Acoustically derived growth rates of sperm whales
(Physeter macrocephalus) in Kaikoura, New Zealand
Brian S. Millera) and Abraham Growcott
Department of Marine Science, University of Otago, P.O. Box 56, Dunedin, New Zealand
Elisabeth Slooten
Department of Zoology, University of Otago, P.O. Box 56, Dunedin, New Zealand
Stephen M. Dawson
Department of Marine Science, University of Otago, P.O. Box 56, Dunedin, New Zealand
(Received 21 June 2012; revised 12 December 2012; accepted 14 December 2012)
A non-invasive acoustic method for measuring the growth of sperm whales was developed based
on estimating the length of individuals by measuring the inter-pulse interval (IPI) of their clicks.
Most prior knowledge of growth in male sperm whales has come from from fitting growth curves to
length data gained from whaling. Recordings made at Kaikoura, New Zealand, were used to estimate the length and growth of 32 photographically identified, resident whales that have been
recorded repeatedly between 1991 and 2009. All whales recorded more than six months apart
(n ¼ 30) showed an increase in IPI. Using established relationships between IPI and total length, it
was found that the average growth rate in the Kaikoura population is lower, especially for smaller
whales (13–14.5 m), than that derived from historical whaling data from other populations. This difference may be due to ecological differences among populations but might also reflect upward bias
in measurements gained in whaling. The ability to track growth of individuals through time is only
possible via non-lethal means and offers a fundamentally different kind of data because differences
C 2013 Acoustical Society of America.
among individuals can be measured. V
[http://dx.doi.org/10.1121/1.4816564]
I. INTRODUCTION
Measuring the length of individuals and quantifying
their growth are fundamental to answering many ecological
questions. Size, as well as being an indicator of physical maturity, can indicate age (e.g., Gaskin and Cawthorn, 1973).
Length distributions can be used to estimate population parameters (e.g., Waters and Whitehead, 1990), and patterns of
growth potentially provide insight into ecological differences
among populations, habitats, and, in the case of sexually
dimorphic species, between the sexes.
Whales, because of their great mass and marine habitat,
are among the most difficult animals to measure alive. For
this reason, most measurement data have come from dead
whales measured at whaling stations or on factory ships (e.g.
Fujino, 1956; Clarke and Paliza, 1972). In some cases, such
data have been deliberately biased (Cooke et al., 1983; Best,
1989; Kasuya, 1999). Nevertheless, whaling data have been
useful in quantifying the basic growth parameters of species
(e.g. Kasuya, 1991). Previous studies of growth in male
sperm whales (Nishiwaki et al., 1963; Gaskin and Cawthorn,
1973; Lockyer, 1981) are few in number and rely upon age
and length data from various 20th century whaling catches.
However, many of the most interesting ecological questions
require individuals to be measured repeatedly throughout
their lives, which is impossible in whaling. While various
a)
Author to whom correspondence should be addressed. Electronic mail:
[email protected]
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Pages: 2438–2445
photogrammetric approaches have been applied to the task
of measuring free-ranging whales (e.g. Cubbage and
Calambokidis, 1987; Best and R€uther, 1992; Gordon, 1991,
Dawson et al., 1995; Jaquet, 2006), none have been applied
sufficiently often, and over a long enough period, to provide
much useful information on growth. New developments in
the theory of how sperm whales make their clicks (Møhl
et al., 2003) facilitate measurement of individual whales
acoustically and by recording the same individuals over
many years, enable quantification of their growth.
