Diving is central to the foraging strategies of many marine mammals and seabirds. Still, the effect of dive depth on foraging cost remains elusive because energy expenditure is difficult to measure at fine temporal scales in wild animals. We used depth and acceleration data from eight lactating California sea lions (Zalophus californianus) to model body density and investigate the effect of dive depth and tissue density on rates of energy expenditure. We calculated body density in 5 s intervals from the rate of gliding descent. We modeled body density across depth in each dive, revealing high tissue densities and diving lung volumes (DLVs). DLV increased with dive depth in four individuals. We used the buoyancy calculated from dive-specific body-density models and drag calculated from swim speed to estimate metabolic power and cost of transport in 5 s intervals during descents and ascents. Deeper dives required greater mean power for round-trip vertical transit, especially in individuals with higher tissue density. These trends likely follow from increased mean swim speed and buoyant hinderance that increasingly outweighs buoyant aid in deeper dives. This suggests that deep diving is either a ‘high-cost, high-reward’ strategy or an energetically expensive option to access prey when prey in shallow waters are limited, and that poor body condition may increase the energetic costs of deep diving. These results add to our mechanistic understanding of how foraging strategy and body condition affect energy expenditure in wild breath-hold divers.

Foraging is one of the most energetically expensive behaviors for predators (Gorman et al., 1998; Goldbogen et al., 2008; Wilson et al., 2013; Williams et al., 2014). Many air-breathing marine predators display a variety of foraging strategies, often centered around differences in diving depth, begging the question of how intraspecific variation in dive depth affects energy expenditure (e.g. Costa and Gales, 2000; McHuron et al., 2018). Because energy expenditure can influence reproductive success and survival in breath-hold divers (Costa, 1993; Melin et al., 2008; Jeanniard du Dot et al., 2018), determining the energetic costs of diving to depth, and what drives variation in these costs, has been an important topic in diving mammal and seabird ecological research for decades (Lovvorn and Jones, 1991; Wilson et al., 1992; Speakman, 1997; Costa and Gales, 2000, 2003; Hansen and Ricklefs, 2004; Trassinelli, 2016; McHuron et al., 2018).

Estimating energetic cost at the temporal scale of seconds may be necessary to parse out drivers of variation in energy expenditure of breath-hold dives. Although indirect calorimetry methods offer reliable estimates of metabolism over coarser time scales, they lack some capacity to pinpoint drivers of diving cost variability in wild animals. For instance, open-flow respirometry can distinguish metabolic costs among behavior types (Feldkamp, 1987b; Culik et al., 1994; Thometz et al., 2014) but cannot usually be applied to freely foraging animals, nor can it fully clarify drivers of within-activity cost variation because it is measured at time scales of ≥3 min (Barstow et al., 1993; Fahlman et al., 2008; Halsey et al., 2011). Similarly, the doubly labeled water (DLW) technique gives accurate measurements of field metabolic rate (FMR) in freely foraging animals (Boyd et al., 1995; Speakman, 1997), but its coarse temporal resolution (e.g. days in pinnipeds) often makes identifying or disentangling drivers of FMR variation difficult or impossible (Costa and Gales, 2000, 2003; McHuron et al., 2018, 2019).

Biomechanical modeling offers a direct and theoretically accurate method to calculate the propulsive energy expenditure of wild diving animals at a temporal scale of seconds. Propulsive thrust and swimming power can be calculated from the drag opposing movement through seawater and the buoyant force acting upon the diver at a given depth (Lovvorn and Jones, 1991; Wilson et al., 1992; Hansen and Ricklefs, 2004; Sato et al., 2010; Miller et al., 2012; Trassinelli, 2016). These calculations require knowledge or estimation of morphological parameters and variables (e.g. drag coefficient, frontal surface area, body density), which have traditionally been determined using videography (Feldkamp, 1987b; Lovvorn and Jones, 1991). Fine-scale depth and movement sensors are now common in animal-borne dataloggers, enabling the estimation of these morphological parameters in wild animals from hydrodynamic gliding performance (Biuw et al., 2003; Miller et al., 2004, 2012, 2016; Aoki et al., 2011, 2017; Narazaki et al., 2018).

Dive depth is expected to influence energetic cost owing to the intersecting effects of buoyancy, drag and behavior (Miller et al., 2012; Trassinelli, 2016). Most air spaces in marine mammals and seabirds are compressible, and thus decrease in volume under increasing pressure with depth (Kooyman, 1973; Ponganis et al., 2015). This compression increases a diver's density and decreases its buoyancy. As body density deviates from neutral in the surrounding seawater, the buoyant force acts to aid or hinder vertical movement. When buoyancy aids movement sufficiently to outweigh the drag resisting movement, burst-and-glide swimming or prolonged gliding can be used to minimize overall travel costs relative to those of continuous swimming (Clark and Bemis, 1979; Lighthill, 1971; Skrovan et al., 1999; Williams et al., 2000). However, the costs saved in the direction aided by buoyancy must be repaid in the direction hindered by buoyancy (Hays et al., 2007; Miller et al., 2012; Adachi et al., 2014). Recent biomechanical models of diving pinnipeds, dolphins and penguins predict that the round-trip cost of a dive to a given depth increases as mean body density deviates from the density of the surrounding seawater (Miller et al., 2012; Trassinelli, 2016). By extension, mean round-trip swimming power and cost of transport (COT; energy to move 1 m; Schmidt-Nielsen, 1972) are predicted to be minimized in dives to twice the depth of neutral buoyancy (as round-trip buoyancy is neutral on average) and to increase in shallower or deeper dives (Trassinelli, 2016).

In the wild, dive depth (thus foraging strategy) is likely driven by the depth of targeted prey rather than cost optimization. High-cost foraging strategies are observed in a variety of diving species, indicating that potential prey reward can motivate or outweigh elevated energetic cost (Aoki et al., 2017; McHuron et al., 2016; 2018; Friedlaender et al., 2019). Additionally, deep and long-duration dives can approach the limits of an animal's oxygen stores (Ponganis et al., 2007; Meir and Ponganis, 2009; Meir et al., 2009; McDonald and Ponganis, 2013). Successful deep diving, including sufficient reserves for foraging, requires relatively fast swimming that minimizes COT. This fast swimming, alongside elevated round-trip effort associated with negative buoyancy, should increase swimming power as a result (Feldkamp, 1987b; Rosen and Trites, 2002; Miller et al., 2012; Adachi et al., 2014; Trassinelli, 2016). Because the extra costs of negative buoyancy result from the mean discrepancy between a sea lion's body density and seawater density, individuals with higher tissue density should face greater increases in mean energetic cost in deep dives (Miller et al., 2012).

Here, we investigated the effect of dive depth and tissue density on swimming power and COT in the California sea lion Zalophus californianus, using biomechanical modeling of animal-borne tag data. We estimated the body density and energy expenditure of free-ranging adult female sea lions in 5 s intervals during ascents and descents, then expanded these data to examine the effect of dive depth and tissue density on energetic cost per second (power) and per meter (COT) during round-trip vertical transit. We hypothesized that (1) round-trip swimming power and COT would increase with dive depth owing to faster swimming and increasingly negative mean buoyancy, and that (2) these increases would be greater in individuals with higher tissue density owing to their greater mean deviance of body density from seawater density.

