Behavioral Ecology
doi:10.1093/beheco/arr038
Advance Access publication 10 June 2011
Original Article
Optimal foraging theory predicts diving and
feeding strategies of the largest marine predator
Thomas Doniol-Valcroze,a Véronique Lesage,a Janie Giard,b and Robert Michaudb
Department of Fisheries and Oceans, Maurice-Lamontagne Institute, 850 Route de la Mer, Mont-Joli
(Qc) G5H 3Z4, Canada and bGroup for Research and Education on Marine Mammals, 108 de la Cale
Sèche, Tadoussac (Qc) G0T 2A0, Canada
a
Accurate predictions of predator behavior remain elusive in natural settings. Optimal foraging theory predicts that breath-hold
divers should adjust time allocation within their dives to the distance separating prey from the surface. Quantitative tests of these
models have been hampered by the difficulty of documenting underwater feeding behavior and the lack of systems, experimental
or natural, in which prey depth varies over a large range. We tested these predictions on blue whales (Balaenoptera musculus),
which track the diel vertical migration of their prey. A model using simple allometric arguments successfully predicted diving
behavior measured with data loggers. Foraging times within each dive increased to compensate longer transit times and optimize
resource acquisition. Shallow dives were short and yielded the highest feeding rates, explaining why feeding activity was more
intense at night. An optimal framework thus provides powerful tools to predict the behavior of free-ranging marine predators
and inform conservation studies. Key words: aerobic dive limit, blue whale, central-place forager, dive-time budget, feeding
behavior, optimal foraging. [Behav Ecol 22:880–888 (2011)]
INTRODUCTION
ir-breathing predators in aquatic environments face the
challenge of feeding underwater while managing oxygen
stores. Diving performance is linked to body mass in endotherms via simple scaling relationships (Schreer and Kovacs
1997; Halsey, Butler, and Blackburn 2006; Brischoux et al.
2008). Dive-time budgets (e.g., surface-to-dive-duration ratio),
however, are not easily explained by mass and metabolic rate
alone (Halsey, Butler, and Blackburn 2006), suggesting that
ecological aspects such as prey depth need to be taken
into consideration. Models based on optimal foraging theory
(Stephens and Krebs 1986; Perry and Pianka 1997) have been
proposed to explain observed patterns of dive-time budgets
across taxa (Mori 1998; Stephens et al. 2008). Although developed for constant-rate foragers, these models can be adapted to predict time allocation in the dive cycle of other diving
predators like single- and multiple-prey loaders.
Because diving predators return repeatedly to the surface to
breathe, they can be studied under the framework of centralplace foraging (Orians et al. 1979) with the surface acting as
the central place (Houston and McNamara 1985). As distance
to food increases, central-place foragers should compensate
travel costs by increasing their energy gain, which divers
achieve by increasing time spent foraging at depth (Mori
1998), thereby increasing prey encounters and captures
(Thompson and Fedak 2001). Because oxygen is acquired at
the surface with diminishing returns, recovery times increase
rapidly with the lengthening of the preceding dive (Kooyman
and Ponganis 1998). Thus, shallow dives yield a higher net
rate of oxygen acquisition and deeper dives result in a higher
A
Address correspondence to T. Doniol-Valcroze. E-mail: thomas
[email protected].
Received 29 June 2010; revised 14 December 2010; accepted 9
February 2011.
Crown copyright 2011. Published by Oxford University Press on behalf of
the International Society for Behavioral Ecology. All rights reserved.
For permissions, please e-mail: [email protected]
proportion of time spent recuperating at the surface (Kramer
1988). To maximize the proportion of time spent in the food
patch, both surface time and bottom time should increase
with target depth (Houston and Carbone 1992).
Predictions of how divers respond to prey depth and foraging costs have been tested in birds qualitatively (Carbone and
Houston 1994; Carbone and Houston 1996; Walton et al.
1998) and quantitatively (Mori 2002; Halsey et al. 2003; Cook
et al. 2008). Tests on large divers, however, have been hampered by the difficulty of documenting underwater feeding
behavior and the lack of systems, experimental or natural,
in which variations in prey depth are large enough to examine
how predators adjust their allocation of time within dives.
Blue whales (Balaenoptera musculus) represent an ideal model
species for testing predictions of optimal models in a natural
setting. They track the diel vertical migrations of euphausiids
between the surface and deeper water layers (Fiedler et al.
1998; Calambokidis et al. 2007; Oleson et al. 2007), making
it possible to study the time allocated to foraging over a large
range of target depths. Moreover, their narrow trophic niche
ensures that they feed on the same prey regardless of the time
of day, allowing meaningful comparisons of feeding behavior
across the diurnal cycle.