The typical vocalizations of sperm whales are broadband echolocation clicks that often show a multiple pulse
structure (Backus and Schevill, 1966). Norris and Harvey
(1972) hypothesized that this multiple pulse structure arises
from a single impulsive sound, created at the museau de
singe, that is reflected within the head of the whale and
hence that time interval between these pulses represents the
time taken for sound to travel the length of the spermaceti
sac. Hence the hypothesis predicts that due to allometric
relationships between head length and whale length, the
inter-pulse interval (IPI) can be used as a measure of whale
length. Rhinelander and Dawson (2004) showed that IPIs are
stable within individuals over short periods and vary among
individuals of different length, confirming that IPIs are a
reliable measure of whale length. Gordon (1991) and
Rhinelander and Dawson (2004) used simple photogrammetric techniques to measure whale length and quantified the
relationship between photogrammetrically measured length
and IPI. Gordon derived this relationship mostly from
0001-4966/2013/134(3)/2438/8/$30.00
C 2013 Acoustical Society of America
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Author's complimentary copy
PACS number(s): 43.80.Ka, 43.64.Tk, 43.80.Jz, 43.64.Yp [JJF]
L ¼ 1:257 I þ 5:736;
ðn ¼ 33; r2 ¼ 0:77; SE0:0201 m=ms and 0:1239 mÞ:
(1)
Methods of computing IPI have also advanced recently.
Adler-Fenchel (1980), Gordon (1991), Goold (1996),
Rendell and Whitehead (2004), and Rhinelander and
Dawson (2004) computed IPI from recorded sperm whale
clicks using various signal processing techniques and classification criteria but from a small number of carefully
selected individual clicks. Large numbers of clicks were considered unsuitable for analysis and discarded because they
did not show the multipulse structure clearly.
After investigating the radiation pattern of sperm whale
clicks, Møhl et al. (2003) proposed the bent-horn model of
sound production, which is a refinement of the original Norris
and Harvey model. The new theory explains why many clicks
do not appear to contain a clear multi-pulse structure
(Zimmer et al., 2005a). According to the bent horn model,
only on-axis clicks, recorded either directly in front of or
behind the acoustic axis of the whale, exhibit a clear-multi
pulse structure. The time delay between pulses of an on-axis
click corresponds to the acoustic propagation delay as sound
travels from the museau de singe reflects off the frontal sac
and travels forward out of the anterior surface of the junk. In
off-axis clicks, these pulses are present but obscured by interference arising from the off-axis angle of the whale (Zimmer
et al., 2005a). In the earlier studies of sperm whale IPI mentioned in the preceding text, the discarded clicks were most
likely to have been recorded off-axis.
A new approach to IPI computation, based on the bent
horn model of sound propagation, was proposed by Teloni
et al. (2007). They postulated that the ensemble average of
the cepstrum of hundreds of clicks should yield a consistent
estimate of IPI. Using statistical bootstrapping, Antunes
et al. (2010) were able to supplement and adapt the methods
of Teloni et al. (2007) orer to estimate IPIs from recordings
containing as few as 50–400 clicks. Antunes et al. found that
autocorrelation based methods of IPI computation were the
most reliable for IPI computation; however, they found that
when using small number of clicks occasionally cepstral
methods converged when autocorrelation did not. The
advance offered by the Teloni et al. (2007) method is considerable; it is not only objective, which facilitates automation,
but also requires fewer assumptions than previous criteria
for computing IPI and hence allows for analysis of additional
recordings not previously considered suitable for IPI measurement, thus increasing sample size.
The acoustic data set from Kaikoura contains dozens of
individuals that have been recorded many times, and over
J. Acoust. Soc. Am., Vol. 134, No. 3, Pt. 2, September 2013
many years (maximum 14.7 yr), and most of the audio
recordings in this data set come from photographically identified whales. Growcott et al. (2011) described the relationship between IPI and length. Here we build upon that
knowledge, implementing the approach of Teloni et al.
(2007) to IPI measurement to quantify growth of individuals
recorded repeatedly over many years. To our knowledge,
this is the first application of passive acoustic methods to
measure growth in any marine mammal.
II. METHODS
A. Data collection
Data for this project were collected from 1990 to 2009
as part of a long-term research program off Kaikoura, New
Zealand, conducted by Otago University’s Marine Mammal
Research Group. In brief, data collection involved making
acoustic recordings of photographically identified whales
(Arnbom, 1987; Childerhouse et al., 1996). Field work from
1990–2000 was previously described by Rhinelander and
Dawson (2004). All recordings analyzed in the original study
by Rhinelander and Dawson (2004) were made directly
behind whales after they fluked up to ensure that the first
8 min of recordings contained clicks that were largely parallel to the main acoustic axis as the whale descended.
