Integrating isotopic and nutritional niches reveals multiple dimensions of individual diet specialisation in a marine apex predator

Abstract Dietary specialisations are important determinants of ecological structure, particularly in species with high per‐capita trophic influence like marine apex predators. These species are, however, among the most challenging in which to establish spatiotemporally integrated diets. We introduce a novel integration of stable isotopes with a multidimensional nutritional niche framework that addresses the challenges of establishing spatiotemporally integrated nutritional niches in wild populations, and apply the framework to explore individual diet specialisation in a marine apex predator, the white shark Carcharodon carcharias. Sequential tooth files were sampled from juvenile white sharks to establish individual isotopic (δ‐space; δ13C, δ15N, δ34S) niche specialisation. Bayesian mixing models were then used to reveal individual‐level prey (p‐space) specialisation, and further combined with nutritional geometry models to quantify the nutritional (N‐space) dimensions of individual specialisation, and their relationships to prey use. Isotopic and mixing model analyses indicated juvenile white sharks as individual specialists within a broader, generalist, population niche. Individual sharks differed in their consumption of several important mesopredator species, which suggested among‐individual variance in trophic roles in either pelagic or benthic food webs. However, variation in nutrient intakes was small and not consistently correlated with differences in prey use, suggesting white sharks as nutritional specialists and that individuals could use functionally and nutritionally different prey as complementary means to achieve a common nutritional goal. We identify how degrees of individual specialisation can differ between niche spaces (δ‐, p‐ or N‐space), the physiological and ecological implications of this, and argue that integrating nutrition can provide stronger, mechanistic links between diet specialisation and its intrinsic (fitness/performance) and extrinsic (ecological) outcomes. Our time‐integrated framework is adaptable for examining the nutritional consequences and drivers of food use variation at the individual, population or species level.


