a clear ontogenetic trend amongst some shark species towards relatively tall and narrow dorsal fins in later ontogeny, regardless of hypothesised functionality (Gayford, Godfrey, et al., 2023;Gayford, Whitehead, et al., 2023;Irschick & Hammerschlag, 2015;Sternes & Higham, 2022).Our results are consistent with this trend, both in the total data set, and in each of the sexes (Figures 2, 5 and 6; Tables 2, 5 and 6).Broadly equivalent results were reported by Irschick and Hammerschlag (2015).Similar to our observations of caudal fin scaling, dorsal allometry is predominantly restricted to adults (Tables 5 and 6), consistent with ideas discussed earlier surrounding the prominent usage of nursery areas and the predation pressure imposed by cannibalism.Whilst allometry is present in adults of both sexes, in males, it is only the width of both dorsal fins that exhibits allometry, whereas in females, all dorsal measurements have allometric trajectories (Tables 3 and 4).
This result mirrors that found in Mustelus henlei, where it was speculated that ecological differences between the sexes could result in different functional demands with regard to thrust generation and/ or stability, thus imparting different selective regimes upon each sex (Gayford, Godfrey, et al., 2023).Regrettably, this hypothesis cannot be proven nor discounted on the basis of our results as to the best of our knowledge these are the only two studies to date to have considered sex-based differences in ontogenetic scaling coefficients among elasmobranchs.Additionally, functional studies of dorsal fin function, let alone ontogenetic shifts in dorsal fin function, are absent for either M. henlei or C. leucas.A final intriguing finding relating to the dorsal fins is that both the first and second dorsal fins display similar scaling coefficients (Tables 2-6).The second dorsal fin is rarely considered in ecomorphological studies of shark body form; however, there is evidence that the second dorsal fin of some taxa may be involved in thrust generation, even where this does not appear to be the case for the first dorsal fin (Maia & Wilga, 2013;Maia et al., 2017).Hydrodynamic and/or kinematic studies targeting C. leucas would be necessary to determine the extent to which the first and second dorsal fins of this species perform similar functions.
Our results provide limited evidence to suggest that the function of the second dorsal fin may be similar to that of the first dorsal fin, or that at least they are subject to similar selection pressures in the bull shark.

| Ecomorphology of the pectoral fins
Although experimental studies are restricted to only a handful of taxa, it is thought that pectoral fin function in sharks differs between benthic and pelagic species: in benthic taxa, the pectoral fins tend to have a low aspect ratio and are predominantly involved in manoeuvrability and turning, whereas in pelagic taxa lift generation is thought to be their primary function (Fish & Shannahan, 2000;Wilga & Lauder, 2000).We did not measure aspect ratio; however, positive allometry in both pectoral width and length in juveniles (Figure 6; Table 6) suggests that changes to pectoral fin aspect ratio may occur, and at the very least, the pectoral fins become larger through development relative to body size.Additional research will be required to determine how these morphometric changes relate to swimming kinematics.Evidence for similar ontogenetic shifts in pectoral fin morphology in response to shifts in habitat usage is mixed (Gayford, Whitehead, et al., 2023).Additional studies considering a greater range of taxa will be required to determine the extent to which ontogenetic shifts in pectoral aspect morphology are present across elasmobranch diversity.

| Ecomorphology of the anal and pelvic fins
We incorporated measurements of the anal and pelvic fins into our analyses (Figure 1; Table 1).The anal fin becomes progressively smaller through ontogeny, a transition that is restricted to adults (Figures 2-6; Tables 2-6).A similar transition appears to occur in the pelvic fin, however only in juvenile males (Figures 2-6; Tables 2-6).
Unfortunately, little is known about the functionality of these fins besides obvious cases of specialisation (Macesic & Kajiura, 2010;Porter et al., 2022;Thomson & Simanek, 1977), and thus it is difficult to interpret these results in isolation.The trend towards increased pelvic fin width may relate to the development of the claspers (male intromittent organs), however the potential importance of additional factors cannot be ruled out.Additional studies are required to improve our understanding of the function of these appendages, and the extent to which shape variation may be adaptive.

