1. Physics of Living Systems
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Energetic and physical limitations on the breaching performance of large whales

  1. Paolo S Segre  Is a corresponding author
  2. Jean Potvin
  3. David E Cade
  4. John Calambokidis
  5. Jacopo Di Clemente
  6. Frank E Fish
  7. Ari S Friedlaender
  8. William T Gough
  9. Shirel R Kahane-Rapport
  10. Cláudia Oliveira
  11. Susan E Parks
  12. Gwenith S Penry
  13. Malene Simon
  14. Alison K Stimpert
  15. David N Wiley
  16. KC Bierlich
  17. Peter T Madsen
  18. Jeremy A Goldbogen
  1. Hopkins Marine Station of Stanford University, United States
  2. Saint Louis University, United States
  3. Cascadia Research Collective, United States
  4. Accademia del Leviatano, Italy
  5. West Chester University, United States
  6. Institute of Marine Sciences, University of California, United States
  7. Okeanos R&D Centre and the Institute of Marine Research, University of the Azores, Portugal
  8. Department of Biology, Syracuse University, United States
  9. Institute for Coastal and Marine Research, Nelson Mandela University, South Africa
  10. Department of Birds and Mammals, Greenland Institute of Natural Resources, Greenland
  11. Moss Landing Marine Laboratories, San Jose State University, United States
  12. Stellwagen Bank National Marine Sanctuary, United States
  13. Duke University Marine Laboratory, United States
  14. Aarhus Institute for Advanced Studies, Aarhus University, Denmark
  15. Aarhus University, Denmark
Research Article
Cite this article as: eLife 2020;9:e51760 doi: 10.7554/eLife.51760
6 figures, 1 video, 3 tables and 2 additional files

Figures

Breaching whales.

(A) A tagged humpback whale (NMFS permit #16111). (B) A tagged humpback calf (NMFS permit #14682). (C) A tagged minke whale (NMFS permit #14809). (D) An untagged Bryde's whale breaching (credit K. Underhill, Simon's Town Boat Company). (E) A tagged gray whale falling back into the water (NMFS permit #16111). (F) An untagged sperm whale (permit #49/2010/DRA). (G) A tagged right whale (MMPA permit #775–1875). (H) An untagged blue whale partially emerging from the water while participating in a 'racing behavior' (NMFS permit #16111).

Representative breaching kinematics of a humpback whale.

Three metrics of pitch are shown: the pitch changes of the body (red), pitch oscillations due to the fluke stroke (orange), and the sum of the two (blue). Two measurements of speed are shown: speed calculated from orientation corrected depth rate (purple), and speed calculated from the accelerometer vibrations (blue). Depth is also shown (black). Images from the onboard camera are shown at specific landmarks during the breach. The video of this breach is included in the supplementary materials (Video 1).

The diversity of underwater breaching behavior is illustrated by the depth profiles of 152 breaching accelerations performed by 37 humpback whales.

Four representative trajectories illustrating U, V, I, and J-shaped breaching profiles are highlighted, showing both the beginning of the upwards acceleration (solid line) and the 16 s prior to the breach, provided for context (dotted line).

Representative breaching kinematics of a minke whale (A), a Bryde’s whale (B), a gray whale (C), a sperm whale (D), and a right whale (E).

Three metrics of pitch are shown: the pitch changes of the body (red), pitch oscillations due to the fluke stroke (orange), and the sum of the two (blue). Two measurements of speed are shown: speed calculated from orientation corrected depth rate (purple), and speed calculated from the accelerometer vibrations (blue). Depth is also shown (black). The graphs show the 12 s before the whale emerges from the water, with gray shaded areas representing time before the breaching maneuver begins.

Breaching speed is correlated with starting depth (A) and average stroke frequency (B), but not with breaching pitch (C), or breaching roll angle (D).
Figure 5—source data 1

Data from 187 breaches performed by 28 individual humpback whales, two minke whales, one Bryde’s whale, one gray whale, three sperm whales, and two right whales.

https://cdn.elifesciences.org/articles/51760/elife-51760-fig5-data1-v1.csv
The cost of breaching increases with body size, in humpback whales.

(A) The mass-specific energy expenditure required to perform high-emergence breaches (blue) and high-performance lunges (red) is shown for five humpback whales of different sizes. Because the whales breached with different percentages of their bodies emerging from the water (dark blue numbers), the expected relationship between mass and the energetic cost of breaching with 80% body emergence, is shown for comparison (light blue line). The modeled breaches were calculated using average parameters from the trajectories of the five individuals shown (65° pitch; body width = 18% of length; 1.75 m/s starting velocity; 0.65 m/s2 acceleration; no plateau phase). Both the model and the data show that the mass-specific cost of breaching increases with body size. (B) This pattern is largely driven by the higher speeds that larger whales need to emerge from the water. (C) To attain the higher speeds required to emerge from the water, larger whales need to generate higher mass-specific mechanical power outputs or extend the duration of their trajectories (green numbers).

Videos

Video 1
Camera-tag video of a humpback whale performing a breach.

The trajectory of this breach is shown in Figure 2.