| INTRODUC TI ON
Trophic interactions are key determinants of ecosystem structure and function and understanding these can help predict the impacts and persistence of organisms across environmental contexts (Machovsky-Capuska, Senior, et al., 2016b;Rader et al., 2017;Senior et al., 2016;Slatyer et al., 2013). Nonetheless, adequately quantifying diet in free-ranging animals remains a significant challenge, especially for cryptic species, because direct foraging observations are often unfeasible or spatiotemporally restricted. Stable isotopes (SI) are a widely adopted solution for establishing time-integrated diets because they assimilate foraging information (food use and/ or foraging habitat) over periods defined by rates of consumer tissue isotopic turnover (Ramos & Gonzalez-Solis, 2012). Carbon and nitrogen SI are most commonly measured, separating primary production sources (δ 13 C) and trophic levels (δ 15 N), although other SI can help distinguish additional foraging attributes (δ 18 O, δ 2 H, habitat use; deHart & Picco, 2015; δ 34 S, pelagic vs benthic feeding; Raoult et al., 2019). "Isotopic niches" (Newsome et al., 2007) are thus widely adopted as proxies for foraging niches (despite caveats; Shipley & Matich, 2020), enabling standardised comparisons across ecological hierarchies, from individuals to communities (Ingram et al., 2018;Jackson et al., 2011). While δ-space metrics offer useful insights into realised foraging niches, translation to proportional resource use (p-space) through Bayesian SI mixing models is a requisite step for linking diet specialisation to its ecological outcomes (Newsome et al., 2012;Stock et al., 2018).
Although MNNF is widely used in some systems (e.g. primates; Hou et al., 2021;Raubenheimer et al., 2015), field-based applications have been limited for many species by the difficulty or impossibility of collecting long-term dietary data, necessitating expedient measures (e.g. stomach contents, regurgitations, scats ;Denuncio et al., 2021;Grainger et al., 2020;Machovsky-Capuska et al., 2018;Senior et al., 2016) that provide only spatiotemporal snapshots of individuals' food and nutrient acquisition. Combining spatiotemporally integrated food biomass assimilation estimates from SI mixing models (Phillips & Koch, 2002) and MNNF could provide a powerful framework for assessing food and nutrient consumption across time scales, but this has not yet been attempted. Moreover, establishing interrelationships in specialisations across different niche spaces (e.g. δ-, p-and N-space), and their hierarchical partitioning between individuals and species/populations, is necessary for enhancing our understanding of key ecological processes (Carscadden et al., 2020;Takola & Schielzeth, 2022). For instance, examining interplays between variation in food use and nutrient acquisition can reveal animals' nutritional priorities and how physiological requirements are met under ecological constraints (e.g. food availability or competition; Hou et al., 2021;Raubenheimer et al., 2015), which is critical for predicting responses to novel ecological circumstances Machovsky-Capuska, Senior, et al., 2016b).
Combining MNNF and SI could enable nutritional assessments at any level of the ecological hierarchy (individuals, populations or species), although quantifying individual-level nutritional niches is particularly valuable. Specifically, fitness and performance outcomes of diet variation manifest at the individual level (Costa-Pereira, Toscano, et al., 2019b), and individual diet specialisations, defined where individuals of similar ages/sexes use different subsets of a broader population-level niche due to phenotypic trait variation, resource availability and competition (Araujo et al., 2011;Bolnick et al., 2002;Svanback & Bolnick, 2007), are increasingly recognised as important determinants of ecosystem dynamics (Bolnick & Ballare, 2020;Ingram et al., 2011). This is particularly important in apex predators because, whilst they generally exert high per-capita trophic influence on community structure, individual specialisation implies that not all individuals are ecologically equivalent, complicating both our understanding (ecological) outcomes. Our time-integrated framework is adaptable for examining the nutritional consequences and drivers of food use variation at the individual, population or species level.
Individual specialisation explicitly defines whether individuals' resource use is a subset of that of the overall population, rather than relative to available resources in the environment as per "classical" niche specialisation (Matich et al., 2021;Newsome et al., 2012). Thereby, it is quantitatively formalised using variance partitioning, with total population niche width (TNW) equalling the sum of the between-individual component (BIC) and withinindividual component (WIC) of variation and individual specialisation increasing as the WIC:TNW ratio decreases (as BIC exceeds WIC; Bolnick et al., 2002;Ingram et al., 2018;Roughgarden, 1972Roughgarden, , 1974. Individual variation in resource use can be inferred from SI by comparing tissues with different isotopic turnover rates, or more ideally, using serially accreted, metabolically inert substrates (e.g. hairs, baleen, vertebral and tooth growth bands) that integrate sequential, temporally distinct foraging information (Matich et al., 2021;Newsome et al., 2009;Trueman et al., 2019).
Here, we integrate MNNF and SI to explore individual dietary specialisation across multiple niche spaces (δ-space, p-space and N-space) in a marine apex predator, the white shark Carchardon carcharias. White sharks are ecologically important yet threatened, cryptic predators (Rigby et al., 2019;Shea et al., 2020). Their diet generally consists of smaller elasmobranchs and teleosts, with the inclusion of larger or higher trophic level prey (e.g. whales, dolphins, sharks) as they transition into subadulthood/adulthood (>3 m total length; Estrada et al., 2006;Grainger et al., 2020;Hussey et al., 2012;Pethybridge et al., 2014;Tamburin et al., 2020).
Individual specialisation in white sharks has been inferred previously from whole-lifetime vertebral SI profiles (annual increments; Kim et al., 2012). However, vertebral profiles are limited for detecting fluctuations in specialisation over shorter timeframes, or through ontogeny (between different years/ages, e.g. Svanback et al., 2015), since they only resolve WIC at interannual or greater timescales (across multiple years). Therefore, we used a novel approach, sampling sequentially formed tooth files, the potential of which for fine-scale (month increment) individual-level diet reconstruction in elasmobranchs has been recently highlighted Zeichner et al., 2017), analogous to more widely used systems in other species (e.g. mammalian hair/vibrissae ;Newsome et al., 2009). Our specific aims were to (1) link SI and MNNF via mixing models to evaluate individual specialisation at the level of isotopes (δ-space), food use (p-space) and nutrient intakes (N-space), (2) examine potential effects of sex and size on individual specialisation in each niche space and (3) evaluate the relationship between individual specialisation across p-and N-space (i.e. whether individuals are similarly specialised, relative to the population, in both prey use and nutrient intakes). More generally, this illustrates an important application of our broader framework for quantifying time-integrated nutritional niches in field studies using SI, which could be flexibly adapted across taxa at either the individual, population or species level. Sampled sharks were of the size range commonly encountered in coastal eastern Australia (Bruce & Bradford, 2012;Spaet et al., 2020). Captured sharks were frozen (−20°C) until necropsy, where sex, PCL, fork length (FL) and total length (TL) were measured, and jaws were excised and refrozen (−20°C) until further processing. Samples of prey species (dolphins, sharks, benthopelagic and benthic rays, pelagic, benthic, reef-and estuary-associated teleosts, cephalopods) consumed by white sharks in eastern Australia based on stomach contents (Grainger et al., 2020) were collected ( Table 1). Prey were sampled either through the NSW SMP (bather-protection nets) or catches from commercial fishers operating off coastal beaches and shelf waters (generally <100 m depth) between Sydney and Port Stephens (Figure 1), an important region within the spatial range of eastern Australian white sharks (Bruce et al., 2019;Spaet et al., 2020) (Dicken, 2008;Fallows et al., 2013;Tucker et al., 2019). Prey was stored frozen (−20°C), then partially thawed, measured and weighed, and approximately 1 g of muscle (adjacent to the first dorsal fin for fish and dolphins, central disc musculature for rays, mantle for cephalopods) was excised for isotopic analysis. Blubber was also collected from dolphins since it represents a significant proportion of their total body mass (~21%-26%), in addition to muscle (~26%-37%; Mallette et al., 2016), and a lipid-rich carbon source for juvenile white sharks (Grainger et al., 2020).