Additional photographic and acoustic data collection
occurred in 2002 and between 2005 and 2009. The 2002
recordings were made with the same Sonatech 8178 hydrophone, Sony TCDD10-PROII digital audio tape recorder,
and protocols for acoustic recording and photographic identification from 1996 to 2000. Recordings from 2005 were
made with a custom-built stereo hydrophone array similar to
that described by Barlow et al. (2008) and a laptop running
ISHMAEL software with a National Instruments DAQ6062E
data acquisition card (2005–2006) or an Edirol R4 hard disk
recorder (2006–2009). Hydrophones in the stereo hydrophone array were not individually calibrated, but an identical
array had a reasonably flat (64 dB) frequency response from
2 to 40 kHz (Barlow et al., 2008). The Edirol R4 and
National Instruments 6062E were set to 96 kHz sample rate
and had a flat frequency response from 10 Hz to 40 kHz
(3 dB). A pinger producing a tone of 10.100 kHz was used
to check that sampling rates were accurate, and an adjustment was applied to data recorded using the NI 6062E to
correct for discrepancies between the requested and actual
sampling rate. The 6062E data acquisition card sampled
with 12-bit precision, while the Edirol R4 was set to either
24 -or 16-bit precision. PAMGUARD (version 1.6) was only capable of using 16-bit wav files, so 12 -and 24-bit recordings
were converted to 16-bit wav files before analysis. The
hydrophone elements on the stereo array were spaced 5 m
apart and the deepest element was deployed to a depth of either 65 or 105 m.
B. Data analysis
A custom software plug-in implementing the IPI computation method from Teloni et al. (2007) was developed for
the computer program PAMGUARD (version 1.6). PAMGUARD is
Miller et al.: Acoustically measured growth in sperm whales
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juvenile and female whales, while Rhinelander and Dawson
measured pubertal and mature male sperm whales between
12.5 and 15.2 m in length. Growcott et al. (2011), using a
new digital stereophotogrammetric system, has extended the
number of individuals with independent measures of IPI and
length, facilitating a new regression equation for IPI (I measured in ms) and photogrammetric length (L measured in
meters) (Growcott et al., 2011)
Ct ¼ FFT 1 ½logðjFFTðxt ÞjÞ;
(2)
where xt is the digital representation of the time domain
waveform and FFT and FFT-1 are the fast Fourier transform
and inverse fast Fourier transform, respectively, as in Teloni
et al. (2007). The time delay at the peak of the cepstrum was
stored as the IPI of that click and used to create a histogram
of IPI for each recording. On a basic level, this IPI histogram
was similar to the methods used by Rhinelander and Dawson
(2004), who estimated the IPI from the autocorrelation function of individual clicks and then computed the mean and
standard error of all IPIs.
In addition to constructing the IPI histogram, the plug-in
also computed the ensemble average of the cepstrum from
all detected clicks. The peak value of the ensemble average
of the cepstrum was located and the time delay of the peak
kept as the ensemble IPI as described by Teloni et al.
(2007). The ensemble IPI computation allows analysis of
recordings that were made from arbitrary locations with
respect to the whale. Implementing both methods in the
module required little extra processing, and facilitated comparison of the methods (see Sec. III).
The peak width of the ensemble IPI was used as the
measure of uncertainty for each recording. Peak widths were
measured at 75% of the maximum value, a value that was
empirically shown to give reasonable results. A threshold
width of 1 ms was used to exclude measurements with high
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J. Acoust. Soc. Am., Vol. 134, No. 3, Pt. 2, September 2013
uncertainty (typical IPI values ranged from 5 to 8 ms). Of
279 analyzed recordings, only two were excluded due to
high uncertainty. We compared the IPI histogram and ensemble IPI results from the PAMGUARD plug-in to the IPIs of
36 recordings from the same data set that had been analyzed
previously by Rhinelander and Dawson (2004).