Biomechanical modeling of body density and dive costs is relatively simple in California sea lions, making them a good model species. They often descend and ascend nearly vertically (present study) and have key morphometric and hydrodynamic coefficients reported from controlled studies (Feldkamp, 1987b). Adult female sea lions can dive to over 500 m, with foraging strategy (depth; benthic or pelagic) varying both within and among individuals (Melin et al., 2008; Kuhn and Costa, 2014; McHuron et al., 2016; 2018). California sea lions appear to dive on inhalation (McDonald and Ponganis, 2012), resulting in positive buoyancy near the surface. However, they also have a relatively low lipid mass typical of otariids (Liwanag et al., 2012), causing negative tissue buoyancy in seawater. These combined traits should produce a shift between strong positive buoyancy in shallow depths and strong negative buoyancy at deeper depths, which may result in effects of buoyancy and density on travel costs. Furthermore, sea lions swim with a foreflipper propulsion mechanism comprising a brief power stroke and subsequent glide of varying duration (Feldkamp, 1987a) typical of otariids and many seabirds (Clark and Bemis, 1979; Fish, 1994, 1996). Thus, our methods could be applied, with caution, to a variety of other diving species.

List of symbols and abbreviations

     
  • a

    acceleration (m s−2)

  •  
  • Af

    frontal surface area of the sea lion (m2)

  •  
  • AIC

    Akaike's information criterion

  •  
  • BMR

    basal metabolic rate

  •  
  • CD,f

    drag coefficient referenced to the frontal surface area

  •  
  • COT

    cost of transport (J kg−1 m−1)

  •  
  • CSL

    California sea lion

  •  
  • d

    depth

  •  
  • DLV

    diving lung volume; lung volume at start of dive

  •  
  • DLW

    doubly labeled water

  •  
  • FB

    buoyancy (N)

  •  
  • FD

    drag (N)

  •  
  • FMR

    field metabolic rate

  •  
  • g

    acceleration due to gravity (9.81 m s−2)

  •  
  • GLMM

    generalized linear mixed model

  •  
  • Mb

    body mass

  •  
  • mCSL

    mass of the sea lion (kg)

  •  
  • MSA

    minimum specific acceleration

  •  
  • Nm

    muscular efficiency (efficiency of converting chemical energy into muscular work)

  •  
  • Np

    propeller efficiency

  •  
  • Pi

    metabolic power input to produce Po (W)

  •  
  • Po

    power output; mechanical power to produce observed thrust (W)

  •  
  • PSMR

    power requirement of the standard metabolic rate (W)

  •  
  • Rc

    ratio of observed air-space compression to that expected in a perfectly compliant air space

  •  
  • RQ

    respiratory quotient

  •  
  • SMR

    standard metabolic rate

  •  
  • t

    timestamp

  •  
  • TLC

    total lung capacity

  •  
  • U

    speed (m s−1)

  •  
  • VGas,depth

    respiratory volume at a specified depth (l)

  •  
  • VTissue

    tissue volume excluding air spaces (l)

  •  
  • ε

    conversion factor between Po and Pi

  •  
  • θ

    descent angle relative to gravitational force

  •  
  • λ

    ratio of active to passive drag

  •  
  • ρCSL

    body density of the sea lion (kg m−3)

  •  
  • ρSW

    seawater density (kg m−3)

  •  
  • ρTissue

    tissue density (non-gas component) of the sea lion's body (kg m−3)

Data collection

Lactating adult female California sea lions [Zalophus californianus (Lesson 1828)] were captured with custom hoop nets at San Nicolas Island, CA, USA (33°14′12.3″N, 119°32′54.3″W), in November 2012 (n=4) and 2014 (n=4). Sea lions were weighed (±0.1 kg), and the standard length (cm) and circumference of maximum girth (cm) were recorded (Table 1).

Table 1.

Morphometrics and best-fit body-density model parameters

Morphometrics and best-fit body-density model parameters
Morphometrics and best-fit body-density model parameters

Sea lions were instrumented under isoflurane gas anesthesia (Gales and Mattlin, 1998; McDonald and Ponganis, 2013) with VHF radio transmitters and dataloggers. Instruments were mounted on a neoprene base attached to mesh netting with cable ties; this package was glued with quick-set epoxy to the pelage on the dorsal midline to approximate the location of the center of mass (e.g. McDonald and Ponganis, 2014; McHuron et al., 2016, 2018). In 2012, the dataloggers used were Daily Diary tags (Wildlife Computers, Redmond, WA, USA), recording pressure and temperature at 1 Hz and three-axis acceleration at 16 Hz. In 2014, the dataloggers used were OpenTags (Loggerhead Instruments, Sarasota, FL, USA), recording pressure and temperature at 10 Hz and acceleration, orientation (magnetometer) and rotational velocity (gyroscope) along three axes each at 50 Hz. Sea lions were also instrumented for other studies with physiological loggers in 2012 (McDonald and Ponganis, 2014) and satellite tags in 2014 (McHuron et al., 2018).

After instrumentation, sea lions were placed in a large kennel to safely recover from anesthesia (up to 60 min) and released. Following one or more trips to sea (5.2 to 16.8 days of data), sea lions were recaptured and instruments were recovered.

Data calibration and initial processing

Daily Diary data (corrected depth, temperature, three-axis acceleration) were converted with a Data Analysis Program (DAP) processor (Wildlife Computers). Raw OpenTag data were processed in MATLAB 2015b and 2016b. Depth data were calculated from pressure and temperature data at the sampling rate of the tag (10 Hz), then corrected for zero-offset with custom-written scripts. Acceleration data from both tags were calibrated along each axis to [−1 1], the range expected due to gravity (Ware et al., 2016).

Calculating body density, swimming power and COT

Thrust, power and COT were calculated in 5 s intervals following published methods (Feldkamp, 1987b; Miller et al., 2004, 2012; Sato et al., 2010; Aoki et al., 2011; Trassinelli, 2016) with slight modifications. The thrust needed for a swimming animal to achieve an observed speed can be estimated from the drag (FD) and buoyancy (FB) forces acting on the animal. Drag varies as a function of morphometrics and swim speed, and buoyancy is estimated from animal density relative to the that of the surrounding medium. In marine mammals, body density increases with depth as the volume of air spaces is compressed under hydrostatic pressure. When body density sufficiently surpasses seawater density (ρSW) below a given depth, negative buoyancy aiding descent outweighs drag opposing descent, allowing the animal to glide passively to depth. We used these periods of gliding descent, in which glide speed is not influenced by active swimming, to estimate body density of California sea lions (ρCSL) in 5 s time intervals using published equations (see below). For each dive with a qualifying glide, we described ρCSL as a function of depth with a model based on air-space compression, diving lung volume (DLV; lung volume at the start of dive), and tissue density (ρTissue). This allowed us to estimate the buoyancy of each sea lion across depth on a dive-by-dive basis. During descent or ascent (active or passive) at a given depth, the buoyancy and drag vectors acting on the sea lion together give the thrust (N) produced by the sea lion to achieve the observed speed. Power (W kg−1) is the product of thrust and swim speed, weighted by the efficiency of converting metabolic energy into foreflipper energy output. COT (J kg−1 m−1) is the metabolic energy used per meter traveled. We estimated power and COT in 5 s intervals during swimming and gliding in descents and ascents for which ρCSL was estimated, then calculated mean power and COT for these entire dives (descent and ascent phases) from 5 s interval data. Elements of this process are described in detail below.