| Tooth development and sampling
Shark teeth are a composite material, comprising an outer, highly mineralised (high-fluoride carbonated apatite) enameloid layer (~1%-8% organic protein matrix by weight; collagen and other proteins) surrounding an inner osteodentine pulp that is less mineralised (~15%-20% organic matrix; mostly collagen; Berkovitz & Shellis, 2017;Enax et al., 2012). Isotopic dietary signatures are assimilated into the organic matrix (hereafter "collagen") during formation until the tooth becomes fully mineralised and inert, prior to eruption (Becker et al., 2000;Zeichner et al., 2017). As with other elasmobranchs, sharks develop teeth continuously below the jawline which rotate forwards in files in a conveyor belt style process to replace existing functional teeth on the outer jaw edge ( Figure 2). Thereby, sampling tooth rows within a file from the inner (newest tooth) to outer jaw edge (oldest tooth) provides a sequential record of foraging patterns over temporally distinct periods (when each tooth formed) defined by rates of tooth replacement and isotopic turnover during odontogenesis .
The full tooth file (5-6 rows) immediately right of the lower jaw symphysis was sampled from each white shark ( Figure 2). The lower jaw was used as it generally contained more rows per file (5-6) than the upper jaw (3-4). Recent SI analyses of shark tooth collagen have indicated isotopic variability across teeth assumed to be of similar age (i.e. same row in different files; Shipley et al., 2021). Therefore, using a single file may have underestimated overall variability within the jaw. However, white sharks possess independent dentition, whereby teeth from different files can be lost and replaced at different times (Berkovitz & Shellis, 2017), complicating comparisons across files and introducing uncertainty regarding the temporal window sampled if rows (of potentially different ages) across different files are aggregated. Despite the caveat of using a single row, this preserved the assumption that rows within a file offered sequential, temporally distinct foraging information (Zeichner et al., 2017), and sampling from a consistent jaw location in all individuals minimised potential biases related to variation in rates of tooth loss/ replacement in different areas of the jaw. Using the best available information (from species with greatest similarities in detention and size to white sharks, where possible), we estimated tooth replacement at 18-36 days row −1 (sandbar sharks Carcharhinus plumbeus; Wass, 1973; Table S1 for other species) and isotopic turnover (residence time) as ~32-83 days (leopard sharks, Triakis semifasciata; Zeichner et al., 2017). Thereby, sampled tooth files were estimated to integrate diet over ~90-216 days (depending on replacement rate and the number of available rows).

