The utility of bioenergetics modelling in quantifying predation rates of marine apex predators: Ecological and fisheries implications

Predators play a crucial role in the structure and function of ecosystems. However, the magnitude of this role is often unclear, particularly for large marine predators, as predation rates are difficult to measure directly. If relevant biotic and abiotic parameters can be obtained, then bioenergetics modelling offers an alternative approach to estimating predation rates, and can provide new insights into ecological processes. We integrate demographic and ecological data for a marine apex predator, the broadnose sevengill shark Notorynchus cepedianus, with energetics data from the literature, to construct a bioenergetics model to quantify predation rates on key fisheries species in Norfolk Bay, Australia. We account for the uncertainty in model parameters by incorporating parameter confidence through Monte Carlo simulations and running alternative variants of the model. Model and parameter variants provide alternative estimates of predation rates. Our simplest model estimates that ca. 1130 ± 137 N. cepedianus individuals consume 11,379 (95% CI: 11,111–11,648) gummy sharks Mustelus antarcticus (~21 tonnes) over a 36-week period in Norfolk Bay, which represents a considerable contribution to total predation mortality on this key fishery species. This study demonstrates how the integration of ecology and fisheries science can provide information for ecosystem and fisheries management.

Scientific REPORTS | 7: 12982 | DOI: 10.1038/s41598-017-13388-y over a 36 week period from September to May (spring-summer-autumn seasons) during which N. cepedianus are known to aggregate in the bay. The model incorporates (1) routine energy expenditure of free-swimming N. cepedianus in Norfolk Bay, (2) population size of N. cepedianus in Norfolk Bay, (3) demographic information for N. cepedianus and for prey species, (4) energy content of various prey species inhabiting Norfolk Bay, and the (5) relative importance of these prey species to the diet of N. cepedianus in Norfolk Bay. To account for uncertainty in model structure and input parameters, we built variants of the model based on three alternative techniques for measuring diet composition (see Methods). Separate models were run for each of the three diet variants taking into account two estimates of N. cepedianus population sizes in Norfolk Bay during the 36 week period: 562 ± 71 and 1130 ± 137 sharks. For each of the six scenarios considered, 1000 Monte Carlo simulations were performed to account for uncertainty in model parameters (see Methods).
Our sampling data indicate that N. cepedianus occurring in Norfolk Bay have an average body mass of 42 kg (Table 1). Accordingly, we estimate that the average free-swimming routine energy expenditure of N. cepedianus in Norfolk Bay is approximately 1150 kJ day −1 at a water temperature of 16.7 °C (assuming Q 10 = 2.2 and RQ = 0.88). During spring, when water temperature drops to 14.0 °C, routine energy expenditure is predicted to decrease to 930 kJ day −1 , and during summer, when water temperature increases to 19.1 °C, routine energy expenditure is predicted to increase to 1390 kJ day −1 (Q 10 = 2.2 and RQ = 0.88).
The number of prey consumed over the 36 week period, along with the relative importance of the different prey species (or groups), varied among the three models and six scenarios (Table 2, Fig. 2). For example, the consumption rate of M. antarcticus differed among models (Fig. 2, Table 2). Moreover, uncertainties and variations in model parameters that likely fluctuate within and between years (i.e. water temperature and number of N. cepedianus) or parameters lacking specific data for N. cepedianus (Q 10 ) produced differences in modelled prey consumption rates (Fig. 3). Changes in all three parameters led to differences in modelled consumption rates of M. antarcticus (Fig. 3 Table 2). This is influenced by the large average weight of skates and eagle rays (Table 1), resulting in those species having the highest average relative weight, i.e. skates 43% and eagle rays 16% (Appendix S1). All shark species (or groups) were consumed in lower numbers compared to model variant 2, including M. antarcticus (Table 2). Between 2241 (95% CI: 2119-2364) and 4653 (95% CI: 4396-4911) M. antarcticus individuals were estimated to be consumed over the 36-week period annually in Norfolk Bay. Estimates of teleost and cephalopod consumption were also higher in model variant 3 than in model variant 2 (Table 2).