For computation of growth rates, all recordings of each
individual whale were considered for analysis if the total
time between first and last recordings spanned 6 months or
more. IPIs from these recordings were obtained using the
PAMGUARD IPI plug-in, and the mean of all recordings made
within 6 months of each other was taken as an average measure of IPI for each individual during the years that they
were recorded. Average growth rates, g(t), were then computed for each consecutive pair of mean IPIs as
gðtÞ ¼
Lðtnþ1 Þ Lðtn Þ
;
tnþ1 tn
(3)
where tn is the time of the average measurement and L is the
length derived from the average IPIs using Eq. (1).
Direct comparison among growth rates in Kaikoura to
those obtained from whaling data was not possible due to the
lack of age data on individuals in Kaikoura. Furthermore, no
analytical functions (e.g., von Bertalanffy growth curves)
were fitted to whaling data by their original authors.
Nishiwaki et al. (1963) and Lockyer (1981) published only
hand-drawn curve fits without the raw data, and Gaskin and
Cawthorn (1973) published a subset of their data along with
their hand-drawn curve fit. To compare our results with
measurements made during whaling, we compared growth
as a function of length. A piecewise polynomial smoothing
spline was fit to digitized growth curves published by
Nishiwaki et al. (1963), Gaskin and Cawthorn (1973) and
Lockyer (1981), and instantaneous growth rate was computed via differentiation and plotted as a function of whale
length (Fig. 3). These instantaneous growth rates were then
comparable to the average growth rates estimated in this
study.
III. RESULTS
A. Comparison of IPI computation methods
There was good correspondence between the ensemble
IPI and IPIs measured manually by Rhinelander and
Dawson (2004) for all 36 recordings, and the mode of the
IPI histogram had good correspondence between paired
measurements for 34 of the 36 recordings. For all of these
recordings, the number of detected clicks used by the
PAMGUARD plug-in for IPI measurement ranged from 105 to
2604, while the number of clicks used by Rhinelander and
Dawson ranged from 6 to 45. Linear regression between the
ensemble IPI estimate, I, and those computed by
Rhinelander and Dawson (2004), x, reveal an excellent oneto-one relationship (I ¼ 1.01 * x þ 0.0096; r2 ¼ 0.952; solid
line Fig. 1). The relationship between the modal value of the
IPI histogram, H, did not show as good a relationship with
the Rhinelander and Dawson measurements (H ¼ 1.21 *
x 1.65; r2 ¼ 0.368; dashed line Fig. 1), indicating that the
Miller et al.: Acoustically measured growth in sperm whales
Author's complimentary copy
freely available, open source software for passive acoustic
monitoring (Gillespie et al., 2008). The IPI plug-in presented
here depends on the basic functionality provided by
PAMGUARD core modules. Existing PAMGUARD plug-ins used in
this study include the hydrophone array manager, multichannel data acquisition (both from live input and archived
audio files), bandpass filters, and click detection.
Acoustic data were first high-pass filtered with an eighth
order Butterworth filter using PAMGUARD’S IIR filter module
with the corner frequency set to 1.5 kHz. Filtered data were
then input into PAMGUARD’S built-in click detector. For single
hydrophone recordings, the click detection threshold was set
so that detected clicks correspond to those from the target
whale (which was typically the loudest in a recording). For
stereo recordings, the click detection threshold was usually
set lower, and the built-in angle vetoes of the click detector
adjusted so that only clicks coming from the target whale
were kept. The angle veto works by excluding clicks from
further analysis if they have a bearing that is dramatically
different than that of the target whale. The time window for
detected clicks was set to 40 ms with 10 ms preceding the
detection and 30 ms following the detection. Detected clicks
were then used as input into the IPI computation plug-in.
IPI measurement followed the methods outlined by
Teloni et al. (2007) and to a lesser extent Rhinelander and
Dawson (2004). Before IPI measurement, the IPI plug-in filtered any clicks that had more than three consecutive samples within 90% of the full scale amplitude to exclude clicks
that had been clipped, as the cepstrum of a clipped waveform
could be distorted by artifacts. Next, the cepstrum of each
individual click was computed as
TABLE I. IPI measurement summary showing the number of recordings, n,
number of years spanned; initial IPI, I0; last IPI, It; initial size, L0; last size,
Lt; change in size, DL; and average growth over all years, DL/Dt for each
whale. IPIs are measured in milliseconds, while lengths are measured in
meters.