F I G U R E 1
Capture locations, dates, sex, size (total length, TL; fork length, FL; precaudal length, PCL; size class, small and large juveniles) and the number of teeth sampled (n) from white sharks for stable isotope analysis that was included in data analyses. The location of the sampling region in eastern Australia is indicated in the inset map (black square). Shark ID numbers correspond to those used in all other figures. The coastline shapefile and bathymetric data were sourced from the GSHHG Database (Wessel & Smith, 1996; available from https://www.ngdc.noaa.gov/mgg/shore lines/) and GEBCO 2020 15 arc-second bathymetric grid (GEBCO Compilation Group, 2020; available from https://www.gebco.net/data_and_produ cts/gridd ed_bathy metry_data/gebco_2020/), respectively. for 1 week. The EDTA was replaced weekly until samples were fully gelatinised (~1 month) by centrifuging (2500 rpm, 3 min) and pipetting off the supernatant. Samples were then rinsed 5 times in Milli-Q water (vortex mixed and centrifuged between each rinse) and dried (50°C, 48 h). Whilst slow, demineralisation was performed using TA B L E 1 Mean (SD) atomic elemental ratios and isotopic signatures for prey species of white sharks collected in central New South Wales, Australia. Overall average values for source groupings used in mixing models are shown in bold. Values have not been lipid extracted or adjusted for trophic enrichment. For the dolphin source, isotopic signatures and elemental atomic ratios were calculated using weighted averages of δ 13 C, δ 15 N, and elemental concentrations (weight % of C, N and S) in muscle and blubber, weighted by the body mass percentages of each tissue in dolphins (Mallette et al., 2016), since both muscle and blubber are dietary substrates for white sharks. Sulfur was not detected in sufficient quantities in dolphin blubber and thus δ 34 S signatures were from muscle only, and C:S atomic and N:S atomic ratios were undefined for this tissue (weight % S = 0). Abbreviations and source grouping descriptions are in the  Note: Tissues: M = muscle, B = blubber; sources: 1 = Whale, 2 = dolphin, 3 = shark, benthopelagic rays and non-pelagic teleost, 4 = benthic rays and cephalopods, 5 = pelagic teleost, 6 = estuary-associated teleost.
EDTA rather than HCl to ensure sufficient material for δ 34 S analysis (>9 mg) given the small volume of some tooth samples. Dried, demineralised samples were ball milled to a powder prior to isotope analyses.
Prey muscle and blubber were dried (50°C, 48 h) and then ho- between shark tooth collagen and other tissues and suggested this was driven by a dominating de novo pathway using protein and nonprotein substrates to synthesise glycine, a non-essential, glycolytic and principle amino acid in collagen (also see Guiry & Szpak, 2020;Whiteman et al., 2018). Considering this, and the lipid-rich composition of some white shark prey (e.g. dolphins, whale blubber), we did not lipid extract prey samples and implemented concentrationdependent mixing models (see below), following Wolf et al. (2015) and Arostegui et al. (2019). Additionally, to better reflect that juvenile white sharks often consume whole dolphins (Grainger et al., 2020),

| Tooth collagen quality assurance and control
The amount and quality of collagen extracted from teeth was evaluated by calculating the organic matrix yield (ratio of demineralised to mineralised dry mass), and examining whether the atomic C:N ratios (C:N atomic ) of demineralised samples fell within the recommended range of 3.0-3.3 to avoid potential isotopic effects from noncollagenous proteins or lipids (mostly on δ 13 C; Guiry & Szpak, 2020).
Given this, and to standardise sample sizes to n = 5 per individual for subsequent isotopic niche comparisons, row 6 samples were excluded from further analysis. Of the remaining 60 samples, 11 had C:N atomic >3.3 ( Figure S1). Consequently, we modelled linear relationships between C:N atomic and δ 13 C, and adjusted δ 13 C for samples where a significant negative relationship (see Guiry & Szpak, 2020) F I G U R E 2 Cleaned lower jaw of a white shark (1.85 m TL) indicating dentition and descriptive terminology adapted from Becker et al. (2000). The tooth file sampled in all sharks is bracketed in orange.
was observed and C:N atomic was >3.3 (n = 7 teeth) using a scaled offset equation approach following Shipley et al. (2021) (Figure S1).
No correction was applied to an additional 7 samples with C:N atomic between 2.9 and 3.0 because no obvious deviations in δ 13 C were evident ( Figure S1) and the lower C:N atomic limit (3.0) is conservative (Guiry & Szpak, 2020).