For any thorough study of foraging strategies, it is crucial to
detect feeding events equally well regardless of depth or time
of day. Previous studies of rorquals and other pelagic feeders
have relied mostly on visual examination of time-depth profiles
for the detection of feeding events, usually identified by the
occurrence of vertical excursions greater than an arbitrary
threshold, called ‘‘wiggles’’ (Croll et al. 2001; Schreer et al.
2001). However, not all feeding events are characterized by
a wiggle. Blue whales perform discrete feeding events called
lunges, which are characterized by an acceleration when approaching prey and a sudden deceleration when opening
their mouth to engulf quantities of water and food equivalent
to over 100% of their body volume (Goldbogen et al. 2010).
Lunges close to the surface and vertical lunges during descent
Doniol-Valcroze et al.
•
Optimal foraging in a diving predator
or ascent phases have been documented previously in rorqual
whales and are not detectable on time-depth profiles (Woodward 2006; Calambokidis et al. 2007; Goldbogen et al. 2008).
Fortunately, the kinematics of feeding lunges can be used to
pinpoint the moment and location of each feeding attempt
(Goldbogen et al. 2008).
Accurate predictions of predator behavior remain elusive in
natural settings, particularly in the marine environment. Our
objective was to test whether a simple optimal model could predict the diving and feeding behavior of free-ranging blue
whales. Specifically, we predicted that surface and foraging
times increase with target depth to compensate longer transit
times and that the number of discrete feeding events, assessed
using a novel automated method, increases accordingly.
MATERIALS AND METHODS
Data collection
We deployed velocity-time-depth recorders (VTDR; Wildlife
Computers, Redmond, WA) and radio transmitters on blue
whales in the St Lawrence River estuary (Quebec, Canada)
during the time of greatest abundance and presumed feeding
activity in the region (August–September). Tags were deployed from a 5 m rigid-hulled inflatable boat using a pole
or crossbow and were attached to whales with suction cups.
VTDRs recorded time, depth, and instantaneous swim speed
with a pressure transducer resolution of 0.25 m for the first
15 m. We also deployed one digital acoustic recording tag (Dtag, Johnson and Tyack 2003), which lacked a velocity meter
but recorded the animal’s pitch, roll, and heading as well as
ambient noise (including flow noise) every second. Whales
were radio-tracked from a distance of 500–1000 m to minimize
disturbance. We recorded surface activity and tracked whales
until tags were released due to corrosion of a magnesium cap
and subsequent entry of air or water under the suction cup or
until nightfall. Following their release, tags were located using
the radio-transmitter’s signal and retrieved by boat.
Dive characteristics and feeding events
Data were corrected for electronic drift using the software Instrument Helper (Wildlife Computers). We validated zerooffset corrections by comparing depth and respiration patterns
of a large number of dive sequences with observations of
breathing events recorded from the research vessel. This fine
degree of correction allowed us to investigate near-surface diving and feeding activity, a section of whale habitat often discarded in other studies due to limitations in tag resolution
and availability of data for cross-validation. The first few dives
following tag deployment were scrutinized for any atypical behavior indicative of a reaction to tagging.
Estimates of swim speeds for the D-tag were obtained following Goldbogen et al. (2008). We used the PRAAT software
(Boersma and Weenink 2009) to extract flow noise at 150
Hz (at which contrasts due to speed changes were strongest).
We established the relationship between flow noise (converted to dB re. 1 lPa2 Hz21) and swim speed calculated for
segments steeper than 45 by dividing vertical velocity by the
sine of pitch angle. We used the resulting calibration curve to
calculate swim speed every second.
Because visual techniques are ill-suited for the large data sets
needed for conclusive testing of biological hypotheses (Lesage
et al. 1999), we have used a novel method to automatically
detect feeding lunges of blue whales. Depth and swim speed
data were analyzed using a custom-made program in Visual
Basic (available from the authors) to identify dive phases and
calculate the number of wiggles and feeding attempts per dive.
Wiggles were defined as vertical excursions of more than 8 m
881
(following Croll et al. 2001) made of an ascent followed by
a descent without a return to the surface (0 m). Lunges were
identified independently of depth values using velocity reading
measured every second (Figure 1). Unlike Goldbogen et al.
(2006), we did not detect lunges using an absolute speed
threshold because velocity readings recorded by VTDRs can
underestimate true speeds and depend on their position on
the body (Baird 1998). Instead, we first flagged swim speeds
95th percentile of all velocity values recorded for the individual under scrutiny as indicators of potential accelerations typical of lunge feeding. Swim speeds following such an extreme
velocity were searched until 4 consecutive speeds , 95th percentile were detected. The abruptness of deceleration was determined by comparing mean speed over the 10 s following the
last extreme swim speed to the mean speed during the acceleration period. A ratio 0.5 between mean acceleration and
deceleration was considered indicative of a feeding event.