Estimating body density from hydrodynamic gliding performance

The acceleration or deceleration that a sea lion experiences during gliding descent is the result of buoyancy and drag (FB and FD) acting upon it. Drag resists the sea lion's forward motion through seawater. It is described as a function of ρSW (kg m−3), the sea lion's frontal surface area (Af, m2) calculated from the maximum girth measurement assuming a circular cross-section (Aoki et al., 2011, 2017), the drag coefficient referenced to the frontal surface area (CD,f=0.07; Feldkamp, 1987b; Aoki et al., 2011, 2017) and the square of observed speed (U, m s−1):
formula
(1)
Feldkamp (1987b) reported CD,f values of 0.070, 0.069 and 0.046 for three juvenile sea lions in his controlled study; we elected to use 0.070 here because it agreed closely with the value of 0.069 (see ‘Drag coefficient sensitivity analysis’, below).
Buoyancy results from the difference in density between the sea lion's body (ρCSL; kg m−3, including air spaces) and that of the surrounding seawater (ρSW):
formula
(2)
where mCSL is the mass of the sea lion (kg) and g is the acceleration due to gravity. We used mCSL and Af data from the initial capture because Af was not collected at recapture. Acceleration (a) in the direction of motion during gliding descent results from the difference between buoyancy and drag, weighted by the descent angle (θ) relative to the gravitational force (Miller et al., 2004; Aoki et al., 2011):
formula
(3)
Eqns 1–3 can then be combined (Aoki et al., 2011) and rearranged to solve for ρCSL as a function of known and measured variables during gliding descent:
formula
(4)

We wrote custom MATLAB code to identify and analyze periods of gliding descent that maintained near-vertical body orientation (within 10 deg of vertical). Body orientation relative to the horizon (θ) was measured from heave-axis (parallel to swimming path) acceleration data (e.g. Sato et al., 2002; Watanabe et al., 2006; Aoki et al., 2011). Shallow-angle glides were excluded to avoid the increased influence of lift generated by the relatively large foreflippers at less-vertical swim angles (Aoki et al., 2011; Narazaki et al., 2018). Additionally, all active stroking was excluded from analysis, along with a 5 s buffer after the last stroke. This 5 s buffer was determined from visual inspection of strokes, U and depth data. These strokes and other sharp accelerations that could influence glide speed were identified from peaks in the acceleration metric minimum specific acceleration (MSA; calculated from three-axis acceleration following Simon et al., 2012) during descent, similar to published methods (Miller et al., 2016; Aoki et al., 2017). MSA peaks were considered strokes if they exceeded a conservative threshold of 0.13g estimated from visual inspection. Raw data (depth, time, θ) from each gliding descent were extracted in 5 s intervals (Miller et al., 2004, 2016; Aoki et al., 2011, 2017).

We used the raw gliding descent data (Fig. 1A) to calculate additional variables (U, a and ρSW) needed to estimate ρCSL in each 5 s interval with Eqn 4. U was calculated as the change in depth over the time interval, weighted by descent angle (e.g. Miller et al., 2004). Because each value of U was considered to represent speed at the mean time point of each 5 s interval, the acceleration value (a) for each 5 s interval was calculated as the change in U divided by the change in corresponding time, as follows. When 5 s data intervals occurred both before and after the current 5 s interval, differentials in both U and timestamps (t) corresponding to U were used to estimate acceleration at the beginning [aprevious=(UcurrentUprevious)/(tcurrenttprevious)] and end [anext=(UnextUcurrent)/(tnexttcurrent)] of the current 5 s interval, and the mean a of the current 5 s interval was taken as the average value of those estimated accelerations [a=(aprevious+anext)/2]. When a 5 s interval occurred only before or after the current interval (but not both), a was calculated from the differences in U and time between the current and neighboring intervals (e.g. in the first interval of a glide, a=anext as shown above). ρSW was calculated at the sampling rate of the pressure and temperature sensor of each datalogger using the International Equation of State of Seawater (UNESCO, 1981), assuming a salinity of 34.84‰ (Vogel, 1994; Aoki et al., 2011, 2017), and was averaged in 5 s intervals. ρCSL was calculated in each identified glide interval using Eqn 4 (Fig. 1B).

Fig. 1.

Dive-by-dive estimation of body density across depth in one sea lion (C22). (A) Glide speed data (5 s intervals) plotted as a line or curve per distinct glide. (B) Body densities (ρCSL) in those same 5 s intervals estimated with Eqn 4. (C) Individual-dive body-density models (Eqn 5) used in buoyancy, thrust, power and cost-of-transport (COT) calculations. The mean ratio of observed air-space compression to that expected in a perfectly compliant air space (Rc) and tissue density (ρTissue) from preliminary model outputs were held static, and diving lung volume (DLV) was estimated for each dive. (D) DLV increased with dive depth in three deep divers (C22, S2, S7) and one shallow benthic diver (C14).

Fig. 1.

Dive-by-dive estimation of body density across depth in one sea lion (C22). (A) Glide speed data (5 s intervals) plotted as a line or curve per distinct glide. (B) Body densities (ρCSL) in those same 5 s intervals estimated with Eqn 4. (C) Individual-dive body-density models (Eqn 5) used in buoyancy, thrust, power and cost-of-transport (COT) calculations. The mean ratio of observed air-space compression to that expected in a perfectly compliant air space (Rc) and tissue density (ρTissue) from preliminary model outputs were held static, and diving lung volume (DLV) was estimated for each dive. (D) DLV increased with dive depth in three deep divers (C22, S2, S7) and one shallow benthic diver (C14).

ρCSL was modeled as a function of depth for each dive with at least three 5 s glide intervals, a step that was necessary to estimate buoyancy during active swimming (when ρCSL could not be directly calculated). For each dive, a nonlinear model for ρCSL based on gas compression owing to hydrostatic pressure was fitted to calculated ρCSL data as a function of depth (d):
formula
(5)
where
formula
(6)
formula
(7)
Here, VTissue (l) is the tissue volume excluding air spaces, VGas,depth (l) is the respiratory (or air space) volume at a given depth, DLV (l) is the diving lung volume or respiratory volume at the surface preceding a dive, ρTissue (kg m−3) is the density of tissue excluding air spaces, and Rc is a constant between 0 and 1, introduced here to describe the ratio of observed air-space compression relative to that expected from Boyle's law on a perfectly compliant air space.

In the first model run, three unknown parameters were estimated for each dive: ρTissue, DLV and Rc. The best-fit combination of these parameters for each dive was detected automatically using the fit function in the curve fitting toolbox in MATLAB 2021b. Prior to fitting these models, the upper and lower constraints of each parameter were set at realistic levels, as follows. Following visual inspection of raw 5 s ρCSL data, the range of ρTissue was limited between 1030 and 1090 kg m−3. Based on mass-specific total lung capacity (TLC) estimates (Kooyman, 1973; Fahlman et al., 2011), DLV was limited between 0 and 10 l. The range of Rc was set between 0 (i.e. a straight line) and 1 (compression expected from Boyle's law on a perfectly compliant ideal gas space). Each sea lion's mean Rc and ρTissue values (Tables 1 and 2) were reported following this first model run.

Table 2.

Effect of CD,f on model parameter estimates

Effect of CD,f on model parameter estimates
Effect of CD,f on model parameter estimates

Because Rc and ρTissue did not show relationships with time or each other in any sea lion, we re-ran the ρCSL models (Eqn 5) with static values of Rc and ρTissue set equal to the mean values for each sea lion. This allowed us to more accurately estimate DLV, which is expected to change on a dive-by-dive basis. Mean DLV values from this second model run are reported in Tables 1 and 2. For each sea lion, this second model run was used to estimate ρCSL as a function of depth on a dive-specific basis, and to extrapolate body density at depths shallower and deeper than those observed during each glide (Fig. 1C). We did not have sufficient data to estimate body density from ascents owing to a lack of sufficient glides, as glide speed was almost always influenced by residual momentum following active stroking ascent. We thus did not attempt to model possible gas absorption during a dive, which could reduce lung volume and therefore increase body density at the end of a dive (Fahlman et al., 2020).