| Bayesian stable isotope mixing models
To provide ecological context to individuals' isotopic niches, proportional prey consumption by individual sharks was modelled using the MixSIAR Bayesian SI mixing model (Stock et al., 2018).
The reliability and precision of these models generally decreases as the number of sources exceeds the number of isotopes +1 (four sources in our three-isotope system; Phillips et al., 2014;Stock et al., 2018). Given the large number of known prey of white sharks (  (Benjamini & Hochberg, 1995) to determine whether prey did not differ significantly and could thus be grouped (Phillips et al., 2014). However, significant differences were found among most prey species ( Figure S2).
Consequently, mixing spaces were visually inspected and prey were grouped into six sources that had (1) general similarity in isotopic signatures, and (2) similar nutritional compositions. This provided logical groupings of species that were nutritionally similar ( Figure S3), which was a priority for subsequent nutritional modelling, and were generally separated from other sources on at least one isotopic axis ( Figure S4). Assigned source groupings represented the maximum level of simplification possible without excluding known important prey (Grainger et al., 2020) and thereby violating mixing model assumptions (Stock et al., 2018), or pooling nutritionally and functionally different prey and thus producing uninterpretable groups.
Since mixing models are sensitive to trophic enrichment factors (TEFs, Δ), performing sensitivity analyses to different TEFs (where they are available/applicable) is recommended (Phillips et al., 2014;Stock et al., 2018). Currently, the only experimentally measured TEFs for shark tooth collagen are from small leopard sharks Triakis semifasciata fed low-lipid tilapia Oreochromis sp. (TEF A , Table 2) or squid Loligo opalescens (TEF B , Table 2) diets (Zeichner et al., 2017). However, TEF estimates from single diet items may not reflect natural scenarios where individuals consume mixed diets (Petta et al., 2020), and the appropriateness of these estimates for white sharks, which are higher trophic level predators that consume high-lipid prey, is uncertain since both trophic level and dietary lipid content can influence trophic enrichment (Hussey et al., 2014;Newsome et al., 2014;Shipley & Matich, 2020;Wolf et al., 2015). Shipley et al. (2021) recently identified that constant isotopic offsets between tooth collagen and muscle across several larger, more ecologically equivalent shark species to juvenile white sharks, were likely driven by differences in tissue-specific fractionation, indicative of a larger Δ 13 C and smaller Δ 15 N in teeth than muscle. Consequently, we used these offsets as quantitative proxies for the difference between muscle and tooth TEFs and thereby estimated an additional TEF (TEF C ,  (Krajcarz et al., 2019;McCutchan et al., 2003), and methionine, the predominant sulfur-containing amino acid in fish collagen (Guiry & Szpak, 2020), is essential in most animals, undergoing direct dietary routing which supports limited fractionation for sulfur (Brosnan & Brosnan, 2006;Nehlich, 2015). Therefore, Δ 34 S was set to 0.0 ± 0.5 (mean ± SD) for all TEF scenarios ( Table 2) to accommodate uncertainty and measurement error (Raoult et al., 2019).
Mixing polyhedron simulations (3,000 iterations) were used to determine whether tooth samples fell within the 95% mixing region under each TEF scenario and thereby satisfied mixing model assumptions (Phillips et al., 2014;Smith et al., 2013). Most samples fell outside the 95% mixing region on the δ 15 N axis under TEF A ( Figures S6A and S7A), so this scenario was excluded. All samples fell within the 95% mixing region for TEF B (Figures S6B and S7B) and TEF C ( Figure S7C, Figure 3), although probabilities were higher under TEF C for 73.3% of samples. The Δ 13 C for TEF C fell within the range of values measured in leopard sharks, but Δ 15 N was smaller ( Table 2). This is consistent with observations of reduced Δ 15 N in  (Table S2; see Data Sources section; also see Grainger et al., 2020). Compositions were extracted, where possible, from studies conducted in geographical proximity to the present study (Tait et al., 2014), and values for closely related taxa (same genus/family) were used if compositions were unavailable for particular prey species (Table S2; Eder & Lewis, 2005). Compositions of prey species were generally similar within source groupings (Table S2, Figure S3) and  c-index nutrients (response) was also evaluated using a beta GLM to test whether similar levels of individual specialisation (i.e. differences from the population) were maintained by individuals across different niche spaces. A positive relationship was predicted in this circumstance. All data analyses were conducted in R (v4.2.0; R Core Team, 2021), and figures were generated using ggplot2 (Wickham, 2016). Where relevant, results are reported as means ± SD unless otherwise indicated.

| Isotopic niche metrics
Across all sharks, tooth collagen isotopic signatures ranged from −15.2 to −12.5 (mean ± SD = −13.5 ± 0.7‰) for δ 13 C, 12.5 to 15.2 (13.7 ± 0.7‰) for δ 15 N and 15.6 to 19.2 (17. F I G U R E 3 Isotopic signatures of prey source groups (squares, mean ± SD) and individual tooth samples (circles) on all three isotopic axis combinations for the TEF C scenario. Prey signatures have been corrected for trophic enrichment, and errors are the combined source + trophic enrichment SD following Stock and Semmens (2016 Figure 4). However, individuals' isotopic niches occupied only subsets of these ranges, with high among-individual variation and no clear groupings in δ-space according to size and sex ( Figure 4).
For example, some biologically "similar" individuals (age, sex, capture date and location; Figure 1) occupied different isotopic niches (e.g. ws8 and ws9 (large females), and ws11 and ws12 (large males)), suggesting temporally consistent differences in foraging patterns ( Figure 4). This was best explained by shark size (Table S3) O-index values were not related to sex or size class, with AIC c favouring a null model (Table S3).