The start of each deceleration determined the exact moment
of the opening of the mouth (Goldbogen et al. 2006) and the
depth of each lunge. The accuracy of our automated lunge detection method was validated in 2 ways. First, we compared detection of surface lunge-feeding activity with visual observations
from the research vessel. Second, using the D-tag record, we
compared lunges detected using flow noise with those identified
by rolling angles over a 45 threshold (Woodward 2006).
Target depth was defined as the mean depth of feeding activity for each dive (Figure 1). Although bottom phase usually
corresponds to the time spent at a fixed percentage of maximum depth (Lesage et al. 1999), we calculated it as the time
between first reaching target depth and last passing that
depth during the ascent phase. Shallow dives constituting
the post-dive surface interval, and which contributed to oxygen replenishment and dive recovery, were separated from
deeper dives using a K-means cluster analysis (Hartigan and
Wong 1979) based on depth and duration to separate dive
types into 2 categories. Total surface time was obtained by
summing durations of all short dives and surface intervals
following longer deeper dives.
Statistics were performed in the R programming language
(R Development Core Team 2008). Some scripts were modified from the diveMove package (Luque 2007).
Optimal model
For a detailed description of the model, see Houston and
Carbone (1992). Dives are divided into 3 components: s is
the round-trip travel time between the surface and the foraging stratum, t is the time spent in the foraging stratum (bottom time), and s is the time spent at the surface. The oxygen
used during these 3 periods depends on the different rates of
oxygen consumption, m1, m2, and m3, respectively. The oxygen
accumulated by a diver spending time s at the surface is assumed to balance oxygen used during the dive:
Kð1 2 e 2 as Þ ¼ m1 s 1 m2 t
ð1Þ
where K is the total oxygen storage capacity and a is the initial
rate of oxygen replenishment. The optimal surface duration
s* is obtained by solving:
Kð1 2 e 2 as Þ 2 m1 s 2 aKe 2 as ðs 1 sÞ ¼ 0
ð2Þ
Given s* and m2, Equation 1 can be used to yield estimates
of t*, the optimal foraging time.
Parameters
Several parameters are needed to generate predictions of optimal
time allocation and feeding strategies (Table 1). We obtained m1,
Behavioral Ecology
882
Figure 1
Examples of daytime (a) and
nighttime (b) foraging dives
by a blue whale in the St Lawrence River estuary. Top panel
shows depth recorded every
second (bold line). Circles:
feeding attempts; dashed line:
surface; dotted line: target
depth. Bottom panel: speed recorded every second (thin
line). Note the occurrence of
a feeding lunge during the ascent phase of the daytime dive
(with no corresponding wiggle). In this example, the individual performed 6 lunges
during the daytime dive versus
9 lunges during the same period of time (13 min) at nighttime.
a, and K from the allometric relationships described in Kleiber
(1975) and Stephens et al. (2008), assigning blue whales a mass
of 92 671 kg (Croll et al. 2001). Stephens et al. (2008) found
that a 5% increment to the allometric coefficient for O2 stores
yielded values closer to the empirical observations of dive-pause
ratios in Halsey, Butler, and Blackburn (2006), likely because
some species have higher mass-specific O2 storage capacities.
We noted that using this increment yielded similar O2 stores
(4925 L) to those obtained by Croll et al. (2001) in their detailed
calculation of blue whale O2 stores (5015 L).
Vertical travel speed is needed to express t as a function of
target depth. Although the cost of swimming is expected to
decrease in large animals, allowing them to swim faster (Eckert
et al. 1999), the speed of divers in optimal models is often
assumed independent of body size (Mori 2002). Stephens
et al. (2008) used a vertical speed of 1 m s21 for animals of
all possible masses. Exploration of our data set showed that
blue whale vertical speeds during feeding dives (dives with 1
or more lunges) had a mean of 0.97 m s21 (25–75% quantiles: 0.72–1.21). To improve comparability, we used 1 m s21.