FIG. 1. Comparison of interpulse intervals (IPIs) computed by Rhinelander
and Dawson (2004) with Pamguard IPI plug-in. Circles and solid line show
the ensemble average and fit, while squares and dashed line show the mode
from the IPI histogram. Error bars show the peak width at 75% of the peak
amplitude. The dotted line shows a perfect one-to-one relationship.
ensemble IPI method provides the most similar results to
those of Rhinelander and Dawson (2004).
B. Acoustically measured growth rates from Kaikoura
Thirty-two whales were recorded over multiple field
seasons, and all whales showed an increasing or stable IPI
over time (Table I). Nine whales were recorded on several
occasions over time spans of more than 8 yr, and all of these
whales showed an increase in IPI over the total time,
although not every whale showed growth over all consecutive recordings (Fig. 2. There was not a strongly predictive
relationship between growth rate and length for whales
measured in this study; however, the growth rates of the fastest growing whales were almost all lower than the average
growth rates measured during industrial whaling (Fig. 3; see
Sec. IV).
Whale
n
Years
I0
It
L0
Lt
DL
DL/Dt
HL120
HL140
HL160
HL190
HL40
HR110
HR210
HR25
HR80
LNL100
LNL160
LNL240
LNR200
LSL20
LSR100
LSR40
LSR60
MLN160
MLN40
MLN80
MLS100
MLS70
MNS50
MTB170
MTL40
MTR100
MTR140
MTR80
NN160
NN20
NN40
NN80
5
6
21
3
25
5
5
2
11
6
28
6
2
9
3
4
10
8
8
6
9
6
15
4
4
4
11
6
13
20
2
8
6.92
9.20
9.24
5.07
8.60
0.48
7.01
2.12
5.78
7.58
9.59
7.02
0.50
8.54
2.05
0.93
8.56
2.75
13.03
2.10
14.73
2.02
3.98
1.10
3.07
2.59
7.59
5.50
3.95
11.00
4.86
3.07
6.563
6.396
6.208
8.229
6.354
5.800
6.458
5.863
7.646
6.802
6.167
6.375
6.521
6.417
5.906
6.438
6.229
7.781
7.229
6.583
6.739
7.250
6.443
6.188
5.708
6.250
6.708
6.333
7.167
6.083
6.688
6.521
6.708
7.118
6.879
8.292
7.255
5.800
7.443
6.000
7.708
7.208
7.188
7.146
6.521
7.417
6.042
6.472
7.188
7.833
7.375
6.799
7.191
7.448
6.662
6.208
5.958
6.722
7.554
6.542
7.420
6.578
7.042
6.809
13.95
13.75
13.51
16.02
13.69
13.01
13.82
13.09
15.30
14.25
13.46
13.72
13.90
13.77
13.14
13.80
13.54
15.46
14.78
13.98
14.17
14.81
13.80
13.49
12.89
13.57
14.13
13.67
14.70
13.36
14.11
13.90
14.13
14.64
14.35
16.10
14.81
13.01
15.05
13.26
15.37
14.75
14.73
14.68
13.90
15.01
13.31
13.84
14.73
15.53
14.96
14.25
14.73
15.05
14.08
13.51
13.20
14.15
15.18
13.93
15.01
13.97
14.55
14.26
0.180
0.896
0.833
0.078
1.118
0.000
1.222
0.170
0.077
0.504
1.266
0.956
0.000
1.240
0.168
0.043
1.189
0.064
0.181
0.267
0.560
0.246
0.271
0.025
0.310
0.585
1.050
0.259
0.310
0.614
0.439
0.357
0.026
0.097
0.091
0.015
0.130
0.000
0.174
0.080
0.013
0.066
0.132
0.136
0.000
0.145
0.082
0.046
0.139
0.023
0.014
0.140
0.038
0.135
0.071
0.023
0.101
0.227
0.143
0.047
0.079
0.056
0.090
0.119
Both the ensemble IPI, and the mode of the IPI histogram, as computed by the PAMGUARD plug-in, provide an
automated estimate of IPI that is very similar to the manual
measurement methods used by Rhinelander and Dawson
(2004); however, the ensemble IPI appears to be slightly
more robust than the IPI histogram (Fig. 1). The automated
nature of the analysis greatly reduces the time required to
estimate IPI; however, automated analysis should be used
with caution when multiple whales have been recorded
simultaneously. In these cases, the threshold for click detection should be adjusted, or preferably other Pamguard modules, such as angle vetoes, should be used to remove clicks
from other whales.