Discussion
Bioenergetics model. Quantifying predation rates by marine predator populations is a significant challenge in ecology and fisheries science. Previous studies that have incorporated predator abundance estimates with bioenergetics models to quantify predation mainly includes marine mammals 17,18,27 , and fisheries species, such as tunas 28,29 . Although previous studies have constructed bioenergetics models for sharks (e.g. [30][31][32], few have incorporated abundance estimates that allow consumption rates to be scaled up to the population level 16,19 . The paucity of marine studies is not surprising given the difficulties associated with observing predators in general, and obtaining the suite of relevant parameters required for bioenergetics models. To compensate for this, these models are often based on best available assumptions, such as published data from similar species. Here, we present three model simulations using a combination of field data for predator and prey demographics and ecology, and information on energetics from the literature. Model 1 centres on the main strengths of available data, which is a very good understanding of N. cepedianus and M. antarcticus demographics and ecology in Norfolk Bay. This model provides estimates of predation mortality for M. antarcticus, a key fisheries species, in an area closed to commercial and recreational fishing to protect the population (see below). The second and third models take a broader system approach, and were populated with as much information that could be obtained for other prey species.
For fisheries applications, model 1 is the simplest to obtain data for as it only requires data for the predator and the target fisheries species. However, model 1 does not consider the input of other prey species (number or energetic value) to the diets of N. cepedianus, and this could be driving the higher estimates of M. antarcticus consumed compared to the other models. Still, higher estimates of M. antarcticus consumption may be the most appropriate if a conservative approach is considered best for fisheries management 10 . For ecosystem studies, model 3 is likely more accurate than model 2. Model 2 (based on % weight) overestimates mammal consumption. Marine mammals are not seen in Norfolk Bay in large numbers (Barnett pers. obs.), and the closest haul-out site is over 50 km away 25 . Either predation is significantly less, as predicted in model 3, or N. cepedianus are feeding on mammals elsewhere before entering Norfolk Bay. In general, % weight alone is not a good indicator of prey value as issues such as partial and differential digestion can provide ambiguous interpretations 33 . Furthermore, as digestion proceeds, only the components that are indigestible, or slow to digest, remain identifiable and potentially measureable 33 . For example, cephalopod beaks and fish otoliths are often all that remains of these animals in stomach samples. In model 3, the increase in the importance of batoids is primarily driven by the large average size of S. whitleyi and M. tenuicaudatus caught in Norfolk Bay, which influences their average % weight in the model (Appendix S1). The importance of batoids is likely overestimated in this model because smaller size classes of skates and eagle rays were not caught in the fishing gears used (inflating average size of batoids), and the likelihood that larger batoids are consumed by multiple N. cepedianus. This had some effect on the model output, such as lowering the estimates of M. antarcticus consumed ( Table 2).
A major challenge with bioenergetics models is the level of uncertainty associated with input parameter values 27 . A few of the parameters in our model undoubtedly introduce some uncertainty. For example, Q 10 for N.  cepedianus is unknown, and available literature suggests it could be between 1.3 and 3.0. This difference in Q 10 can lead to estimates that differ by ~2000 individual M. antarcticus consumed over the sampling year (Fig. 3). There could be some uncertainty regarding dietary composition, as stomach content analysis only provides information for a snapshot in time. However, stomach data were collected over three years and studies show that N. cepedianus diet composition can be linked to prey abundance 25 , as discussed in fisheries section below. Thus, uncertainty associated with parameters such as Q 10 , water temperature, N. cepedianus body mass (which are all related to uncertainty in metabolic rate), other metabolic rate parameters (power equation coefficient and power equation exponent) and prey composition, were factored into our analysis by running Monte Carlo simulations. Furthermore, uncertainty in N. cepedianus abundance was also factored in by using two different scenarios for each of the three versions of the model. Models can be updated when improved estimates for the different parameters become available. For instance, when technology becomes available for sharks of this size, conducting respirometry experiments and integrating field-derived activity data for N. cepedianus to determine species-specific metabolic rate may improve estimates of energetics and prey consumption 34 , as it addresses the most likely variable component of our bioenergetics model. Considering the best available information, we assumed similar activity for day and night based on N. cepedianus cruising speeds calculated from acoustic telemetry not being significantly different 35 . However, given that N. cepedianus appear to move over a larger area at night and the significant increase in movement rates between cruising and burst speeds 35 , field activity studies may also elucidate diel patterns in active metabolic rates.  36 . It is however important to recognise that predation rates on each species by N. cepedianus likely varies between locations, depending on differences in prey availability, water temperature and N. cepedianus abundance. For example, the high consumption of M. antarcticus coincides with it being one of the most relative abundant prey in Norfolk Bay and neighbouring bays 6,25 (Appendix S2). Similarly, increases in consumption of S. acanthias that coincide with high relative abundance in the neighbouring Derwent Estuary have been reported 25 . Likewise, in Tasmania and southern Africa, N. cepedianus consumed more marine mammals in the region with the highest concentration of seal rookeries, while chondrichthyans were the most important prey in the other regions 25,37,38 . Catches of some other species are high in neighbouring bays compared to Norfolk Bay. For example, S. acanthias and C. milii are caught in higher numbers in the neighbouring Fredrick Henry Bay and Pittwater, respectively. The greater presence of these species would likely result in an increase in their occurrence in the diet of N. cepedianus at those locations (Appendix S2). In general, N. cepedianus target other elasmobranchs and marine mammals globally, but the main species consumed within these groups can vary 25 . However, sharks from the genus Mustelus (family Triakidae) and other triakid species are the most common prey consumed by N. cepedianus in all regions globally 25 , suggesting that, when they are abundant, triakids are the main prey.