The metabolic rate during foraging m2 has not been measured in blue whales and needs to be estimated. Houston and
Carbone (1992) warned against estimating m2 from surface
behavior alone, precisely because under optimal strategies,
the animal will choose the behavior that avoids costly surface
times. Acevedo-Gutierrez et al. (2002), who were the first to
use optimal models to better understand the feeding behavior
of rorquals, calculated m2 from the observed allocation of
time in their data. However, to estimate m2 using optimal
models, one has to trust that whales employ optimal strategies
in the first place. To avoid circular reasoning, we chose instead to estimate m2 from energetic considerations alone. In
a detailed simulation of the engulfment process of fin whales,
blue whale’s closest relative, Potvin et al. (2009) estimated that
the energy spent by a 20 m, 50 tons fin whale during the preengulfment and engulfment phases of a lunge was 298 080 J
over a 13-s period. Because this energy was spent accelerating
during the pre-engulfment phase, and fighting drag and
pushing the engulfed was mass during the engulfment phase,
we assumed that it was spent on top of the normal energetic
budget of a swimming whale (i.e., on top of the 3.75 3 basal
metabolic rate). Potvin et al. (2009) assumed similar costs
during the purging phase, though it is unclear if these costs
applied to the entire between-lunges interval. We assumed
this was the case and that an extra cost of 22 929 J s21 applied
to the entire foraging time. Goldbogen et al. (2010) found
that lunging cost was likely to scale allometrically with body
length because mass-specific engulfment volume (which generates most of the drag-related costs) increases with body
length. Given the similar body shapes of fin and blue whales,
Table 1
Value and source of parameters used in equations of the optimal model
Parameter
Description (units)
Formula
Value
References
M
K
a
m1
m2
Body mass (kg)
Total oxygen storage capacity (L)
Initial rate of oxygen replenishment (s21)
Metabolic rate while traveling (L O2 s21)
Metabolic rate while foraging (L O2 s21)
—
0.03 M1.05
0.90 M20.33
0.00065 M0.75
1.78 m1
92 671
4925
0.002
3.45
6.13
Croll et al. (2001)
Stephens et al. (2008)
Stephens et al. (2008)
Kleiber (1975) and Stephens et al. (2008)
Potvin et al. (2009) and Goldbogen et al. (2010)
Doniol-Valcroze et al.
•
Optimal foraging in a diving predator
we assumed that the scaling relationship for fin whales of different lengths also applied to blue whales. Because mass-specific
engulfed volume scales with L0.94 and the mass M scales with
L2.6 (Goldbogen et al. 2010), lunging costs must scale with
M1.36.
For a 92 tons whale, this cost is 22 929 3 (Mblue/Mfin)1.36 ¼
53 068 J s21. And the metabolic rate during foraging is
m2 ¼ 3:75 3 3:39M0:75
blue 1 53 068
¼ 120 589 J s 2 1 ¼ 6:13L O2 s 2 1 :
To predict the number of feeding events, we examined the
data to see if the rate at which feeding lunges were performed
changed over the course of a dive. We did not find any indication to that effect and therefore assumed a constant rate. The
model predicts a bottom time of 0 at target depths of 0 m because theoretically, an animal does not need to dive when feeding at the surface. Lunge feeders, however, need to take 1
lunge to have any feeding success. Thus, we set the minimum
number of lunges in the model to 1.
Testing model predictions
We compared predictions of the model over a range of target
depths with actual diving data for bottom time t, dive duration
(s 1 t), the number of feeding lunges, n and the feeding rate
n/(s 1 t 1 s), as well as surface time and dive:pause ratio. To
conform to the model’s assumption, we only retained dives of
approximately square shape, defined by a ratio between bottom time and dive duration greater than 0.2 (Lesage et al.
1999). Because there are no absolute criteria to assess a model’s validity (Mayer and Butler 1993), we tested the fit
of the model in several ways. First, we calculated the Pearson’s
product–moment correlation (Guisan and Zimmermann
2000) and the modeling efficiency (Mayer and Butler 1993)
as overall measures of agreement between observed and predicted values. We calculated the slope and intercept of the
linear regression of observed versus predicted values and
tested whether they deviated significantly from 1 and 0, respectively (Smith and Rose 1995). However, when performed
with large sample sizes, these tests may detect statistically significant deviations that are not necessarily indicative of a poor
fit (Smith and Rose 1995). Therefore, to better understand
potential biases in prediction accuracy, we computed the mean
squared deviation (MSD), which calculates the deviation of
each predicted value from the 1:1 line (rather than from the
regression line as in the case of the mean squared error, MSE).
MSD is more conservative than MSE and can be decomposed
into 3 additive components with distinct and clear interpretations (Gauch et al. 2003): squared bias (SB) resulting from
unequal means, non-unity slope (NU) which arises when the
slope of the least-square regression differs from 1, and lack of
correlation (LC) which indicates how scatter around the regression line decreases the correlation coefficient.
Whales feed in bouts within which dives are likely to have
similar characteristics. Lack of independence between dives
of the same individual may result in spurious conclusions
due to autocorrelation. To avoid this, we drew 10 000 random
samples containing 10% of the dives and counted the draws
for which the slope and intercept of the regression between
observed and predicted values deviated significantly from 1
and 0, respectively. Individual variability was assessed by examining dive variables for each tagged whale separately.
RESULTS
We deployed instruments on 10 blue whales from 2002 to 2009.
Tags remained on whales for 2–25 h, and individuals were
883
tracked from the surface for 2–11 h, yielding 6501 dives over
139 h of data, of which 66 h included surface observations.
Maximum depth of nonfeeding dives was 154 m and maximum duration was 23 min. Seven individuals performed at
least one feeding lunge on the first dive following tagging
and 2 others did so during the second dive, suggesting minimal impact of tagging on feeding behavior.