Tables

Table 1
Performance and kinematics of breaching whales.

Mean ± standard deviation are presented along with maximum and minimum values, shown in parentheses. It was not always possible to measure all of the metrics for each breach. Velocity for the gray whale and Bryde’s whale breaches were measured using the accelerometer vibrations, while all other velocities were measured using the orientation corrected depth rate.

Humpback whaleHumpback juvenileMinke whaleBryde’s whaleGray whaleSperm whaleRight whale
# individuals25321132
# events
(full, partial breaches)
46
(39, 6)
106
(66, 33)
22
(11, 10)
2
(2, 0)
1
(1, 0)
6
(5, 0)
4
(1, 3)
depth (m)24 ± 12
(4, 52)
9 ± 8
(2, 54)
7 ± 5
(2, 21)
12 ± 1
(12, 13)
520 ± 6
(12, 29)
21 ± 11
(10, 31)
duration (s)7.9 ± 2.3
(4.4, 13.7)
5.2 ± 2.4
(1.9, 17.6)
7.5 ± 3.8
(2.9, 18.2)
5.3 ± 2.2
(3.8, 6.9)
7.97.3 ± 1.8
(5.0, 10.2)
8.8 ± 2.2
(6.9, 11.5)
# strokes4.1 ± 1.5
(1.7, 6.7)
2.8 ± 1.6
(1.1, 10.7)
3.8 ± 1.8
(1.7, 7.5)
-2.83.8 ± 1.2
(2.1, 5.6)
3.6 ± 1.7
(2.0, 5.4)
stroke frequency (Hz)0.4 ± 0.1
(0.2, 0.7)
0.5 ± 0.2
(0.2, 1.1)
0.5 ± 0.1
(0.3, 0.7)
-0.30.5 ± 0.1
(0.3, 0.6)
0.4 ± 0.1
(0.3, 0.4)
exit speed (m/s)6.1 ± 1.8
(2.6, 8.9)
3.6 ± 1.4
(1.1, 7.6)
2.7 ± 0.6
(1.6, 3.4)
5.3 ± 0.6
(4.8, 5.7)
3.75.4 ± 1.1
(4.2, 6.5)
3.0 ± 0.8
(2.2, 3.8)
exit pitch (°)56 ± 13
(14, 80)
52 ± 13
(19, 82)
52 ± 10
(26, 66)
42 ± 25
(24, 59)
2349 ± 18
(20, 70)
49 ± 14
(36, 68)
exit roll (°)119 ± 57
(4, 178)
84 ± 58
(2, 179)
132 ± 39
(37, 177)
83 ± 116
(1, 165)
488 ± 37
(39, 140)
80 ± 67
(2, 163)
emergence (%)63 ± 19
(26, 100)
55 ± 23
(20, 120)
39 ± 9
(20, 53)
68 ± 24
(51, 85)
5865 ± 13
(49, 82)
33 ± 9
(24, 46)
Table 2
Breaching trajectories were broadly categorized based on their shape.
TrajectoryStarting locationCharacteristicsSpecies# events
U-shapesurfacehorizontal acceleration slightly below the surface; rapid upward pitch change to emerge from water (Whitehead, 1985a)humpback1
humpback, juv.80
minke17
grey1
V-shapesurfacepowered or unpowered descent; abrupt, upward change of direction to start ascenthumpback21
humpback, juv.18
minke4
Bryde’s2
sperm5
right2
J-shapedepthslow ascent from depth; abrupt rapid acceleration towards surfacehumpback4
humpback, juv.4
sperm1
I-shapedepthholding station at depth; abrupt, rapid acceleration towards surfacehumpback20
humpback, juv.4
minke1
right2
Table 3
Kinematic and energetic parameters for five breaches and five high performance lunges performed by five humpback whales spanning a range of sizes.

Length
(m)
Mass
(kg)
Emergence
(%)
Duration
(secs)
Final velocity
(m/s)
Stroke freq
(Hz)
Energy
(MJ)
Max power
(kW)
BreachBreachLungeBreachLungeBreachLungeBreachLungeBreachLunge
7.87000868.06.86.25.30.70.50.90.755
10.517000798.14.77.15.00.60.42.81.21510
12.730000619.12.96.05.00.40.33.71.62318
14.746000848.53.38.24.80.50.39.82.65025
14.8460008212.76.18.15.40.50.210.33.63823

Additional files

Supplementary file 1

Parameters used to calculate the energetics of breaching and lunge feeding, in humpback whales.

(A) Lower and upper bounds of daily Field Metabolic Rate (FMRdaily) for five humpback whales across a range of sizes.

FMRdaily, WM was calculated using the equation for marine mammal FMRdaily proposed by Williams and Maresh (2015). FMRdaily, Nagy was calculated using the equation for terrestrial mammal FMRdaily proposed by Nagy (2005) and multiplied by 1.5. The cost of a high-performance breach and a single high-performance lunge are expressed as percentage of daily energy budget. B) Kinematic and morphological parameters used to calculate the energetics of breaching and lunge feeding.

https://cdn.elifesciences.org/articles/51760/elife-51760-supp1-v1.docx
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