Calculating power and COT during ascent and descent

The relationships established between depth and ρCSL in each modeled dive permitted the calculation of FB (Eqn 2) in these dives, allowing calculation of the thrust, power and COT used in active swimming during these dives. U, depth, ρCSL and ρSW were calculated or measured for each 5 s interval (using methods described in the previous section) in both ascents and descents of each dive with a body-density model, and these were used to calculate FB, FD, thrust, power and COT in each 5 s interval. As with the ρCSL analysis, 5 s intervals were only included in the analysis if body orientation remained within 10 deg of vertical, to minimize confounding effects of foreflipper lift generation (Narazaki et al., 2018).

The swimming thrust (Ft, N) necessary to achieve an observed ascent or descent speed is given by the sum of the buoyancy (FB) and drag (FD) vectors acting on the sea lion:
formula
(8)
Here, λ is the ratio of active to passive drag and is assumed to be 1 (Aoki et al., 2011; Miller et al., 2012). The power output (Po, in W) needed to produce that thrust is given as the product of the observed thrust and speed:
formula
(9)
Po is related to metabolic power input (Pi) by a dimensionless conversion factor (ε), which represents the efficiency in converting Pi into Po (Watanabe et al., 2011). This conversion factor is given as the product of propeller efficiency (Np) and the efficiency of converting chemical energy into muscular work (Nm; muscular efficiency), where Nm is approximately 0.25 at optimal contraction speed (Cavagna et al., 1964; Webb, 1975; Miller et al., 2012):
formula
(10)
where
formula
(11)
Feldkamp (1987b) found that Np in California sea lions increased with U and plateaued above 2.5 m s−1. We multiplied these published Np data (fig. 8 in Feldkamp, 1987b) by an Nm value of 0.25 to find ε, then fitted a third-order polynomial to the resulting relationship (as in Feldkamp, 1987b) to obtain ε as a function of U. In each 5 s interval, ε was determined using this relationship and the observed U. To standardize among individuals, we used mass-specific power (Pi/mCSL in W kg−1). COT was calculated in each 5 s interval as the total power divided by U (m s−1):
formula
(12)
where
formula
(13)

Here, the total power input is the sum of Pi and the power requirement of a constant basal or standard metabolic rate (PSMR). To calculate PSMR, we used a standard metabolic rate (SMR) of 10.23 ml O2 kg−1 min−1 found for female sea lions in conditions defined for basal metabolic rate (BMR) (Hurley and Costa, 2001). We assumed a calorific equivalent of 19.84 J ml−1 O2 at a respiratory quotient (RQ) value calculated as 0.75 in swimming sea lions that was unaffected by swim speed (Feldkamp, 1987b). This constant RQ ignores the possibility of sea lions entering anaerobic metabolism during their longest and deepest dives (which would alter the RQ and SMRs), as we could not measure the onset of anaerobic metabolism. The calorific cost of thermoregulation was not included as it is considered negligible during foraging behaviors due to thermal substitution (Hind and Gurney, 1997; Lovvorn, 2007).

Calculating mean dive power and COT during vertical transit

Fine-scale (5 s interval) estimates of energy expenditure were expanded to evaluate energetic costs and benefits of dive-depth strategy. This analysis focused on the combined travel costs of descent and ascent, giving estimates of the round-trip energy per second and meter used by sea lions in observed dives to a range of depths. Bottom-time dive costs were not included in this analysis because swimming costs were not estimated at shallow swim angles (see previous section). Because bottom time was excluded, the data presented here estimate round-trip vertical-travel costs. For each dive in which body density was modeled, mean Pi (‘power’ from here on) and COT were calculated by averaging data from all 5 s intervals of that dive. Only dives with complete data were included; those missing data from any 5 s interval (e.g. owing to horizontal excursions; criteria presented earlier in the Materials and Methods) were excluded.

Statistical analyses

The effects of depth and dive phase (descent or ascent) on fine-scale (5 s interval) body density, thrust, power and COT were not tested statistically because all explanatory variables were used in the calculation procedure. These descriptive results were instead evaluated qualitatively in the context of published data. We ran linear regressions to test the hypothesized effect of dive depth on DLV in individuals (e.g. McDonald and Ponganis, 2012).

To investigate the effect of dive depth on mean estimated costs of vertical travel (power and COT), we ran generalized linear mixed models (GLMMs) using the fitglme function in the Statistics and Machine Learning Toolbox in MATLAB 2021b. Mean dive power and COT were each the response variable for three GLMMs: (1) dive depth as a fixed effect and sea lion ID as a random intercept, (2) dive depth as a fixed effect and sea lion ID as both random intercept and slope, and (3) no fixed effect but including sea lion ID as a random intercept. We used Akaike's information criterion (AIC) values to compare the three GLMMs for each response variable. Adjusted R2 estimated by GLMMs were used to assess the amount of variation explained by each model. Each GLMM model was validated by examining normalized residuals for normality, homoscedasticity and lack of temporal autocorrelation.

We ran linear regressions to test the effect of tissue density (ρTissue) on mean power and COT among sea lions, in three separate dive-depth ranges (0–100, 100–200 and >200 m). We assessed relationships among mean speed, mean power and dive depth, and also the relationship of buoyancy and speed at 5 s intervals, in a descriptive qualitative manner in the context of GLMM results, because these variables were used to calculate each other.

Drag coefficient sensitivity analysis

The drag coefficient (CD,f) is the only variable in the body density equation (Eqn 4) that was neither measured nor estimated from tag data. In his controlled study, Feldkamp (1987b) reported a different CD,f value for each of three juvenile sea lions: 0.070, 0.069 and 0.046. We selected a CD,f of 0.070 in our study because this value closely matched the CD,f of 0.069 measured in a second sea lion. However, because the lowest CD,f in that study (0.046) describes the largest of the three individuals (37.5 kg versus 22.1 and 23.3 kg), we considered that CD,f may have a relationship with individually variable factors such as mass, length or fineness ratio. Hence, we performed a sensitivity analysis on the effect of CD,f on body-density models (including the parameters ρTissue, Rc and DLV) and the effect of dive depth on mean round-trip power and COT. This sensitivity analysis was performed by re-running dive-by-dive model estimations with CD,f set to 0.046 (the low estimate in Feldkamp, 1987b), 0.056 (20% lower than 0.070) and 0.084 (20% higher than 0.070). We then re-estimated round-trip power and COT for all sea lions using a CD,f of 0.046 (the most deviant from 0.070) and used GLMMs to investigate the effect of dive depth on mean round-trip power and COT.

Body density estimates across a range of depths

As predicted, ρCSL increased with depth in agreement with air-space compression for all sea lions (e.g. Fig. 1B). In most sea lions, passive gliding was observed beginning at or below depths where ρCSL exceeded ρSW, consistent with expected behavioral minimization of swimming cost. Depth ranges of ρCSL observations varied among sea lions, reflecting diving strategy (depths accessed).

