Interactions between multi-species marine predator aggregations and the energy landscape

(a). The model

Hydrodynamic forces acting on a swimming shark are typically divided into lift (L) and drag (D) components, the former acting perpendicular to the direction in which the shark swims and the latter parallel to it (figure 1). Both components can be expressed using the respective hydrodynamic coefficients, C_L and C_D, with

and

in which S is a reference area (it can be any area, but we used the maximal cross section of the body as used in other shark studies [17,21,22], which is convenient when used in conjunction with the prismatic coefficient introduced below), ρ is the density of water and v is the swim speed. Both coefficients are functions of the angle of attack, which is set by the shark adjusting its body posture and the orientation of its fins relative to the body (figure 1a,b).

Generating hydrodynamic forces obviously requires moving relative to water. Movement requires power, and if this is not provided by active swimming, a shark will descend through the water column in the same way that a soaring bird will descend in still air. The (stabilized) swim speed of a shark v and its swim path angle relative to the horizon γ (see the inset to figure 1c) are solutions of the pair of equilibrium conditions:

and

which balance the hydrodynamic forces acting on the shark with gravity and thrust $\eta P/v$. Here, L and D are the lift and drag defined in equations (2.1) and (2.2), W is the submerged weight, and P and η are respectively the mechanical power provided by the shark and the efficiency of translating this power into thrust. For a given angle of attack (the angle between the body and the swimming direction), the ratio of (2.4) and (2.3) determines the path angle, and the sum of their squares furnishes the swim speed. In a free glide, when no power is supplied by the shark, they yield;

and

in which

is a combination of morphological parameters having the dimensions of speed. During active swimming, when P > 0, equations (2.3) and (2.4) (subject to equations (2.1) and (2.2)) have to be solved numerically. In both cases, the swim speed and the path angle can be converted into horizontal and vertical velocity components,

Spanning the angle of attack between 0 and 16° (a shark can set its angle of attack by adjusting its body posture and its fins), the horizontal and vertical velocity components of a free-gliding model shark, obtained as the solution to equations (2.5)–(2.8) of equations (2.3) and (2.4), are plotted as a snail diagram [23] on figure 1c. Data were taken from wind tunnel experiments with a model shark [17,21,22]. The model predicts that our shark can minimize its sink rate by adjusting the angle of attack to 11° (point E on figure 1a–d), minimize its glide angle by lowering it to 9° (point G), maximize its horizontal speed component (aka the ‘penetration speed’) by lowering it further to 1° (point P) and maximize its vertical speed component (aka the ‘terminal speed’) by diving vertically at zero angle of attack (point T).

Adding power by active swimming raises the upper part of the snail diagram curve (figure 1d). The minimal power that allows the shark to swim at constant depth can be exploited at the same swim speed where the sink rate was minimal when gliding (point EB on the blue curve in figure 1d); it nullifies the vertical speed when swimming at an angle of attack of 11° (points E and B). With more power (shown in magenta), the shark can ascend or swim faster at a constant depth (point B, figure 1d).

If a shark is swimming into a current with upwelling, the ‘snail’ curve shifts upwards by the speed of the upwelling current, and to the left by the speed of the head-on current (figure 2). The stronger the upwelling current, the less power is needed to maintain depth, and when the speed of the upwelling exceeds the minimal sink rate of the shark (marked by the point E on the black curve on figure 1d) the shark can maintain depth with no power (in our model it would be 0.15v_ref). At the same time, if the upwelling current is accompanied by a significant head-on component, which exceeds the respective horizontal speed of the shark (in our model shark it would be approximately 0.75v_ref), the shark will need to use power to maintain position against the current (even though no power is needed to maintain depth).

Next we consider a pair of morphologically similar sharks, having the same C_D versus C_L relation as in figure 1b (and hence the same normalized snail diagram for a no-current situation as in figure 1c), but differing in their reference speed; one individual having a 1.5 times higher reference speed than the other. We do this to arbitrarily compare species of Carcharhinid shark that are similarly shaped but may differ in length and buoyancy (see below). Additional morphometric differences may further vary the reference speed. In a head-on upwelling current, their snail diagrams shift up and to the left by the (reduced) velocity of the current (figure 2). Although the current is the same for both sharks, the shark with the lower reference speed will experience a larger reduced current speed than the other (compare figure 2a,b). Assisted by the upwelling current, both sharks can now ascend at minimal power (blue curves in figure 2a,b), and hence, in principle, can reduce their routine metabolic rates compared to swimming in a location with no current. The shark with the higher reference speed can maintain position (horizontal and vertical) using 50% less power than if there were no current (cyan B in figure 2a). Its excess horizontal speed can be offset by its zigzagging left-right when swimming against the current. On the other hand, the shark with the lower reference speed must add additional power to maintain its horizontal position, more than required if there were no current (magenta B in figure 2b). In other words, the same location and conditions can be energetically beneficial for one individual (the one with higher reference speed, figure 2a), but detrimental for the other (figure 2b).