Feeding behavior
We identified 1703 dives with at least one feeding attempt and
a total of 2689 lunges (Table 2). All 6 deployments that remained attached into the night showed feeding near the surface (,20 m). Daytime feeding behavior was essentially
bimodal, taking place either in relatively shallow waters
(,40 m) or at depths of about 70–100 m, with some lunges
occurring at intermediate depths during twilight. Foraging
blue whales in the St Lawrence Estuary lunged on average
1.58 (61.26 SD) times per dive, with a maximum of 15 lunges
in one single dive. Feeding occurred throughout the diurnal
cycle but lunges were twice as frequent at night than during
daytime (average of 1 lunge every 2.1 min at night vs. every
4.2 min during daytime). The number of lunges per dive was
lower and less variable at night (1.25 6 0.53 SD) than during
daytime (2.18 6 1.69 SD).
Forty-four surface lunges were observed from the research
vessel, all of which were detected by the automated lungefeeding detection algorithm. Similarly, the program accurately
detected all 35 lunges from the D-tag that were characterized
by a roll greater than 45. The algorithm proved robust at discriminating against other types of speed changes, for example,
drops in speed when surfacing for air or high-speed pursuits
between individuals during social interactions. A feeding
lunge during the ascent to the surface occurred in 89.5% of
daytime dives (e.g., Figure 1).
Although there was a strong correlation between the number of wiggles and lunges per dive (P , 0.001, r 2 ¼ 0.59),
wiggle counts underestimated the number of feeding attempts performed by each individual by 25–85%. The proportion of missed feeding attempts per dive averaged 48% during
the day but increased to 98% during twilight and 100% at
night. This high proportion of missed events was largely due
to the consistent failure of wiggle counts to detect lunges
during the final ascent to the surface and feeding activity at
shallow depths.
Performance of the optimal model
Model predictions of dive characteristics were generated over
the range of feeding depths documented for blue whales (e.g.,
Goldbogen et al. 2011). Characteristics of square feeding dives spanning a range of target depths of 0–134 m were compared with model predictions. In agreement with theory,
bottom times and dive durations increased quickly at first
then at a decreasing rate with increasing depth (Figure
2a,c). Pearson correlation coefficients of 0.74 and 0.87 (P ,
0.001) and model efficiencies of 0.42 and 0.70 indicated
a good match with predicted values for these 2 variables.
The slopes of the linear regression between observed and
predicted values did not differ significantly from 1 despite
the large sample size, showing that prediction accuracy did
not vary with target depth (Figure 2b,d). The intercepts both
differed significantly from 0 with values of 240 s and 239 s,
respectively (P , 0.001). The similar values of the intercepts
show that dive durations were shorter than predicted solely
because their bottom time component was shorter. Decomposition of the MSD indicated that scatter of observed values was
the largest contributor to the observed deviation from the 1:1
Behavioral Ecology
884
Table 2
Characteristics of feeding dives (sample size, depth, dive duration, and number of lunges performed per dive, 6SD) of 10 St Lawrence blue
whales equipped with data recorders
Day (.50 m)
ID
Tag
Tag
Tag
Tag
Tag
Tag
Tag
Tag
Tag
Tag
n
0201
0301
0401
0402
0403
0404
0501
0502
0602
0901
Day (50 m)
Depth (m) Duration (s) Lunges/dive n
7 100 6 23
0
n/a
0
n/a
11 86 6 11
0
n/a
8 91 6 24
2 78 6 30
22 76 6 17
25 69 6 16
15 75 6 9
750 6 100
n/a
n/a
860 6 300
n/a
690 6 260
500 6 180
520 6 130
530 6 120
460 6 81
6.7 6 2
n/a
n/a
7.7 6 3.7
n/a
4.8 6 3.5
1.5 6 0.71
4.9 6 1.6
4 6 1.2
3.8 6 0.94
2
49
170
50
28
5
4
145
43
154
Night
Depth (m) Duration (s) Lunges/dive n
30
30
4.4
12
11
27
29
15
23
8.4
6
6
6
6
6
6
6
6
6
6
2.3
8.6
2.5
6.1
10
19
3.5
7.7
13
5.1
500
390
110
210
190
540
390
110
300
110
6
6
6
6
6
6
6
6
6
6
330
150
75
140
130
42
200
62
150
68
3
3.2
1.4
2
2.2
2.6
1.8
1.3
2.5
1.3
6
6
6
6
6
6
6
6
6
6
2.8
1.2
0.58
1
1.5
2.5
0.5
0.63
1.4
0.58
Depth (m) Duration (s) Lunges/dive
0
n/a
n/a
26 3.4 6 1.3
90 6 16
145 1.8 6 0.95 91 6 31
105 0.98 6 2
81 6 50
0
n/a
n/a
12 1.1 6 0.72 79 6 20
0
n/a
n/a
83 13 6 4.9 140 6 89
132 3.6 6 1.6
85 6 22
0
n/a
n/a
n/a
1.6 6 0.5
1.3 6 0.46
1.1 6 0.27
n/a
160
n/a
1.5 6 0.93
1.2 6 0.47
n/a
Daytime feeding dives followed a bimodal distribution and were consequently separated into shallow (50 m) and deep (.50 m) depth
categories. Feeding dives occurring during twilight were performed across a wide range of depths (0–80 m) and were omitted for clarity. n/a, not
applicable.