| Individual-level estimates (TEF C )
Although posterior distributions were variable for some sources/individuals (e.g. shark, benthopelagic ray, non-pelagic teleost, dolphins), significant deviations of individuals from the population (Δ ind-pop ) were still detected for all sources except dolphins, and in all individuals except ws2, ws3 and ws7 (Figure 6a,b). These deviations were small for whale and estuary-associated teleost groups (Δ ind-pop <10% for all individuals), with greater individual variation in the use of shark, benthopelagic ray and nonpelagic teleost, benthic ray and cephalopod, and pelagic teleost source groups (Figure 6b). For these sources, significant Δ ind-pop mostly ranged between (mean ± SD) -12.7 ± 7.9% (ws1, benthic rays and cephalopods) and -23.5 ± 12.5% (ws8, shark, benthopelagic rays, non-pelagic teleosts F I G U R E 4 Two-dimensional projections of tooth collagen isotopic signatures (δ 13 C, δ 15 N, δ 34 S) from 12 white sharks. Dots show isotopic values for individual teeth. Squares and filled ellipses show means and standard ellipses for each individual, with ID labels corresponding to those used in Figure 1. Note that means for sharks 3 and 7 overlap on the δ 13 Cδ 34 S axis. Standard ellipses corresponding to population-level estimates for the between-individual (BIC pop ) and within-individual (WIC pop ) components of variation and total niche width (TNW pop ) are also shown.  (Figure 6b). Individuals ws11 and ws1 displayed greater Δ ind-pop , with higher contributions from benthic rays and cephalopods (+43.3 ± 14.5%) and pelagic teleosts (+41.1 ± 13.5%), respectively ( Figure 6b). Individual ws8 was also comparatively specialised with high contributions of pelagic teleosts (+31.6 ± 18.0%, Figure 6a) relative to the population, although the probability for this difference was not significant (Figure 6b). Although there was a trend towards larger sharks being more dissimilar to the population in p-space (c-index prey , Figure 7), AIC c favoured a null model (no sex or size effects, Table S4). Interestingly, several individuals (e.g. ws1, ws8, ws11) with comparatively broader isotopic niches (higher s-index, Figure 5), had specialised diets (Figure 6a) dissimilar to that of the population (low c-index prey , Figure 7), whilst some individuals with narrow isotopic niches (e.g. ws3, Figure 5) maintained broader diets and high similarity to the population ( Figures 6A and 7).

| Individual-level estimates (TEF C )
Significant Δ ind-pop in nutrient intakes were detected for all individuals, except ws3 and ws7, with the greatest differences being on the %L SI and %W SI axes ( Figure 8c). Nonetheless, the magnitude of deviation from the population was small overall (mean  Table S4). There was no significant relationship between c-index prey and c-index nutrients (beta GLM; est c-index.prey ± SE = 2.0 ± 1.1, z = 1.9, p = 0.061), suggesting that specialisation across p-space and N-space were not consistently correlated (Figure 7). This was predominantly driven by individuals ws1 and ws11 which showed low p-space similarity (c-index prey ) but higher N-space similarity (c-index nutrients ), on par with that of individuals who were less specialised in p-space (Figure 7).