The reference speed is clearly a critical component of our model. Referring to equation (2.7), it can change with the cross-sectional area of the shark S and its submerged weight W. The latter can be estimated by the product;

in which β is the sinking factor (the relative buoyancy deficit), g is the acceleration of gravity and V is the volume of the body. In turn, the volume can be expressed as the product V = k_pcSl, where l is the fork length, S is the cross-sectional area of the shark (this is why it was used as the reference in equations (2.1) and (2.2)), and k_pc is the prismatic coefficient—the ratio between the volume of the body and the volume Sl of the minimal cylinder enclosing it. It is approximately 0.64 for our model shark (see [21] for details). Consequently,

changing mostly with size (the fork length) and the sinking factor (buoyancy). Two morphologically similar sharks having the same sinking factor, but one twice as long as the other, will have a 40% difference in their reference speed.

(b). Reef sharks in a tidally flushed channel

The southern channel of Fakarava atoll, French Polynesia (16°18′ S 145°38′ W), connects to a large lagoon and is tidally flushed with current speeds estimated at approximately 0.5 m s^–1 [6]. The channel contains over 500 sharks, the majority being grey reef sharks (Carcharhinus amblyrhynchos), but other species include blacktip reef (Carcharhinus melanopterus), blacktip (Carcharhinus limbatus), silvertip (Carcharhinus albimarginatus) and whitetip reef sharks (Triaenodon obesus) [24]. Grey reef sharks show very high residency in the channel throughout the year and are present day and night during both incoming and outgoing tides [24,25]. Sharks hunt reef fishes at night, but during the day grey reef sharks select key areas where there is upwelling during incoming tides to rest [6,24]. By selecting these upwelling regions, grey reef sharks may be able to reduce their metabolic costs by up to 15% [6]. We conducted dive surveys within the channel to determine the relative locations of other shark species that make up the overall aggregation. Briefly, divers started the survey close to the ocean drop-off during the incoming tide and drifted with the current through the centre of the channel while filming with a GoPro. Sharks swim against the incoming current (i.e. opposite the direction to the divers) and are not therefore attracted or disturbed by the divers. The surveys were terminated just before entering the lagoon (full details in [24]). The channel was divided into 22 sectors from South to North. Shark count surveys corresponding to 29 drifting dives from South to North during incoming tides allowed us to estimate relative shark abundance for each species across sectors. As the major upwelling sites are located in sectors S11–S12 and S17–S18, we restricted our survey to the section between sectors S09 and S18 [6]. Relative shark abundance was assessed using the maximum number of individuals of each species within a frame of the video (MaxN). For each dive, the highest number in each sector was retained. All dives were performed during incoming tides owing to low visibility during outgoing tides. Shark sizes were estimated by divers during the surveys (data in supplementary material). Our surveys show that silvertips, which are smaller juveniles (105 cm total length (TL); min = 86, max = 123), are mostly found in the centre of the channel, close to the seafloor in a region with minimal upwelling and within the boundary layer over the bottom, but do have some overlap with grey reef sharks (140 cm TL; min = 115, max = 165) (figure 3). Dive surveys and telemetry show that grey reef sharks primarily use the upwelling region during incoming tide (figure 3, [6]). Blacktip sharks, on the other hand (202 cm TL; min = 166, max = 238), are mostly seen in a very small section of the channel towards the centre and western region of the channel. Hence, these species, which differ in length and probably buoyancy, use different resting areas during daytime incoming tides. Of course, space use patterns could be due to other interactions, such as competition. However, no foraging occurs during the day, and there are still locations where species overlap (figure 3). It would appear unlikely that space is by itself a limiting resource, so we propose that these distribution patterns are driven by differences in the energy landscape.

(a). Refuging in predators that never stop swimming

Negatively buoyant sharks that never stop swimming may reduce their metabolic costs by remaining within upwelling currents, although this will depend on the current strength [6]. Our model shows how the energy landscape, in this case defined by upwelling currents, may cause habitat separation between sharks of different length and/or buoyancy. The reference speed, which dictates energy savings or costs in an upwelling, is a function of buoyancy and shark length. Therefore, even with all other morphometrics being identical, differences in shark length can turn an upwelling current from energetically beneficial to detrimental. Upwelling may still be beneficial to all species (if the difference in reference speed is not large), but the extent of this benefit will vary. Of course, there may be species within a multi-species aggregation that are not morphologically similar and will vary in factors such as fin span, lift surface areas (e.g. pectoral fins) and body diameter, all of which influence swimming performance [17]. Furthermore, there can be ontogenetic changes with negative allometry of caudal fin area in some species [29], while buoyancy may increase as individual sharks get older [17]. These could also lead to significant differences between sharks of varying sizes and ages, even when they are of the same species. Overall, we would predict that sharks are likely to use upwelling sites with other individuals/species that are of similar length, buoyancy and morphometrics.