Reanalysis of the Rhinelander and Dawson data shows
that the automated method works surprisingly well even
with as few as 105 clicks. Teloni et al. (2007) suggested
using at least 1000 clicks for stable results. The present
results indicate that fewer clicks can be used under some circumstances, e.g., when using high quality recordings made
directly behind the whale after fluke up. Antunes et al.
J. Acoust. Soc. Am., Vol. 134, No. 3, Pt. 2, September 2013
(2010) found a similar result when investigating semiautomated approaches for computing IPI given a small number of recorded clicks. While they suggest additional statistical and signal processing methods, these methods were
deemed unnecessary because our recordings had large numbers of loud clicks (median of 744 clicks/recording), and the
ensemble average showed little uncertainty with all our
recordings.
By applying the PAMGUARD plug-in to a long term data
set, we were able to observe an increase in IPI over time for
30 of 32 whales in Kaikoura. The two whales that showed
no increase in IPI were both seen only on two occasions less
than 6 months apart. The only parsimonious explanation for
increase in IPI over time is individual growth. The fact that
no individuals showed fluctuation in IPI over time provides
further validation of the IPI computation method described
by Teloni et al. (2007) and, incidentally, further supports the
bent horn model of sound production.
Applying Eq. (1) to these IPI estimates allows us to estimate whale length (Table I; second vertical axis in Fig. 2).
Miller et al.: Acoustically measured growth in sperm whales
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IV. DISCUSSION
We estimated growth rates for all whales that had both identification photographs and recordings that were made greater
than 6 months apart. This is the first time that acoustic estimates of whale length have been used to derive measurements of the growth of individual whales. In contrast to
growth rate measurements made during whaling (Nishiwaki
et al., 1963; Gaskin and Cawthorn, 1973; Lockyer, 1981) or
from stranded animals (e.g. Evans and Hindell, 2004), this
technique is not only non-lethal but also completely noninvasive.
While growth of individuals could be measured using
photogrammetric techniques only (e.g., Durban and Parsons,
2006; Rowe and Dawson, 2008; Webster et al., 2010), there
are several advantages to the acoustic methods presented
here. Stereo photography requires manoeuvring alongside of
the whale (Dawson et al., 1995), which can cause the whale
to turn away or dive early, especially when other vessels
(such as whale watching boats) are present (Richter et al.,
2006). Additionally, identification photographs of the whale
must be taken from directly behind the whale, requiring
additional manoeuvring. In contrast, audio recordings of the
whale can be made from any position, including behind the
whale, which compliments rather than conflicts with the photographic identification efforts. Stereo photogrammetry presently requires a somewhat cumbersome system of two
cameras on either end of a 2.4 m bar, attached, at eye height,
to a short mast. Analysis of the image requires expensive
proprietary software. IPI measurements can be made using
using a single hydrophone, field recorder, and free open
source software. Furthermore, IPI measurements have been
demonstrated to be more precise than all of the photogrammetric techniques reported in Growcott et al. (2011).