| Differences with existing studies
Irschick and Hammerschlag (2015) previously considered ontogenetic scaling trends in C. leucas utilising living individuals in a separate population, generating results that differ from those reported here.
Allometry was only reported in the caudal and dorsal fin, with all other structures appearing to exhibit isometric growth (Irschick & Hammerschlag, 2015).It is possible that these differences are adaptive and result from ecological differences between these geographically and genetically isolated C. leucas populations.Indeed, these populations are reproductively isolated from one another (Devloo-Delva et al., 2023).
Due to the bathymetry surrounding Reunion bull sharks here likely inhabit a more pelagic-like environment compared with the shallow shelf environments in which bull sharks are found in the Western Atlantic.Moreover, it appears that bull sharks from the Indian Ocean are larger than those in the Atlantic (Hoarau et al., 2021).Despite this, there is little to suggest that these populations differ in spatial and/or trophic ecology.Rather, it is likely that the large difference in sample size and ontogenetic coverage is responsible for these discrepancies.Moreover, there are subtle differences in how some of the measurements were obtainedparticularly dorsal fin measurements, and in the number of measurements obtained.Based on our results, we suggest that larger sample sizes (50-100+) should be used wherever possible for studies of shark allometry, particularly given the apparent prevalence of differences in scaling coefficients between different ontogenetic stages (Tables 5 and 6; Gayford, Whitehead, et al., 2023).We also suggest that the number of measurements obtained should be maximised where possible, to maximise the proportion of morphological variance between specimens that is captured by the measurement selection.Nevertheless, the fact that a sample size below 30 was sufficient to detect allometric trajectories in two of the major structures considered in this study (Irschick & Hammerschlag, 2015) is promising, and suggests that where larger sample sizes are unattainable, even relatively small sample sizes may provide valid approximations of ontogenetic trajectories in shark body form.

| CONCLUSIONS
We have reported the ontogenetic scaling coefficients for various components of bull shark morphology, using a large sample size and range of measurements.It appears that a clear shift in functional demands takes place across ontogeny, potentially due to differences in trophic and spatial ecology (as per the allometric niche shift hypothesis), and that this shift has resulted in the evolution of allometric growth in C. leucas.It is important to note that differences in scaling between juveniles and adults do not imply that these shifts occur in conjunction with sexual maturity: allometric shifts in juveniles could occur at any point from birth until sexual maturity, and additional studies will be needed to provide finer temporal resolution.Intriguingly there are numerous cases of sexual dimorphism in scaling trends, and in many cases allometry is recovered only in either adults or juveniles.This highlights the importance of large, diverse sample sizes in studies of elasmobranch scaling.Without stratifying between sexes and size classes, potentially important differences in scaling may be obscured, and where such differences are divergent, (e.g., one class exhibits positive allometry and the other negative allometry), overall results may fail to detect allometry entirely.Nevertheless, comparing our results to a previous study suggests that where large datasets cannot be obtained, smaller sample sizes may provide valid approximations for the ontogenetic trajectories of select morphological structures.Such studies not only improve our understanding of shark ecology and life-history (with potential management implications) but enhance existing knowledge regarding form-function relationships, which are critical to our understanding of diversity and its evolution.
Abbreviation Measurement Definition TL Total length (cm) Distance from the tip of the snout to the dorsal tip of the caudal fin PL Precaudal length (cm) Distance from the tip of the snout to the precaudal pit (caudal peduncle) SF Snout-first dorsal fin (cm) Distance from the tip of the snout to the anterior insertion point of the first dorsal fin LS Lateral span (cm) Distance over the dorsal body surface (curvature), measured between the anterior insertion points of the left and right pectoral fins FS Frontal span (cm) Distance over the dorsal body surface (curvature) at the anterior insertion point of the first dorsal fin, measured between points on the flank on the same horizontal plane as the pectoral fin insertion points PS Proximal span (cm) Distance over the dorsal body surface (curvature) at the posterior insertion point of the first dorsal fin, measured between points on the flank on the same horizontal plane as the pectoral fin insertion points CK Caudal keel circumference (cm) Total circumference at the caudal keel HW Head width (cm) Dorsal width of the head at the posterior most point of the mouth HH Head height (cm) Height of the head measured as a vertical line crossing through the eye EYD Eye diameter (cm) The diameter of the eye EH Base of head-centre of eye (cm)