Average ρTissue was estimated to be 1058.4±1.9 kg m−3, with individual estimates ranging from 1047.5±1.2 to 1067.4±0.3 kg m−3 (Table 1). DLV at the onset of dives averaged 5.4±0.5 l (Tables 1 and 2; range 3.1±0.2 to 7.8±0.1 l). DLV increased with dive depth in four sea lions (Fig. 1D; C22: F1,79=44.4, R2=0.36, P<0.0001; S2: F1,73=128, R2=0.63, P<0.0001; S7: F1,124=49.1, R2=0.28, P<0.0001; C14: F1,23=28, R2=0.53, P<0.0001). Rc averaged 0.40±0.02 (Table 1; range 0.34±0.05 to 0.48±0.02).

Fine-scale energy use during descent and ascent

As expected, all sea lions adjusted power and COT during descent and ascent to account for changes in buoyancy across their range of depth (Figs 2 and 3). Sea lions began descent using elevated power and COT to counter positive buoyancy near the surface, and gradually reduced this effort with depth as the effect of buoyancy shifted from hinderance to aid (Figs 2 and 3). Sea lions ascended from depth with elevated power and COT to counter negative buoyancy, and rapidly reduced this effort near the surface as their buoyancy shifted from negative to positive (Figs 2 and 3). Qualitatively, individuals with higher tissue density used more power throughout ascent (Fig. 3).

Fig. 2.

Example 5 s interval data showing clear and conserved patterns across dives. Data are from three consecutive dives performed by sea lion C22. Drag always opposes the direction of the sea lion's motion. Buoyancy is plotted such that negative values show negative buoyancy. Pi refers to mass-specific power.

Fig. 2.

Example 5 s interval data showing clear and conserved patterns across dives. Data are from three consecutive dives performed by sea lion C22. Drag always opposes the direction of the sea lion's motion. Buoyancy is plotted such that negative values show negative buoyancy. Pi refers to mass-specific power.

Fig. 3.

Patterns of mean power use across depth. A representative dive profile to >300 m (center, black line) is included for reference. Mean±s.e.m. power trends of 5 s interval data from each California sea lion are visualized with a LOESS smoother. Colors indicate mean tissue density (Table 1) relative to that of other sea lions (purple, most dense; yellow, least dense).

Fig. 3.

Patterns of mean power use across depth. A representative dive profile to >300 m (center, black line) is included for reference. Mean±s.e.m. power trends of 5 s interval data from each California sea lion are visualized with a LOESS smoother. Colors indicate mean tissue density (Table 1) relative to that of other sea lions (purple, most dense; yellow, least dense).

The effect of dive depth on mean round-trip costs

The mean power of round-trip vertical travel increased with dive depth (Table 3, Fig. 4A). The best model included dive depth as a fixed effect and explained 55% of the variance in power data (Table 3). Mean power versus depth trends varied among individuals, but positive relationships were found in all sea lions that had usable dives to a wide range of depths (Fig. 4B, Table 4). This effect could be substantial: for example, the deepest dives of sea lion C22 used twice as much energy per second compared with the energy used for her shallowest dives. Furthermore, mean power use in both medium-depth (100–200 m) and deep-depth (>200 m) dives increased as a function of an individual's tissue density (Fig. 4C, Table 5). Tissue density did not affect mean power use in <100 m dives (Fig. 4C, Table 5).

Fig. 4.

Dive depth and body density affect mean power but not mean COT. Colors indicate mean tissue density of individuals from Table 1 (purple, most dense; yellow, least dense). (A) Mean power (Pi) during vertical transit increased with dive depth when full-dive data from all sea lions were considered together (Table 3), indicating that sea lions on average used more energy per second to travel vertically in deeper dives. (B) In four of the eight sea lions, mean power significantly increased with dive depth (indicated with *; statistics in Table 4). The other four sea lions had more limited ranges of dive depth observations. (C) Individuals' mean power costs in medium (100–200 m) and deep (>200 m) dives, but not in shallow (<100 m) dives, increased with their tissue density (ρTissue) (statistics in Table 5). This indicates that high tissue density owing to lower blubber content (poor body condition) may exacerbate increased power costs of deep diving. (D) Mean COT was not affected by dive depth (Table 3). (E) COT only varied with dive depth in one individual (F). Individuals' mean COT did not vary with their tissue density in any range of dive depths.

Fig. 4.

Dive depth and body density affect mean power but not mean COT. Colors indicate mean tissue density of individuals from Table 1 (purple, most dense; yellow, least dense). (A) Mean power (Pi) during vertical transit increased with dive depth when full-dive data from all sea lions were considered together (Table 3), indicating that sea lions on average used more energy per second to travel vertically in deeper dives. (B) In four of the eight sea lions, mean power significantly increased with dive depth (indicated with *; statistics in Table 4). The other four sea lions had more limited ranges of dive depth observations. (C) Individuals' mean power costs in medium (100–200 m) and deep (>200 m) dives, but not in shallow (<100 m) dives, increased with their tissue density (ρTissue) (statistics in Table 5). This indicates that high tissue density owing to lower blubber content (poor body condition) may exacerbate increased power costs of deep diving. (D) Mean COT was not affected by dive depth (Table 3). (E) COT only varied with dive depth in one individual (F). Individuals' mean COT did not vary with their tissue density in any range of dive depths.

Table 3.

Mixed-effects models examining the effect of dive depth on mean power (Pi) and COT

Mixed-effects models examining the effect of dive depth on mean power (Pi) and COT
Mixed-effects models examining the effect of dive depth on mean power (Pi) and COT
Table 4.

Regressions of mean power and COT against dive depth

Regressions of mean power and COT against dive depth
Regressions of mean power and COT against dive depth
Table 5.

Regressions of mean power and COT against tissue density (ρTissue)

Regressions of mean power and COT against tissue density (ρTissue)
Regressions of mean power and COT against tissue density (ρTissue)

Dive depth did not influence mean round-trip COT during vertical travel, as dive depth included as a fixed effect did not significantly improve the GLMM (Fig. 4D, Table 3; likelihood ratio test: χ23=7.70, P=0.053). Mean COT decreased with dive depth in one sea lion (C14), for whom only six dives were usable (Fig. 4E, Table 4). Mean COT did not vary with individuals' tissue density at any depth range (Fig. 4F, Table 5).

Experimentally altering CD,f influenced body-density model parameters and slightly influenced the magnitude of power and COT estimates, but did not alter conclusions drawn from results presented above. Lower CD,f values led to lower ρTissue and higher Rc estimates in all individuals, whereas DLV estimates changed minimally (Table 2). A CD,f of 0.046 instead of 0.070 slightly reduced the magnitude of calculated power and COT (Fig. 5), but did not alter the effect of dive depth on mean round trip power or COT (Table 3). Similarly, the significance of individual regressions and the effect of tissue density on power use in dives to >100 m were unaffected by changing CD,f from 0.070 to 0.046, with only one exception (Tables 4 and 5).

Fig. 5.

Effects of the drag coefficient (CD,f) on power and COT calculations. Data from C22 are shown. A CD,f of 0.046 slightly reduced the value of each data point relative to a CD,f of 0.070, but did not change the overall trend, in both descent and ascent phases of (A) 5 s interval power and (B) 5 s interval COT. (C) Mean round-trip power and COT was reduced, but trends were not affected, with a CD,f of 0.046 relative to 0.070.

Fig. 5.

Effects of the drag coefficient (CD,f) on power and COT calculations. Data from C22 are shown. A CD,f of 0.046 slightly reduced the value of each data point relative to a CD,f of 0.070, but did not change the overall trend, in both descent and ascent phases of (A) 5 s interval power and (B) 5 s interval COT. (C) Mean round-trip power and COT was reduced, but trends were not affected, with a CD,f of 0.046 relative to 0.070.