There are some inherent limitations when measuring
growth rates of sperm whales acoustically. Unless the
researcher is able to track individual whales at depth using a
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hydrophone array, the approach will be more difficult to use
when multiple whales are diving in close proximity. Hence it
is more practical at higher latitudes, where whales are typically spaced further apart (Gaskin, 1970); however, it should
be noted that most of the IPI measurements reported by
Antunes et al. (2010) came from low latitudes. In nursery
groups where many whales are closely grouped together and
dive in synchrony, it is unlikely that IPIs could successfully
be matched to particular individuals. It should be noted that
the limitation stated above arises from the inability to match
photographs with acoustic records for nearby individuals and
not from any inherent limitation in the PAMGUARD IPI plug-in.
Lockyer (1981) noted continued growth in male sperm
whales until they reached physical maturity (at an average
length of 15.85 m). Most of the whales recorded repeatedly
in Kaikoura were between 13 and 15 m and still growing.
This suggests that these whales are socially mature but not
yet physically mature. Age-length keys from Nishiwaki
et al. (1963) and Gaskin and Cawthorn (1973) give age estimates of approximately 17–30 yr for this length range, while
Lockyer (1981) estimates 25–35 yr. The fact that some of the
whales in this study have been seen at Kaikoura for at least
19 yr (eg. NN20, MLS100, HL40) is in accord with these
age estimates.
Growth rates at Kaikoura (Fig. 3) appear well below
those derived from whaling in the Southeast Pacific
(Lockyer, 1981), and most are lower than those from whaling in the North Pacific (Nishiwaki et al., 1963). Perhaps
unsurprisingly, our acoustically measured growth rates
match most closely with those derived from whaling in
Cook Strait (a superset of our study area) in 1963 and 1964
(Gaskin and Cawthorn, 1973), although they still appear to
be slightly lower. Because Gaskin and Cawthorn published
neither error estimates nor raw data for their growth curve, it
is not possible to say whether these differences are
Miller et al.: Acoustically measured growth in sperm whales
Author's complimentary copy
FIG. 2. Interpulse interval (IPI) measurements of nine different whales
recorded over 8 yr or more from 1991
to 2009. Crosses show ensemble average IPIs from independent recordings
and error bars show the IPI peak width
at 75% of the maximum. Note that
error bars refer only to the IPI values
(left axis) and not the length estimates
(right axis). Lines connect average IPI
measurements from consecutive six
month observation periods. Lengths
are derived from Eq. (1).
statistically significant. However, assuming that these differences are real, they could be driven by differing measurement methodology (e.g., measuring tape vs IPI), bias in
whaling data, differences among populations, or density dependent changes.
Our measurement methods, which rely on the relationship between IPI and photogrammetrically measured
lengths, could hardly be more different from measuring dead
whales killed in whaling. Variability in our photogrammetric
estimates arises chiefly from the difficulty of locating exactly
J. Acoust. Soc. Am., Vol. 134, No. 3, Pt. 2, September 2013
Miller et al.: Acoustically measured growth in sperm whales
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FIG. 3. Average growth plotted for measurements with the longest time
span (a) and for each consecutive measurement period (b) and for all individuals. Lengths are derived from interpulse intervals (IPI)s using Eq. (1).
The dashed, dotted, and solid lines show growth of male sperm whales
derived from Nishiwaki et al. (1963), Lockyer (1981), and Gaskin and
Cawthorn (1973), respectively.
the same point to measure from, and the fact that whales are
inherently flexible (Dawson et al., 1995; Growcott et al.,
2012). Gaskin and Cawthorn’ estimates of growth, like those
of Lockyer (1981) and Nishwaki et al. (1963), are based on
lengths measured from dead whales and ages estimated from
counting growth layer groups in teeth. The specific criteria
used for aging were not published by these authors; however,
Evans et al. (2002) reveal substantial differences in the number of growth layers counted among different readers. Also,
tooth wear often removes outer growth layers making older
(larger) individuals appear to be younger than they truly are.
Thus caution is required when comparing the age-length
data from dental growth layers (e.g., Nishiwaki et al., 1963;
Gaskin, 1973; Lockyer, 1981) to the acoustically derived
growth rates.