Besides the aforementioned links to fisheries, N. cepedianus is also linked to fisheries by being an important predator of elasmobranchs and pinnipeds that compete with fisheries 39,40 . In particular, fur seal Arctocephalus pusillus numbers have recovered significantly in Australia since their protection in 1975 and many in the fishing industry deem them as competitors for diminishing resources 40 . In areas of southern Australia with greater pinniped abundance, N. cepedianus likely consume more pinnipeds, and probably play a role in reducing pinniped competition with fisheries. Role of Notorynchus cepedianus. Previous work has inferred high predation pressure by N. cepedianus in coastal areas, as reviewed by Barnett and colleagues 22 . The current study shows that in areas of high abundance, N. cepedianus have significant impacts on the various prey species and very likely play an important role in ecosystem dynamics, e.g. top-down control of ecosystems. Notorynchus cepedianus consume the same prey as white sharks Carcharodon carcharias, including marine mammals, teleosts and elasmobranchs 22,37,41 . However, despite rivalling C. carcharias as the dominant apex predator in temperate waters, the ecosystem importance of N. cepedianus has been largely overlooked. Indeed, N. cepedianus arguably have a greater influence on top-down effects, such as ecosystem structure and controlling mesopredator numbers, as available information suggests they are much more abundant across temperate systems than C. carcharias 26,42 .
Given that water temperature plays an important role in predation rates (Fig. 3), increases in water temperature due to climate change could change the dynamics in shallow coastal bays such as Norfolk Bay. For example, model 1 predicts that 1130 N. cepedianus would consume ~1000 more M. antarcticus in summer compared to spring (Fig. 3). Tasmania is considered particularly susceptible to climate change, with warmer waters extending the southern range of some species along the east coast of Australia 43 . However, Tasmania is the most southern coastal area, and there is nowhere further south for N. cepedianus to move, and so if temperatures increase, they will need to adapt by increasing predation rates to meet the increasing energetic demands, or by spending more time in cooler deeper waters, which may affect their diet.
In conclusion, the integration of multiple types of information from a comprehensive suite of studies on N. cepedianus and its prey in Norfolk Bay has culminated in one of the first quantified estimates of predation for an apex predator shark species. Notorynchus cepedianus is an undervalued predator in coastal systems that competes directly with fisheries for common food resources. Given the wide distribution of N. cepedianus, they likely play an important role in ecosystem dynamics in temperate systems globally. Furthermore, N. cepedianus are intrinsically linked to fisheries, making them a good case study to show how the integration of ecology into fisheries science, i.e. "fisheries ecology", can provide data that can be used for applied outcomes in ecosystem and fisheries management.