line (78–83%). The contribution of bias was ;20% and that
of slope rotation was negligible (,1%). Random resampling
confirmed these results with 96% of runs yielding slope coefficients not significantly different from 1.
The number of lunges per dive also increased with foraging
depth (Figure 3a). Using the mean interval between lunges
(88 s) to predict the number of lunges from modeled values
of bottom times yielded a strong correlation with model predictions (q ¼ 0.73, P , 0.001) and good overall fit (model
efficiency ¼ 0.49). Neither the slope nor the intercept of the
regression line between observed and predicted values differed significantly from 1 and 0, respectively (Figure 3b). Results were the same in 99% of random resampling runs for the
Figure 2
(a) Observed and predicted
values of bottom time as a function of target depth, over the
range of feeding depths documented for blue whales. Each
circle represents one dive.
Solid line: model predictions.
(b) Linear regression of predicted and observed values
(solid line) and 1:1 line
(dashed line). (c) Observed
and predicted values of dive
duration as a function of target
depth. Each circle represents
one dive. Solid line: model
predictions;
dotted
line:
TADL. (d) Linear regression
of predicted and observed values (solid line) and 1:1 line
(dashed line).
intercept and 90% for the slope. Decomposition of the MSD
showed that scatter of points was responsible for 90% of the
observed deviation (rather than bias or rotation).
Optimal surface times predicted by the model were significantly correlated with observed values (q ¼ 0.62, P , 0.001).
Model fit, however, was poor (model efficiency ¼ 215), especially for dives longer than 200 s, which were grossly overestimated (Figure 4a). The dive:pause ratio predicted by the
model was almost invariant with target depth (Figure 4b).
Blue whales feeding at depths over 50 m conformed to this
prediction, but at a ratio 3 times higher than expected. Predicted dive efficiency (bottom time divided by total dive duration plus surface time, Figure 4c) was highest at the surface
Doniol-Valcroze et al.
•
Optimal foraging in a diving predator
885
Figure 3
(a) Observed and predicted
values of the number of lunges
per dive as a function of target
depth, over the range of feeding depths documented for
blue whales. The size of circles
indicates the number of data
points for each depth range
of 10 m. Solid line: model predictions. (b) Linear regression
of predicted and observed values (solid line) and 1:1 line
(dashed line).
and declined steadily with increasing depth. Feeding rates
decreased slowly with increasing depth and matched the overall trend of model predictions though at slightly higher values. Mean feeding rate at the surface was 0.72 lunges min21
with maxima in excess of 1.5 lunges min21. Feeding deeper
than 40 m yielded an average rate of about 0.5 lunges min21.
There was variability in terms of where and when individuals
fed (Figure 5, Table 2). For instance, some individuals were
observed feeding only in shallow waters during the day (e.g.,
Figure 5b), whereas others fed deeper as well (e.g., Figure
5f,g,h). Despite this variability, all individuals conformed to
predictions of dive times and lunge-feeding effort.
DISCUSSION
For pelagic predators, prey behavior determines feeding
depth. Using VTDRs and a novel method to automatically
detect feeding attempts, we have found strong quantitative
agreement between the observed diving behavior of a free-
ranging predator and predictions from a central-place foraging model. With increasing target depth, blue whales increased their time in the food patch, which, combined with
longer transit times, resulted in longer dive durations. Longer
bottom times corresponded to an increase in the number of
feeding events, which, in turn, helped maintain a high feeding rate. Observed data fitted model predictions both for each
individual separately and when pooling individuals together,
even though these individuals were tagged at different times,
in different years, and fed at different sites. To our knowledge,
this is the first time that a theoretical model based on values
derived entirely from the literature and simple allometric relationships can yield quantitatively accurate predictions of
time allocation and feeding behavior of a large marine predator in a natural system.
The model correctly predicted lunge numbers over the
range of target depths observed in the data set. Beyond
150 m, the model predicted a monotonic response that we
were unable to test because St Lawrence blue whales did not
Figure 4
Observed and predicted values
of (a) surface time, (b) surface
time/dive duration ratio, (c)
dive efficiency measured as
bottom time/(dive duration
1 surface recovery time), and
(d) feeding rate over the dive
cycle as a function of target
depth. Each circle represents
one dive. Solid lines: model
predictions.