Wholesale misreporting of whale catches occurred during post-WWII whaling (Zemsky et al., 1995). More subtle
distortion of recorded data also occurred (e.g., Best, 1989;
Kasuya, 1999). Sperm whale catches were managed in part
via minimum length limits. The Russian and Japanese data
from the 1960s and 1970s show a knife-edge distribution of
body lengths at the minimum allowable length (Allen, 1980;
Cooke et al., 1983). This feature is also seen in length data
from the Taiji land station in Japan, (Kasuya, 1999) and also
in data from Durban in South Africa (Best, 1989). Assuming
that the data were not entirely falsified, and that the gunners
were not almost supernaturally gifted at estimating the
length of whales before they harpooned them, it appears that
whalers routinely recorded exaggerated lengths for whales
that were under the limit (Cooke et al., 1983; Best, 1989;
Kasuya, 1999). Hence it is possible that the growth curves
published from whaling data are biased. Exaggeration of
lengths recorded from whales near the length limit would
have the effect of overestimating growth at this life-stage.
It is also possible that growth rate varies among populations. If true, either the whales that repeatedly return to
Kaikoura are not growing as fast as the whales caught during
whaling, or the Kaikoura population does not grow as large as
those taken during whaling. Gaskin and Cawthorn (1973) published the lengths of 238 male sperm whales caught in the
Cook Straight area (which includes our study site) from 1963
to 1964. They reported a mean length of 14.09 m with a minimum length of 10.7 m and a maximum of 16.8 m. The mean
of the initial lengths, I0 in our study was 13.96 m, and the
mean of the final lengths, In, was 14.44 m, both of which are
very similar to the mean reported by Gaskin and Cawthorn;
however, the distributions of lengths were significantly different (Fig. 4; Kolmogorov-Smirnov test; maximum difference
between distributions, D ¼ 0.2877 m; p ¼ 0.0145). The discrepancy between length distributions is likely explained by
our study area being much smaller, and there may have been
some size selectivity on behalf of the whalers in 1963 to 1964.
Both Kasuya (1991) and Kahn et al. (1993) suggested
that density dependent effects on sperm whale size resulted
from the removal of large numbers of whales during commercial whaling. Kasuya (1991) noted an increase in the
length distribution of males and attributed this change to an
increase in available food (or decrease in competition for
food). Similarly, Kahn et al. (1993) found differences in
FIG. 4. Length frequency distributions of whales caught during commercial
whaling and measured acoustically. Solid line shows length distribution of
238 whales caught and measured in 1962/63 (Gaskin and Cawthorn, 1973)
while the dotted and dashed lines show the distribution of initial and final
length distributions of 33 whales measured in this study.
length distribution of females off the West coast of South
America. Both of these studies observed changes five to ten
years after the end of the intensive whaling effort. Sperm
whales were hunted in the Southwest Pacific around New
Zealand from the 1830s until as recently as 1970 with
catches from 1961 to 1970 totaling at least 9720 whales of
which nearly 75% were male (Gaskin, 1973). Sperm whales
are strongly k-selected, and their populations grow very
slowly, probably around 1% p.a. (Whitehead, 2003).
Because the global population in 1999 was estimated to be
around one-third of prewhaling levels (Whitehead, 2002) it
seems extremely unlikely that populations have recovered
sufficient for density dependence to slow individual growth.
V. CONCLUSION
Coupling new analysis techniques with long-term monitoring efforts (in the form of photographic identification and
audio recordings) has provided a unique opportunity to measure acoustically the growth of individual sperm whales in
Kaikoura, New Zealand.
While the idea of acoustic measurement of sperm whale
whale length is not new (Gordon, 1991; Goold, 1996;
Rhinelander and Dawson, 2004; Mathias et al., 2009), this
study does represent the first application of this non-lethal
technique to measure growth of individual whales. It is
hoped that the freely available software presented here will
enable more researchers to add acoustic length estimates to
their analysis toolbox. The plug-in features fully automated
IPI estimation, the ability to work with real-time input as
well as post-processing of archived data. Contact the authors
for a copy of the IPI plug-in.
ACKNOWLEDGMENTS
We thank our colleagues who collected data, Olaf
Jaeke, Lesley Douglas, Quinn Rhinelander, Christoph
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