We quantified free-ranging swimming effort of adult female California sea lions during descents and ascents at 5 s intervals. From these data, we show that vertical travel used more energy per second as dive depth increased, and that dives to medium or deep depths were more costly for individuals with higher tissue density. These results suggest that deep diving is an expensive foraging strategy for a given time underwater in California sea lions, and especially so for individuals in poor body condition. Because these results were likely driven by high tissue density, we expect that similar results will be found in other high-density marine mammals that perform deep dives.

Modeling body density across depth

The body density estimates and models reported here (Fig. 1, Tables 1 and 2), which form the basis for power and COT calculations, are corroborated by isotope dilution and allometric equations. Because four of the sea lions (C22, C20, C14, C16) in this analysis were also injected with DLW for a separate study (McHuron et al., 2018), tissue density (ρTissue) could be calculated from isotope dilution data for comparison (Nagy, 1980; Speakman, 1997). These tissue densities were calculated with total body lipid and total body protein derived from available total body water data (Arnould et al., 1996; Aoki et al., 2011; McHuron et al., 2018), and a total body ash content of 2.8% (Reilly and Fedak, 1990). ρTissue estimated by our model was only 0.22±0.36% (range −0.75 to 1.2%) different than densities calculated from this isotope dilution method, the same order of accuracy as expected from isotope dilution alone (Lukaski, 1987; Aoki et al., 2011). Furthermore, the estimated mean DLV for each sea lion averaged 76.9±5.2% (range 70.1 to 98.1%; except C20, 44%) of the TLC estimated from one allometric equation based on marine mammals (TLC=0.1×Mb0.96, where Mb is body mass; Kooyman, 1989), and 68.0±4.6% of TLC estimated from another (TLC=0.135×Mb0.92; Kooyman, 1973, Fahlman et al., 2011). Hence, the classic assumption of otariid DLV as 50% of TLC (Kooyman and Sinnett, 1982) may underestimate DLV in the wild, and thus the respiratory O2 store and calculated aerobic dive limit of California sea lions may be greater than previously estimated (Feldkamp et al., 1989; Ponganis et al., 1997; Weise and Costa, 2007). Our DLV means may slightly overestimate true DLV means for each sea lion because our analysis could not include many of the shallowest dives owing to lack of gliding; however, even when we estimated each sea lion's actual mean DLV by taking the regression line value (as in Fig. 1D) at the overall mean dive depths listed in Table 6, DLV averaged 71.0±7.9% of TLC estimated from Kooyman (1989), or 62.8±7.0% of TLC estimated from Kooyman (1973) and Fahlman et al. (2011), still substantially greater than the classic assumption of 50%.

Table 6.

Estimated contributions of diving power to total at-sea energy expenditure

Estimated contributions of diving power to total at-sea energy expenditure
Estimated contributions of diving power to total at-sea energy expenditure

Despite model accuracy, factors driving density across depth are more complex than assumed here and in other models (e.g. Aoki et al., 2011; Miller et al., 2016; Trassinelli, 2016). Five-second interval body density data (e.g. Fig. 1B) increased with depth at a rate substantially slower than that predicted by Boyle's law alone (Rc=0.4; Tables 1 and 2). Although this likely reflects gliding behavior and CD,f choice (see ‘Factors influencing Rc’, below), imperfect tissue compliance may also oppose air-space compression under hydrostatic pressure. The respiratory tract tissues of California sea lions and other marine mammals vary in compliance and compressibility, as a function of both individual and air volume in the lung (Scholander, 1940; Kooyman, 1973; Fitz-Clarke, 2007; Fahlman et al., 2011, 2014, 2015). Hence, future work could theoretically improve density models by mathematically estimating the non-linear effect of hydrostatic pressure on air-space compliance. Additionally, active exhaling during a dive or increasing drag with the foreflippers can cause calculated body density to deviate from model predictions (Sato et al., 2002, 2011; Hooker et al., 2005, 2021). Gas absorption may also occur during a dive (Fahlman et al., 2020), which would lead to decreased positive buoyancy at shallower depths during ascent. Though we could not model or estimate this absorption, it would effectively increase the energy needed to ascend, especially in deeper dives with more gas absorption. Despite this complexity, our model fit the dive-by-dive density data well (e.g. Fig. 1) and produced estimates of body density and DLV that agree with other estimates and published work (see above).

High tissue density and DLV

Tissue density was substantially greater than that of seawater (Table 1), producing strong negative buoyancy at depth (Fig. 2). Buoyancy while diving is in large part a function of body condition, and particularly lipid stores (Beck et al., 2000; Biuw et al., 2003; Trassinelli, 2016). We estimated tissue densities (using CD,f=0.070) that exceed those reported for adult cetaceans (Miller et al., 2004, 2016; Aoki et al., 2017; Narazaki et al., 2018) and phocids (Aoki et al., 2011; Sato et al., 2013), indicating lower proportional lipid content in California sea lions. Tissue density estimates using CD,f=0.046 were also denser than those species on average, but individual estimates overlapped with long-finned pilot whales (Aoki et al., 2017) and northern elephant seals (Aoki et al., 2011).

DLV affects body density predominantly at shallow depths, influencing the depth of neutral buoyancy and patterns of energy use across depth, despite its relatively minor impact on overall work compared with the effect of tissue density (Trassinelli, 2016). California sea lions dive on inhalation in a manner similar to other otariids (Kooyman, 1973; Hooker et al., 2005). We found that estimated DLV increased with dive depth in four sea lions (Fig. 1D), supporting past work showing that sea lions adjust DLV to planned dive depth (McDonald and Ponganis, 2012) to maximize respiratory oxygen stores.

Buoyancy and tissue density drive fine-scale costs

As expected, power and COT trends across depth reflect buoyancy changes resulting from air-space compression or re-expansion (Figs 2 and 3). Hence, California sea lions adjust their swimming effort according to the aid or hinderance they experience from buoyancy, as documented in other diving mammals and seabirds (e.g. Webb et al., 1998; Lovvorn et al., 1999; Skrovan et al., 1999; Williams et al., 2000; Sato et al., 2002, 2011; Watanuki et al., 2003, 2006; Hooker et al., 2005; Watanabe et al., 2006; Martín López et al., 2015; Narazaki et al., 2018). The clarity of this trend in all sea lions in this study indicates the ubiquity of cost-saving transit strategies (gliding and stroke-and-glide swimming; e.g. Williams et al., 2000).

Tissue density appears to influence power use during ascent. At a given depth below approximately 50 m during ascent, mean mass-specific power varied among individuals roughly according to tissue density (Fig. 3), likely reflecting buoyant hinderance. Descent patterns did not mirror these ascent trends because all sea lions predominantly glided passively below 50 to 100 m, illustrating how denser individuals in our study did not reap sufficient energetic benefit from passive gliding to outweigh their extra ascent costs (Fig. 3).

Cost per second increases with dive depth

Adult female California sea lions used greater mean round-trip power in deeper dives, but maintained remarkably consistent mean COT across dive depth (Fig. 4). These conclusions did not change when CD,f was changed from 0.070 to 0.046, further supporting these claims (Fig. 5). For the two sea lions with the widest observed dive-depth ranges (C22 and S2), 300 m dives were more than twice as costly per second as 50 m dives (Fig. 4B). The four sea lions without significant increases of power with dive depth all had a far more limited range of maximum depth observations (ranges of 19.4 to 71.5 m) compared with those that did (ranges of 174.4 m to 311.5 m), so it is unclear to what extent this effect of dive depth truly varies among individuals. Similarly, the one sea lion (C20) with a significant negative trend of COT across dive depth had only six full-dive observations. Hence, a deep-diving strategy is expensive for a given time underwater, but not for a given vertical distance travelled.