These differences may then lead to spatial heterogeneity of species distributions within multi-species aggregations, as individuals select the microhabitats that are most energetically profitable for them. Patterns of space use can then determine opportunities to associate with other individuals and potentially drive assortativity. Individual physiology has been linked to patterns of assortativity within fish shoals (e.g. individual aerobic scope), but here, we show how morphology and the energy landscape could also play a role, even between different species [10,18]. We show evidence for this from Fakarava Channel, where grey reef, silvertip and blacktip sharks all use different regions of the channel (with some overlap). Silvertip sharks in the channel are juveniles and therefore small, which may explain why they avoid the major upwelling zone and only remain close to the bottom (where the current is weaker). By having a lower reference speed, the major upwelling zones may not be energetically beneficial, unlike for the larger grey reef sharks, which may also be more buoyant [17]. Swimming kinematic and morphometric data from silvertips in the channel are required to test these ideas. During the outgoing tides, grey reef sharks switch their space use and swimming depth as upwelling zones now become downwelling [6,25]. Turbulence is also generated during the outgoing tide, which impacts the behaviour of the sharks (they disperse and swim in shallower water) and may even limit foraging [6,25]. The energy landscape during the outgoing tide may further reduce the associations between different species.

The energy landscape may influence patterns of associations between species but may also drive the outcome of interactions, such as competition or predation. For example, when sharks are foraging (e.g. in the Fakarava Channel at night), their foraging efficiency relative to competing species will be dependent on their swimming abilities and metabolic costs. Somewhat analogously, wind dynamics contribute to competitive outcomes between species of soaring birds dependent on their wing shape [30]. Within the channels of French Polynesia, great hammerhead sharks (Sphyrna mokarran) are known predators of grey reef sharks [31]. Owing to their greater length and large sinking factor [32], hammerheads should have higher reference speeds and may be better equipped to benefit from strong tidal currents. Current speeds vary between channels and atolls, which may partially explain why great hammerheads tend to be more abundant in high current channels [33]. More accurate measures of buoyancy are needed so that interspecific comparisons of reference speeds can be made.

(b). Pelagic predators foraging on prey patches

A great deal of theoretical work has gone into predicting patch residence times of foragers and how these relate to harvest rates [19]. Modern optimal foraging theory incorporates the energetic cost of foraging in a patch and the risk of predation to the forager, but considerably more research has gone into the effects of predation risk [19,34]. However, the energetic cost of foraging will be directly related to the energy landscape, and we identify how this might apply to predators foraging on fish schools. Pelagic predators, including tuna, billfish, sharks, marine mammals and birds, may forage on bait-fish in pelagic waters [14,16]. While upwelling will not be an issue, current speeds will vary and may still interact with predator length and/or buoyancy. The depth of prey patches will play a role, as the energy landscape of diving animals will depend on the travel distance (especially for CPF) and metabolic costs of diving, and potentially the scaling of metabolic rate with temperature [3,4,35]. Although depth may initially appear to apply only to air-breathing species, large fishes (teleosts and sharks) must also return to surface waters to access warmer waters to maintain cardiac (and digestive) function and growth rates, as well as a metabolic advantage over their prey (as they will have a higher body temperature than cold prey in deeper water) [4]. The costs to exploit prey patches at certain depths will therefore vary between species [4,35]. Therefore, the energetic cost of foraging may be species-specific, which will also alter their quitting harvest rates.

Quantitative tools for analysing animal movements, such as the first passage time (FPT) [36], can measure residence times of marine animals in patches. These have further been modified to quantify patch use in three dimensions (3D FPT or volume-restricted searching) and to detect hierarchical searching, where smaller patches are nested within larger ones [37]. These are important as multi-predator aggregations may similarly form over multiple spatial scales to match those of the prey patches on which they are foraging. Patch leaving decisions will also depend on the abundance and proximity of other patches (‘missed opportunities’ in the foraging model) [38], and these may also interact with the energy landscape in different ways (e.g. travel distances for CPFs, current strength, etc.). Extensive theoretical work on marginal value theory has been developed but should consider the interaction with the energy landscape, and how this may vary for different predators foraging on the same patches.