886
Behavioral Ecology
Figure 5
Observed and predicted values
of dive duration as a function
of target depth for 8 individual
blue whales. Each circle represents one dive. Solid line: model
predictions. (a) tag 0301; (b)
tag 0401; (c) tag 0402; (d) tag
0403; (e) tag 0404; (f) tag 0502;
(g) tag 0602; and (h) tag 0901.
Note: tags 0201 and 0501 contributed only 9 and 6 feeding
dives and thus were not represented here.
feed deep enough. However, blue whales tagged on a California
feeding ground performed 3–5 lunges on average over the
150–300 m depth range (Goldbogen et al. 2011), which corresponds to our predictions and suggests validity of the model
across populations and larger depth ranges.
Body size is the main determinant of a diver’s theoretical aerobic dive limit (TADL). Yet blue and fin whales, the Earth’s
largest predators, have relatively short dive times (Croll
et al. 2001). The high cost of lunging behavior has been proposed as an explanation for this paradox (Acevedo-Gutierrez
et al. 2002). Our results show that this interpretation is incomplete because it does not take into account the ecological
context (prey depth and optimization of energy intake). First,
in the optimal foraging framework, the TADL is not a unique
value but rather depends on the relative time spent foraging
versus traveling (Houston and Carbone 1992). When foraging
is more costly than traveling, the TADL actually decreases with
decreasing target depth (Figure 2c) because predators should
spend an important proportion of their time engaged in
costly foraging. The difference between observed behavior
and the TADL at any particular depth is therefore not as large
as previously suggested. However, optimal dive time and
TADL converge with increasing depth, suggesting the TADL
becomes more constraining at larger depths.
Second, it is in fact optimal to perform dives shorter than
the TADL, especially at shallow depths. Because breath-hold
capacity increases with body mass, large animals that dive
shallowly for ecological reasons could make use of the physiological advantage that their size confers by performing long
dives even at shallow depths (Halsey, Blackburn, and Butler
et al. 2006). We have shown that this was not the case for blue
whales foraging in the St Lawrence Estuary, which performed
shorter dives with fewer lunges at shallow depths (Figures 2
and 3). Similarly, Goldbogen et al. (2011) found no support
for the hypothesis that the number of lunges performed by
Pacific blue whales should increase with decreasing dive
depth. These observations suggest that, in agreement with
optimal theory, blue whales perform shorter dives at shallow
depths because the additional recovery time needed at the
surface if they dived for their entire TADL would decrease
their overall feeding rate.
As predicted, feeding rates were consistently higher at shallow depths (Figure 4d), confirming that diving predators
should forage close to the surface when possible (Kramer
1988; Carbone and Houston 1996). Accordingly, St Lawrence
blue whales concentrated the majority of their feeding activity
at night, when krill was near the surface. Some individuals in
our data set also foraged at shallow depths during the day,
likely taking advantage of particular habitat conditions (e.g.,
currents forcing krill upward or over shallow banks). These
results suggest that, to a certain extent, diving predators may
judge habitat quality in terms of prey accessibility at shallow
depths rather than selecting solely based on prey density or
abundance. Acevedo-Gutierrez et al. (2002) used optimal
models to study the effect of high feeding costs on diving
behavior of rorqual whales, but small sample sizes prevented
them from fully considering the effect of prey depth. We conclude that while the cost of lunges undoubtedly reduces the
duration of feeding dives (via m2), the main reason for blue
whales to perform foraging dives shorter than their TADL is
that it is optimal to do so.
Decomposition of the model error (MSD) showed that most
lack of fit was due to scatter. This could reflect individual preferences and variations in body mass among tagged whales, but
separate examination of individuals showed that all individuals
conformed to model predictions to some degree and that most
of the scatter came from intraindividual variation. Dive time at
a given depth may depend on the quality of food patches
(Mori 1998). Behavioral flexibility should allow individuals
to take advantage of a high-quality patch by feeding more
than predicted and paying the oxygen debt later (e.g., the
individual that took 15 mouthfuls in one dive). Thompson
Doniol-Valcroze et al.
•
Optimal foraging in a diving predator
and Fedak (2001) proposed that simple giving-up rules can
help divers assess patch quality and recognize a poor patch
early in the dive. In this case, it can be beneficial to give up
before reaching the optimal foraging time and start again in
an area of higher prey concentration. The occasional occurrence of wiggles not accompanied by feeding events suggests
that vertical excursions can be exploratory movements or
lunges that were aborted because of poor patch quality. Concurrent measures of krill vertical distribution and density (obtained from in situ measurements or model simulations)
would allow the estimation of feeding efficiency in terms of
net energy gain. Adding this parameter in the optimal model
would presumably explain some of the observed deviance and
improve its explanatory power.