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I G U R E 1 The diagram showing measurements included in morphometric analyses.All measurements were recorded to the nearest cm.Measurements with one arrow point span over the dorsal body surface, and measurements with two arrow points (one at either end) are circumferences, whereas all others are linear measurements.Original illustration modified to generate this diagram produced by Russell Engelman and used under a CC BY 4.0 license (https://creativecommons.org/licenses/by/4.0).F I G U R E 2 Scaling relationships between log10 transformed values of precaudal length (PL) and caudal keel circumference (a), head width (b), eye diameter (c), base of head-centre of eye (d), mouth to base of head (e), right pectoral fin length (f), first dorsal fin width (g), second dorsal fin height (h), second dorsal fin width (i), upper caudal length (j), anal fin height (k), pelvic fin height (i), pelvic fin width (m) and liver mass (n) using the total data set.The grey shaded area represents the 95% confidence interval for the scaling coefficient.Blue dashed lines represent the null hypothesis of isometric scaling.A miniaturised version of Figure 1 is provided to aid interpretation.
andHammerschlag (2015), who examined scaling in another population of C. leucas using a smaller sample size.Whilst adult bull sharks have been known to travel long distances for reproductive/ foraging purposes, young juveniles are typically restricted to shallow nursery areas and exhibit a more benthic lifestyle, although the shift to more pelagic environments typically occurs before maturity F I G U R E 3 Scaling relationships between log10 transformed values of precaudal length (PL) and frontal span (a), caudal keel circumference (b), eye diameter (c), mouth to base of head (d), right pectoral fin length (e), first dorsal fin width (f), second dorsal fin width (g), anal fin height (h), pelvic fin height (i), pelvic fin width (j) and liver mass (k) using the male-only data set.The grey shaded area represents the 95% confidence interval for the scaling coefficient.Blue dashed lines represent the null hypothesis of isometric scaling.A miniaturised version of Figure1is provided to aid interpretation.

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I G U R E 4 Scaling relationships between log10 transformed values of precaudal length (PL) and lateral span (a), frontal span (b), caudal keel circumference (c), head width (d), eye diameter (e), base of head-centre of eye (f), mouth to base of head (g), right pectoral fin length (h), first dorsal fin width (i), second dorsal fin height (j), second dorsal fin width (k), upper caudal length (i), anal fin height (m) and liver mass (n) using the female-only data set.The grey shaded area represents the 95% confidence interval for the scaling coefficient.Blue dashed lines represent the null hypothesis of isometric scaling.A miniaturised version of Figure 1 is provided to aid interpretation.

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I G U R E 6 Scaling relationships between log10 transformed values of precaudal length (PL) and caudal keel circumference (a), head height (b), eye diameter (c), base of head-centre of eye (d), mouth to base of head (e), right pectoral fin length (f), right pectoral fin width (g), first dorsal fin height (h), pelvic fin width (i) and liver mass (j) using the juvenile-only data set.The grey shaded area represents the 95% confidence interval for the scaling coefficient.A miniaturised version of Figure 1 is provided to aid interpretation.
Linear regression results for the Log10 transformed female data set.
al., 2023; Irschick & Hammerschlag, 2015; Irschick et al., 2017).Carcharhinus T A B L E 4Note: Coefficients that differ significantly from isometry (p ≤ .05)are indicated in bold.In all cases other than liver mass (LM), coefficients greater than 1 denote positive allometry, and coefficients lower than 1 denote negative allometry.In the case of LM, coefficients that differ significantly from 3 denote allometry.