Fig 1.
Illustration and diagram showing a gain function of a single dive with the optimal patch time according to the assumption of CPF.
(a) A depth profile of a whale lunging (red lines) four times in a single dive. The energy intake of each lunge is the sum of the Index of Prey Density measured over the lunge duration. (b) Rate of energy intake is plotted as linear functions (Ec; black line on the right-hand side), with each black dot representing the duration and cumulative energy intake at each lunge. Here, the prey density is predicted to decrease after each lunge showing a shape of a diminishing rate of energy gain (slope of a line). The left-hand side shaded in pink indicates the transit duration (descent + ascent) and the post-surface duration. The blue line starting from the sum of the transit and surface duration to the last lunge point on the right-hand side indicates the total rate of energy intake (En) of this whole foraging cycle. The optimal patch time is indicated in red *, which in this case is where Ec and En overlaps.
Fig 2.
Example of video analysis for counting prey.
(a) Video data converted to still image (b) Images converted to grey scale and filtered (3) Image with the body of the whale and large objects removed and the remaining objects (prey) being marked.
Fig 3.
Characteristics of lunge dives.
(a) Diving behavior of a humpback whale (ID: WhC14). Dive profile with lunge events (indicated in red), dorso-ventral acceleration, and swim speed in dives with varying numbers of lunges per dive (b) Relationship between patch residence time and number of lunges per dive, showing positive correlation (Spearman’s ρ = 0.78, P < 0.001).
Table 1.
Tagging results of seven humpback whales.
Fig 4.
Relationship between dive duration and post-surface duration of foraging dives with greater than or equaled to two lunges within 35 m in depth.
This showed positive relationship (Spearman’s ρ = 0.54, P < 0.0001; n = 70).
Fig 5.
Foraging efficiency of lunges.
Foraging models comparing the total rates of energy intake (En) and gain functions using mean values of dives with (ab) two-lunges (n = 50), (efg) three-lunges (n = 17). X-axis shows the foraging duration, composed of transit (descent + ascent) + post-surface + patch residence time. Y-axis shows cumulative energy intake. The total rate of energy intake (En) up to each lunge is represented by a blue line, and the rate of energy intake at each lunge (Ec) is indicated by a black or red line. Error bars on the black dots and the starting point of the blue line (En) represent the standard deviation of the mean values. A linear regression model of Ec versus En (cdhij) of the corresponding foraging model are shown on the right side of each foraging model. The dashed black line represents where Ec/En = 1. (c), (h), and (i) had Ec/En values greater than one (a; Ec/En = 4.1, 95% CI; 3.8–4.3: h; Ec/En = 5.1, 95% CI; 4.5–5.7: i; 1.5, 95% CI; 1.2–1.8). Although (j) also had Ec/En values greater than one the 95CI included Ec/En = 1 (Ec/En = 1.2, 95% CI; 0.99–1.3). (d) had Ec/En values less than one (Ec/En = 0.88, 95% CI; 0.75–0.98).
Table 2.
Values of Ec/En and 95% CI for each lunge in a dive.
Fig 6.
Comparison of Ec values of single lunge dives and first lunge of multiple lunge dives.
The value of Ec for multiple lunge dives are significantly higher than that of single lunge dives.
Fig 7.
Snap shot from the video logger attached to a humpback whale.
Another humpback whale is swimming in front of the tagged whale.
Fig 8.
Relationships between patch residence time and (a) dive depth and (b) the maximum Index of Prey Density (IPD) for four whales. The red points represent absent (n = 232) dives and blue triangles represent present dives (n = 12). The points show the patch residence time, rescaled so that the effect of MIPD is normalized to its mean value in (a), and the effect of depth is normalized to its mean value in (b). The solid lines represent the mean values and the dashed lines represent the 95% prediction intervals of posterior distribution computed from the MCMC simulation. For computing 95% prediction intervals, MIPD was set to its mean value in (a) and depth was set to its mean value in (b).
Table 3.
95% CI for each parameter based on prior distributions computed by MCMC sampling.