The trend of power and the consistency of COT across dive depth each have important implications for our understanding of foraging strategy and energetics, because both time and distance are important factors in the temporally limited foraging trips of income breeders (Costa, 1991). In this context, diving power is important because sea lions should maximize net energetic gain during their limited time underwater. COT is important too, as the vertical distance needed to find prey can be substantial depending on prey availability (McHuron et al., 2016). We show that a deep-diving strategy is a more costly use of time underwater, and those extra costs must be offset by either increased energetic input from prey or reduced costs elsewhere, particularly in travel (McHuron et al., 2018), to maintain net energetic balance.

These trends of power and COT across dive depth likely followed from swim speed. Mean swim speed increased with dive depth (Fig. 6A). Faster swimming increases thrust and Po but improves the conversion efficiency of power (Pi) to Po (Eqns 8–10; Feldkamp, 1987b). In this study, mean round-trip power qualitatively increased with mean swim speed in all individuals (Fig. 6B). A mean swim speed around 2 m s−1 in deeper dives likely serves to minimize COT (Feldkamp, 1987b; Gallon et al., 2007), maximizing available O2. The minimum possible COT should increase in deeper dives as mean body density deviates from mean seawater density (Miller et al., 2012; Trassinelli, 2016), but wild marine mammals are not expected to behave purely in a manner that minimizes COT (Gallon et al., 2007), particularly in shallow dives where oxygen stores are generally not limiting (McDonald and Ponganis, 2013). We did not find the expected increase of mean COT with dive depth, seemingly because sea lions swam slower in shallow dives than expected for optimal COT (Feldkamp, 1987b; Trassinelli, 2016; but see Miller et al., 2012). In deeper dives, sea lions swam at faster speeds of near-optimal COT (Fig. 6A) (Feldkamp, 1987b), which is expected because oxygen management is more crucial (McDonald and Ponganis, 2013). In these deep dives, the byproduct of increased mean speed is increased power (Fig. 6B).

Fig. 6.

Relationships of swim speed with dive depth, power, and buoyancy. Colors indicate mean tissue density of individuals from Table 1 (purple, most dense; yellow, least dense). (A) Mean dive swim speed increased with dive depth. (B) Mean dive power increased with mean dive speed (individual trendlines shown to help visualize this effect). (C) 5 s interval data show variable but increasing swim speeds as hinderance due to buoyancy increases, and also slight increases in swim speed as aid from buoyancy increases (i.e. passive gliding acceleration during descent). Trends are visualized with a smoothing spline (fit function in curve fitting toolbox, with smoothing parameter=0.01, MATLAB 2021b).

Fig. 6.

Relationships of swim speed with dive depth, power, and buoyancy. Colors indicate mean tissue density of individuals from Table 1 (purple, most dense; yellow, least dense). (A) Mean dive swim speed increased with dive depth. (B) Mean dive power increased with mean dive speed (individual trendlines shown to help visualize this effect). (C) 5 s interval data show variable but increasing swim speeds as hinderance due to buoyancy increases, and also slight increases in swim speed as aid from buoyancy increases (i.e. passive gliding acceleration during descent). Trends are visualized with a smoothing spline (fit function in curve fitting toolbox, with smoothing parameter=0.01, MATLAB 2021b).

Buoyancy also contributes to the trends of mean COT and power across dive depth. Mean COT and mean swim speed of a dive are expected to increase as a diver's mean dive body density deviates from the surrounding seawater density (Sato et al., 2010; Miller et al., 2012; Adachi et al., 2014), such that a diver's minimum possible COT and cost-minimizing swim speed should be lowest in dives to approximately twice the depth of neutral buoyancy (Trassinelli, 2016). We found evidence that swim speed and power, but not COT (due to swim speed; see previous paragraph), increased beyond twice the depth of neutral buoyancy (neutral at approximately 20–30 m; Figs 13).

At fine temporal scales, swim speed and buoyancy may be related. Most sea lions swam slowest during minor buoyant hinderance, swimming faster with increasing buoyant hinderance (agreeing with Aoki et al., 2017) and buoyant aid (Fig. 6C). Variation was high within and among individuals. Some sea lions appeared to respond to strong buoyant hinderance by sharply increasing swim speed (by increasing the rate or force of strokes; e.g. Martín López et al., 2015; Tift et al., 2017). Increased swim speed as buoyancy hinders movement agrees with the Actuator Disc model (Weis-Fogh, 1972; Ellington et al., 1984; Miller et al., 2012) and biomechanical modeling of diving dolphins and penguins by Trassinelli (2016), which both predict that the speed of minimum COT increases with the deviation of body density from neutral.

Denser sea lions spend more power to dive deep

Denser sea lions used more mass-specific power in dives below 100 m (Tables 4 and 5, Fig. 4C). The strength of this conclusion is limited somewhat by our small sample sizes in each dive-depth range (0–100, 100–200 and >200 m), but regressions were strong, and these results agree with the logical and theoretical effects of buoyancy. Because the buoyant force acting on a sea lion of a given mass increases as the sea lion's density increasingly differs from that of the surrounding water (Eqn 2), the imbalance between buoyant aid and buoyant hinderance in a dive below twice the depth of neutral buoyancy is exacerbated in denser sea lions. Hence, the minimum power and COT required to dive to and ascend from that depth should be greater for a denser sea lion, aligning with a similar prediction by Miller et al. (2012).

COT did not significantly vary with tissue density in any depth category (Tables 4 and 5, Fig. 4F), nor when dives to all depths were considered (linear regression: F1,6=1.8, R2=0.23, P=0.228). It is possible that this predicted relationship between mean COT and tissue density exists, similar to that inferred by Adachi et al. (2014), and that we did not detect it owing to small sample sizes and swimming behavior (see the section above).

Factors influencing Rc

Rc describes the curvature of density data across depth relative to that expected if gas compression follows Boyle's law exactly, assuming all other values used in Eqn 4 are accurate. Although Rc is not expected to be exactly 1 owing to some degree of imperfect compliance (see ‘Modeling body density across depth’, above), an average value of 0.4 is surprisingly low. This describes weaker curvature of density data than expected, meaning acceleration during gliding descent is less than expected. This low Rc estimate may indicate extra drag from extended flippers to facilitate rotation around the gliding axis. Such a behavior could improve situational awareness at minimal added cost.

Additionally, CD,f substantially affected Rc model estimates in our sensitivity analysis. A CD,f of 0.046, that of the largest 35 kg individual in Feldkamp (1987b), increased Rc estimates to near 0.7 in most sea lions without affecting our conclusions (Fig. 5). If CD,f varies with mass, which is unknown, it is possible that CD,f is less than 0.046 in many adults, with correspondingly higher Rc values.