| Comparison between TEF C and TEF B
Sensitivity analyses suggested similarities but also some differences in model outputs between TEF scenarios, which were more pronounced in p-than N-space. Proportions of dolphin, benthic ray and cephalopod and estuary teleost sources tended to be higher under TEF B for both individual and population estimates, although aside from estuary teleosts for ws2, these differences were not significant (probabilities <0.95 and >0.05; Figures S8 and S9A). The most pronounced differences were in contributions from pelagic teleost, which were significantly lower under TEF B for ws1 (ΔTEF B -TEF C = −54.5 ± 20.5%), ws6 (−21.1 ± 12.0%), ws8 (−47.9 ± 23.1%) and the population (−20.2 ± 12.1%; Figures S8 and S9A). Frequency No significant differences in modelled nutrient intakes between TEF scenarios were detected ( Figures S9B and S10). As with TEF C , no significant relationship between c-index prey and c-index nutrients was detected under TEF B (beta GLM; est c-index.prey ± SE = 3.7 ± 2.0, z = 1.8, p = 0.069), driven again by a low c-index prey and high c-index nutrients for ws1, ws11, and also ws4 ( Figure S11). Comparisons with AIC c favoured no effect of sex or size on c-index prey or c-index nutrients under TEF B , although a trend towards larger sharks having lower c-index nutrients was evident (Table S4, Figure S11), similar to the statistically significant pattern identified for TEF C (Figure 7).

| DISCUSS ION
We have presented a framework unifying SI and nutritional geometry that addresses the challenge of examining time-integrated nutrition intrinsic (physiological) implications, and highlight some conceptual limitations of inferring individual diet specialisation from isotopic variance alone. We first discuss inferences on prey use based on δand p-space analyses, then how these relate to nutritional outcomes.

| δ -space and p-space specialisation: Patterns and discrepancies
Isotopic and p-space analyses characterised white sharks as preyuse generalists at a population level, but prey-use specialists at an individual level. Indeed, total isotopic variability was similar to that previously established for other generalist species in the region single-item diets (Petta et al., 2020;Wolf et al., 2015), is a priority.
Additionally, our mixing space necessitated the use of some generalised prey categories which restricted our ability to discern amongst certain prey (e.g. sharks, benthopelagic rays and non-pelagic teleosts). However, the overall modelled population-level importance of pelagic eastern Australian salmon Arripis trutta combined with a mix of sharks, benthopelagic and benthic rays and non-pelagic teleosts is corroborated by similar findings from stomach contents (Grainger et al., 2020;Hussey et al., 2012;Tricas & McCosker, 1984), SI and fatty acid tracers (Pethybridge et al., 2014;Tamburin et al., 2020) for juvenile white sharks. The relatively infrequent consumption for dolphins, and especially whales, is also consistent with previous studies (Grainger et al., 2020;Hussey et al., 2012). Moreover, prior stomach content information helps to clarify some distinctions among prey that were pooled, notably the likely importance of benthic rays compared with cephalopods (Grainger et al., 2020).
The ecological consequences of individual diet specialisation can depend on the magnitude and specific nature of the trophic interactions that vary between individuals (Araujo et al., 2011;Bolnick et al., 2002;Ingram et al., 2011). However, many isotopic studies assess individual diet specialisation in δ-space alone and thus do not offer specific information on individual differences in food use (Matich et al., 2021;Shipley & Matich, 2020). We addressed this limitation using mixing models, which offered improved insights into individual variation in the likely ecological functional roles of a top marine predator. Specifically, our F I G U R E 7 Posterior mean cosine similarities (c-index) between individual white sharks and the overall population based on modelled prey proportions (c-index prey , p-space) and nutrient intakes (c-index nutrients , N-space) under the TEF C scenario. Marginal boxplots compare variation in c-index prey (top) and cindex nutrients (right) among small (~1.50 m PCL, n = 6) and large (~2.25 m PCL, n = 6) size classes. The predicted relationship (shading = 95% confidence intervals) between the c-index prey and c-index nutrients was not significant (beta GLM, p = 0.061) but is shown to illustrate the deviation of some individuals (e.g. ws1, ws11) from the expected positive relationship.   in predation pressure among white sharks, persisting over significant spatiotemporal scales (3-6 months integrated by teeth files), on several prey species which are themselves important predators in pelagic (e.g. Australian salmon; Hughes et al., 2014) and/or benthic food webs (e.g. hammerhead sharks (benthic/pelagic) or rays (benthic) ;Flowers et al., 2021;Gallagher & Klimley, 2018;Myers et al., 2007). This not only suggests functional inequivalence among individual white sharks but identifies specific trophic routes through which this may arise; in particular, via individual-specific top-down pressure in either benthic or pelagic systems.