Methods
Study site. Norfolk Bay is a relatively shallow (maximum depth of ~20 m), semi-enclosed bay, covering an area of ~180 km 2 , off the southeast coast of Tasmania, Australia (Fig. 1). Norfolk Bay is located within a shark refuge area, and as such, commercial and recreational fishing for elasmobranchs is not permitted. The bay provides an important feeding site for the broadnose sevengill shark Notorynchus cepedianus and aggregations occur in the bay from September to May 26,44 . In this study, the energetics and predation habits of N. cepedianus in Norfolk Bay were analysed over this 36-week period, encompassing the spring-summer-autumn seasons. All field work was conducted under an Australian Fisheries Management Authority Scientific Permit (#901193) and the methods were approved by the University of Tasmania Animal Ethics Committee (#A0012578). Routine energy expenditure of N. cepedianus. The bioenergetics model constructed for this study estimates predation rates by N. cepedianus on the gummy shark Mustelus antarcticus, as well as other prey species, in Norfolk Bay from spring to autumn. To achieve this aim, an estimate of the routine energy expenditure of free-swimming N. cepedianus in Norfolk Bay was required. Over a period of two years and 3 months (to include 3 summers), 294 N. cepedianus individuals were caught in Norfolk Bay using longline fishing methods 24 . For each of these sharks, length measurements, sex and stomach contents (from stomach flushing) were recorded 45 . Since N. cepedianus is an ectotherm, the routine energy expenditure (MR; mg O 2 h −1 ) was calculated for each of these 294 individuals using the allometric power equation for a group of free-swimming ectothermic sharks species, MR = 214M b 0.79 , correct to 20 °C 46 , where M b is body mass in kg, which was estimated for each individual using sex-specific N. cepedianus length-weight data 47 (Table 1). This estimate of overall mean routine energy expenditure is unlikely to vary across a 24-h cycle owing to activity measurements that indicate the rate of movement by N. cepedianus in Norfolk Bay is relatively constant during the day and night 35 . The routine energy expenditure of each individual N. cepedianus was, however, adjusted according to seasonal mean variation in water temperature (measured in the adjoining Fredrick Henry Bay: spring 14.0 °C, summer 19.1 °C, autumn 16.9 °C, overall mean 16.7 °C) using a uniform distribution Q 10 between 1.3 and 3.0. This Q 10 range was applied because it represents the temperature sensitivity of metabolism reported across nine species of elasmobranchs 48,49 . We also allocated an additional 5% energy expenditure to account for the cost of growth, which is estimated at approximately 8.7-14.6 cm year −1 given the size range of N. cepedianus in Norfolk Bay 50 , and is consistent with the little available literature that suggests between 3.5 and 7.2% of metabolic rate is invested in growth in sharks 30,51 . We also allocated another 5% increase in energy expenditure to account for the cost of reproduction, but only in one-third of the mature females, which was based on N. cepedianus probably having a three-year reproductive cycle 52 . Some mature females in Norfolk Bay have been found to be ovulating, in the initial stages of pregnancy, or starting a new vitellogenic cycle 52 . The cost of reproduction is unlikely to be much higher because Norfolk Bay and its neighbouring coastal areas are not used as pupping grounds, mating rarely occurs there, and most female N. cepedianus are non-gravid while in Norfolk Bay 52 .
After accounting for the effect of temperature, growth and reproduction on the estimated energy costs for each individual N. cepedianus, we then averaged energy expenditure across all individuals, to derive the mean routine energy expenditure of N. cepedianus in Norfolk Bay, assuming that our sample of 294 individuals is a reasonable representation of the population demographics at any given time. We then converted the units of routine energy expenditure from mg O 2 h −1 to kJ sampling year −1 , given there are 6048 h in a 36-week-period, and there is 68.3 mg O 2 kJ −1 given a respiratory exchange ratio of 0.88 53 . We then used population estimates of N. cepedianus in Norfolk Bay at any given time 26 to obtain the routine energy expenditure of the entire population while in Norfolk Bay from spring to autumn.