Dive depth and foraging strategy

Deep diving appears to be a high-cost energetic strategy for a given time underwater (Fig. 4A,B), and particularly for denser sea lions (Fig. 4C), but several factors contribute to the overall energy expenditure of a sea lion's foraging trip. Lactating females are central-place foragers (Costa, 1991), so foraging trips are limited in duration and distance. Alongside diving power, horizontal travel may largely drive variation in the energy required to access prey. For the four sea lions in this study that have concurrent published FMR data (McHuron et al., 2018), diving power accounted for 8.7±1.6% (range 5.6 to 14.0%) of the overall at-sea energy expended (Table 6). Unsurprisingly, this variation qualitatively mirrors the proportion of time at sea spent diving (Table 6). Estimated BMR (3.38 W kg−1; Eqn 12) accounted for another 68.8±3.7% (range 61.1 to 77.2%; Table 6) of total at-sea cost, leaving 31.2±4.3% (range 22.8 to 38.9%; Table 6) of the total cost unexplained (e.g. thermoregulation, digestion, travel). Excluding estimated BMR, diving power comprised a substantial proportion (22.4±5.5%; range 12.7 to 38.1%) of at-sea energy expended. Most of the variation in these estimates could be attributed to one sea lion, C14. Relative to the others, she spent more time diving and therefore spent more of her total energy expenditure on diving power (Table 6), but traveled far less overall (122 km compared with 343–503 km), performed almost exclusively shallow benthic dives instead of the mixed-depth strategy used by the others (McHuron et al., 2018), and remained within 11 km of San Nicolas Island (compared with 83–94 km), yielding a medium overall FMR (Table 6).

Given the elevated energetic cost per unit time, is deep diving a less preferable strategy for California sea lions? California sea lions are traditionally described as epipelagic divers, with a generalist epipelagic diet targeting nutritious schooling prey such as sardine (Antonelis et al., 1984; Feldkamp et al., 1989; Lowry et al., 1991; Lowry and Carretta, 1999; Orr et al., 2011; Melin et al., 2012; Kuhn and Costa, 2014; McHuron et al., 2016), although large inter- and intra-individual variation in foraging strategy is observed in some populations (McHuron et al., 2016). Some individuals use a deep-diving strategy consistently (McHuron et al., 2016, 2018); however, mean dive depth and duration increases substantially during anomalously low prey availability (Feldkamp et al., 1991; Melin et al., 2008; Weise et al., 2010) and during seasonal drops in productivity (Villegas-Amtmann et al., 2011), suggesting that most individuals prefer shallow diving when prey are abundant. Decreased abundance of shallow prey (i.e. McClatchie et al., 2016), therefore, may drive California sea lions (particularly those that do not specialize in deep diving) to rely more heavily on a higher-cost deep-diving strategy. As we show, a switch to a deeper-dive strategy would be costlier for sea lions in poor body condition (Fig. 4C). Longer and deeper dives are also more likely to require anaerobic metabolism, prolonging the subsequent surface interval needed for recovery, thereby reducing time spent foraging relative to energy spent (Kooyman et al., 1980; Ponganis et al., 1997; McHuron et al., 2016).

Despite the increased power requirements, some individuals specialize in this high-cost, high-reward strategy. California sea lions use three main strategies: an epipelagic strategy, a mixed epipelagic/benthic strategy and a deep-diving strategy (Weise et al., 2010; Villegas-Amtmann et al., 2011; McHuron et al., 2016). Some adult females specialize in one strategy, whereas others switch freely between strategies (McHuron et al., 2016). Notably, deep-diving specialists at San Miguel Island and San Nicolas Island (Channel Islands, CA, USA) exhibited intermediate FMRs, whereas the FMR of mixed-strategy foragers increased with dive depth (McHuron et al., 2016, 2018). Prey quality may contribute to these trends: deep mesopelagic divers likely target a consistent stock of mesopelagic fishes of greater nutritional quality at predictable locations, whereas the mixed epipelagic/benthic foragers appear to target less nutritious adult Pacific hake (Merluccius productus; Bailey et al., 1982; Lowry et al., 1991; Huynh and Kitts, 2009; Litz et al., 2010; Orr et al., 2011; Melin et al., 2012; McHuron et al., 2016, 2018). If mesopelagic prey are indeed both predictably available and of high quality, deep-diving specialists may achieve lower FMR by minimizing the dives and travel distance needed to meet their energetic demands, despite increased costs while diving. For example, fin whales overcome increased energetic costs by increasing their energy intake fourfold in deeper dives (Friedlaender et al., 2019). Perhaps similarly to deep-diving California sea lions, deep-diving and negatively buoyant long-finned pilot whales appear to use a high-cost strategy, presumably seeking large energetic rewards (Aoki et al., 2017). Future studies combining fine-scale energetic cost estimates (as in this study) with prey-capture data from accelerometry (e.g. Cole et al., 2021) or video will help clarify the effects of dive depth, dive type (benthic, pelagic) and habitat on patterns of at-sea energy balance in California sea lions and likely in other species.

Conclusions

Foraging costs in California sea lions are strongly tied to buoyancy at fine temporal scales, owing to high tissue densities and compression of a moderate to high DLV. DLV increased with dive depth in some sea lions. All individuals exhibited patterns of power use across depth that indicate a primary role of buoyancy in determining swimming cost in a given moment, with initial descent and the majority of ascent accounting for much of the dive cost. An individual's tissue density appeared to drive the magnitude of mass-specific power used to ascend at a given moment at depth, a trend that was not clearly mirrored in the descent phase because minimum mass-specific power is limited to 0 (passive gliding) regardless of tissue density.

California sea lions used more propulsive energy per second (power) to descend and ascend in deeper dives, and the mean costs of medium and deep diving increased as a function of individuals' tissue density. Mean COT did not vary with dive depth. Stronger buoyancy resulting from higher tissue density, alongside the behavioral response of swim speed, appears to drive the observed results. Faster swimming in deep dives keeps COT minimized despite the additional costs of ascending against negative buoyancy, allowing sea lions to exploit prey in dives that approach limits of oxygen stores, but comes at the cost of greater energy spent per unit time. Deep diving may therefore be an energetically expensive strategy, although these costs could be buffered by a decreased dive rate or offset by increased energy gain as part of a high-cost, high-reward strategy.

We thank Stephanie Flora and Karin Forney for help with custom-written code. Jim Harvey contributed valuable insight and feedback on the manuscript. The Moss Landing Marine Labs Vertebrate Ecology Lab provided many helpful suggestions. Some portions of the Introduction, Materials and Methods, Results, and Discussion in this paper have been reproduced from the Master's thesis of M.R.C. (Moss Landing Marine Laboratories at San Jose State University, 2020).

Author contributions

Conceptualization: M.R.C., C.W., B.I.M.; Methodology: M.R.C.; Formal analysis: M.R.C.; Investigation: M.R.C.; Resources: C.W., E.A.M., D.P.C., P.J.P., B.I.M.; Data curation: M.R.C., C.W., E.A.M., B.I.M.; Writing - original draft: M.R.C.; Writing - review & editing: M.R.C., C.W., E.A.M., D.P.C., P.J.P., B.I.M.; Visualization: M.R.C.; Supervision: B.I.M.; Funding acquisition: M.R.C., P.J.P., B.I.M.

Funding

This research was supported by the Council on Ocean Affairs Science and Technology, California State University (COAST) Graduate Student Research Award (CSUCOAST-COLMAS-SJSU-AY1617 awarded to M.R.C.), the H.T. Harvey Memorial Research Fellowship, the MLML Scholar Award, the San José State University (SJSU) Archimedes Scholarship, and the Earl H. and Ethel M. Myers Oceanographic and Marine Biology Trust (all awarded to M.R.C.). Additional support was provided by the Office of Naval Research (award number N000141210633 awarded to P.J.P. and B.I.M., and N000141612852 awarded to B.I.M).

Data availability

All relevant data can be found within the article and its supplementary information.

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Competing interests

The authors declare no competing or financial interests.