Small
Establishing individual-level diets with mixing models also highlighted some important differences between δ-and p-space with wider implications regarding the conceptualisation and interpretation of δ-space variance as a proxy for individual diet specialisation.
Specifically, although larger sharks had broader relative isotopic niche breadths (larger s-index) and could be inferred to exhibit greater di-  et al., 2016). Elucidating such dynamics requires considering the functional relationships between different foods, which may offer similar nutritional properties ("substitutable" feeding), or be nutritionally different and imbalanced, yet able to be combined in proportions necessary for a specific nutritional goal ("complementary feeding"; Behmer et al., 2001;Raubenheimer, 2011;Raubenheimer & Jones, 2006;. Nutrient balancing through complementary feeding has been documented in many species (herbivores, omnivores, carnivores) in the laboratory , and leveraged to infer nutritional priorities (targeted macronutrient balance) in field-based settings, although predominately in primates (Hou et al., 2021;Raubenheimer et al., 2015).
Knowledge on whether similar mechanisms operate in free-ranging carnivores remains limited (Kohl et al., 2015;Machovsky-Capuska, Coogan, et al., 2016a). Most of the prey sources on which white sharks differentiated their diets were nutritionally distinct. Thus, maintenance of similar intakes to the overall population for some individuals (e.g. ws1, ws11), despite widely differing prey use, could suggest complementary feeding mechanisms in white sharks. Overall, these findings highlight the utility of our approach for elucidating nutritional specialisation/generalism and mechanisms of nutrientspecific foraging (e.g. substitutable vs. complementary feeding) in species where time-integrated foraging observations are otherwise impossible. Although we applied this in the context of individual diet specialisation using serially sampled tissues, mixing models can estimate individual-and population-level diets from single samples (albeit without accommodating WIC; Manlick et al., 2019;Stock et al., 2018) and comparing diet variation in p-vs N-space across individuals or populations can offer insights into animals' nutritional priorities (see Raubenheimer et al., 2015;Remonti et al., 2016).
Despite the overall similarity of individuals in N-space, significant deviations in nutrient intakes were still detected, especially for larger sharks, which could potentially reflect varying macronutrient preference or physiological requirement (e.g. Grainger et al., 2020;Han et al., 2016). Alternatively, these differences could indicate nutritional constraints, which may have fitness or performance consequences . Indeed, fitness and performance parameters have been related to increased isotopic variance (Costa-Pereira, Toscano, et al., 2019b) and individuals' use of specific foods (Robertson et al., 2015;Votier et al., 2010), but the physiological basis for these relationships remains unclear. Adopting a nutrient-specific approach to modelling foraging can directly link food use to fitness/performance (Jensen et al., 2012), and we suggest that expanding our approach by relating time-integrated nutrient intakes (estimated via SI) to fitness/performance proxies measured on the same individuals (e.g. performance surfaces mapped over Nspace; Simpson et al., 2004) could establish such links in field-based contexts. Doing so would help better define animals' fundamental dietary niches as the breadth of nutrient intakes over which performance/fitness is maintained, which is critical for understanding individual/species' resiliencies to environmental variation or disturbance (Machovsky-Capuska, Senior, et al., 2016b; also see Takola & Schielzeth, 2022).

| CON CLUS IONS
We have presented a unification of stable isotopes and nutritional geometry that simultaneously evaluated individual specialisation across isotopic, prey use and nutritional niches and distinctions among these, in juvenile white sharks. By revealing individual-level differences in prey use, our findings highlight the potential variable trophic roles played by individual white sharks in either benthic or pelagic food webs. Additionally, modelling individual-level diets demonstrated the limitations of inferring individual diet specialisation from isotopic niche size alone, which is a product of multiple, complicating factors in addition to diet breadth. Extending our analysis into nutrient space suggested white sharks as nutritional specialists at both the individual and population level, and the potential for specialisation on different prey that provide complementary means of achieving a similar nutritional goal. While we applied our framework using the sequential dentition of elasmobranchs, the method could equally be applied in other systems (e.g. other serially accreted tissues like hair/whiskers, tissues with different turnover rates,or repeated sampling of individuals where feasible ;Newsome et al., 2012;Semmens et al., 2009;Votier et al., 2010). Integrating a nutritional dimension of individual diet specialisation could help better define nutritional generalism and establish mechanistic links, formulated around macronutrient balance, between individual fitness, foraging specialisation and its ecological outcomes. The wider adoption of nutrient-specific approaches is a priority in trophic ecology (Danger et al., 2022) and linking SI with nutritional geometry more generally holds potential for a range of important questions, such as understanding the nutritional consequences (or drivers) of food use variation between populations (e.g. Manlick et al., 2019) or under a changing climate (e.g. Young et al., 2015).

ACK N OWLED G EM ENTS
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