Scientific REPORTS | 7: 12982 | DOI:10.1038/s41598-017-13388-y Energy content of prey. The bioenergetics model constructed required an estimate of energy content for the key prey species of N. cepedianus in Norfolk Bay. Previous work identified the key prey species of N. cepedianus in Norfolk Bay 25 . The key prey species were categorized into fur seal Arctocephalus pusillus, other mammals, M. antarcticus, school shark Galeorhinus galeus, dogshark Squalus acanthias, unidentified sharks, eagle ray Myliobatis tenuicaudatus, Melbourne skate Spiniraja whitleyi, banded stingaree Urolophus cruciatus, unidentified batoids, elephantfish Callorhinchus milii, teleosts, and cephalopods ( Table 1). The average available energy content (kJ) of each of these prey species or groups was calculated as the product of the energy-density of the tissue and their average body mass, multiplied by a factor of 0.73 to account for energy assimilation efficiency 54 . Tissue energy-density values were obtained for the various prey species or groups from bomb calorimetry measurements published in the literature, and where such data were unavailable we substituted for closely related species (Table 1). The body masses of the various chondrichthyan prey species were calculated by applying length-weight conversions derived using published and unpublished data ( Table 1). The body lengths used in these length-weight conversions were recorded during long line sampling and gill-net surveys in Norfolk Bay and adjoining Frederick Henry Bay 24,55 ; McAllister unpublished data; CSIRO, Australia, unpub. data. Average body mass for cephalopods was based on arrow squid Nototodarus gouldi, as it is abundant in the bay, and the most commonly consumed cephalopod species 25 . Average body mass of marine mammal was based on fur seal adult males and sub-adult of both sexes, which are the most common marine mammal in the Norfolk Bay region 56 . We assume that the whole-body of the prey is consumed by N. cepedianus, even if it is consumed by several individual N. cepedianus, as is likely the case for large prey items, such as mammals.

Model simulations, variants and sensitivity analyses.
To account for uncertainty in model structure and input parameters, we built variants of the bioenergetics model by incorporating parameter confidence through Monte Carlo simulations. Using our calculated value for the routine energy expenditure of the entire population of N. cepedianus in Norfolk Bay across the 36-week period each year, and the total energy available from each prey species (or group), we ran three model variants to estimate local predation rates by N. cepedianus on the various prey in Norfolk Bay. The three model variants provide estimates of N. cepedianus predation rates depending on the relative fraction that each prey species (or group) contributes to supporting the energy expenditure of N. cepedianus, which we based on three alternative techniques that are commonly used for measuring diet composition: (1) the frequency a prey species occurs in the diet, (2) the weight of each prey species (or group) as a fraction of the total weight of all prey consumed, and (3) the number of each prey consumed as a fraction of the total number of all prey consumed 33 .
The model estimates predation rate (P x ; sampling year −1 ) on species x (or group x) over a sampling year following the equation, P x = MR × F x /E x , where MR (kJ sampling year −1 ) is the routine energy expenditure of N. cepedianus, E x is the available energy content (kJ) of species x (or group x), and F x is the fraction of the diet of N. cepedianus represented by species x (or group x). Thus, the three model variants provide alternative estimates of F x , therefore leading to different estimates of P x . In model variant 1, which focuses only on the predation rate of M. antarcticus, F x was set as 0.25 based on stomach flushing data that showed 25% of N. cepedianus sampled in Norfolk Bay had consumed M. antarcticus 25 . In model variant 2, F x is set as equal to the partly digested weight of each prey species (or group) in the stomach of N. cepedianus, divided by the total partly digested weight of all prey items present in the stomach. The weight of prey items was measured from regurgitated stomach contents at varying stages of digestion, obtained from stomach flushing N. cepedianus sampled in Norfolk Bay 25,45 . In model variant 3, F x is the proportion that each prey contributes to the overall diet, calculated by multiplying the average weight of each prey (Table 1) by the number of that prey present in the stomach (Appendix S1), as determined from stomach flushing of N. cepedianus sampled in Norfolk Bay 25,45 . For the much larger mammalian prey species, ingestion weight was calculated as the average weight of the ingested pieces of mammal (Table 1). We only included pieces of mammal in the weight calculations that minimal digestion had occurred.
The three model variants were run using two alternative variations in the population size estimate of N. cepedianus in Norfolk Bay (Table 2). For the two population scenarios, we considered a log-normal distribution with mean of 562 ± 71 sharks, and another scenario with mean of 1130 ± 137 sharks 26 . These means are based on mark-recapture estimates spanning 20 and 44 weeks sampling, respectively. Given the potential temporal fluctuations in abundance in Norfolk Bay over the study period, both mean values are included in the model to span the potential range of abundance values for Norfolk Bay in this study. Natural fluctuations in abundance occur over days or weeks, as evident by tracking data that shows individual N. cepedianus move in and out of the bay during a season 26 . All simulations were done in the statistical package R 57 . For each of the six scenarios considered, 1000 Monte Carlo simulations were performed to account for uncertainty in N. cepedianus prey composition, body mass, and routine energy expenditure parameters (Q 10 , water temperature, the allometric power equation coefficient and the allometric power equation exponent) by drawing samples from a log-normal distribution with mean and standard deviation as presented in Table 1.