Recovery surface times following deep dives were shorter
than predicted by the model (Figure 4a). Stephens et al.
(2008) recognized the sensitivity of model predictions to a,
the initial proportional rate of oxygen replenishment, and
used an ad hoc coefficient to obtain realistic dive times for
divers of intermediate mass (150 kg). It is possible that this
value of a does not provide a realistic measure of the O2
exchange performance by large whales. Our definition of surface time could also underestimate time allocated to O2 recovery, for instance, if gas exchange continues during the first
few seconds of a dive (before lung collapse) or if an O2 debt is
accumulated and not repaid until the end of a dive bout, as
in Steller sea lions, Eumetopias jubatus (Fahlman et al. 2008).
Conversely, some short dives were followed by longer than
expected post-dive periods, suggesting that other factors, for
example, CO2 build-up due to unequal rates of exchange
between O2 and CO2, can constrain surface times (Boutilier
et al. 2001). Additional efforts are clearly needed to model
respiratory gas exchanges in cetaceans.
Blue whales obtained very advantageous dive/surface ratios
during numerous shallow dives by limiting their recovery time
to a single breath at the surface (i.e., near-instantaneous surface
times of 1–3 seconds). At larger depths, their diving strategy
allowed them to maintain a stable ratio (Figure 4b). This ratio,
however, was 3 times higher than expected, presumably because
surface times were overestimated by the model. Dive efficiency,
measured as bottom time divided by total dive duration plus
surface time, was predicted to peak at the surface and to decrease with increasing depth (Figure 4c). At depths over 20 m,
blue whales followed this pattern at slightly higher values than
predicted but not at shallow depths for which dive efficiency was
lower than expected because of shorter bottom times.
Blue whales performed the predicted number of lunges despite bottom times being slightly shorter than model predictions.
The average difference between predicted and observed bottom
times (;40 s) was roughly half of the mean interval between
lunges. Thus, whales save time by performing the last lunge
during the ascent to the surface, essentially transferring the time
necessary to process water and food into the incompressible
transit time. This is also true for shallow dives with only one
lunge, in which case blue whales were likely coupling respiration
with the purging phase of the lunge, as suggested by Goldbogen
et al. (2011). Combining foraging, ascent and even respiration
thus represents additional strategies to maintain a high lunge
rate and maximize energetic efficiency.
Many marine predators have to optimize a short seasonal
window of feeding opportunity. Recent results from biologging studies in natural systems have provided an increasing
body of evidence that divers employ strategies based on optimal decisions to maximize foraging efficiency. Dive time allocation in diving birds has been shown to vary with distance
(Heath et al. 2007) and prey density (Mori et al. 2002; Cook
et al. 2008) in accordance with theoretical predictions. Diving
seabirds also select optimal stroke frequency patterns during
887
vertical movements (Mori et al. 2010). Differences in the optimal diving depths of penguins can help explain coexistence
of sympatric species (Mori and Boyd 2004b). Seals also seem
to conform to optimal theory when allocating time within
dives (Boyd et al. 1995) and choosing time spent in food
patches of different quality (Mori and Boyd 2004a). Humpback whales have been observed foraging shallower than the
depth of maximal prey density (Goldbogen et al. 2008), fitting
predictions of optimal models (Mori 1998).
Direct measures of how optimal strategies increase feeding
success, however, are rare and altogether missing in large diving
predators like cetaceans. We have shown for the first time that
a simple model of optimal time allocation using allometric arguments can explain not only the dive time budgets of a large marine predator but also its feeding strategies as a function of the
distance between surface and prey. Allometric relationships have
considerable potential for explaining patterns across taxa but
often fail to address specific ecological situations. As suggested
by Stephens et al. (2008), combining optimality and allometry
can better explain the actual foraging choices made by airbreathing divers. With the increasing availability of data loggers
placed on free-ranging animals, this framework opens new avenues of study to better understand the behavior of marine
predators. Such models could help predict responses of predators to environmental changes and anthropogenic pressures,
placing them directly at the interface between ecology and
conservation.
We thank Paul Couture for Visual Basic programming, Robin Baird,
and Michel Moisan for tag development, Yves Morin, Daniel Lefebvre,
Renaud Pintiaud, Michel Moisan, Caroline Guimont, Sean Thompson,
and Jeremy Winn for help with fieldwork, and Becky Woodward for
providing access to the D-tag data. We also thank Sébastien Lemieux
Lefebvre, Arnaud Mosnier, and Frédéric Bailleul for advice on this
project. Finally, we thank Dr Sue Healy, Dr Jeremy Goldbogen, and
one anonymous referee for their constructive comments on the manuscript. This work was supported by the Species at Risk and Oceans
Management programs of Fisheries and Oceans Canada, and by the
Saguenay—St Lawrence Marine Park.
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