SC/F16/JR14

The number of sperm whales in the western North Pacific in
the JARPN II Offshore survey area
TAKASHI HAKAMADA AND KOJI MATSUOKA
The Institute of Cetacean Research, 4-5, Toyomi-cho, Chuo-ku, Tokyo, 104-0055, Japan.
Contact E-mail: hakamada@cetacean,.jp

ABSTRACTThe number of sperm (Physeter macrocephalus) whales in the western North Pacific in early andlate seasons in the JARPNII offshore component were estimated based on 2008-2014 JARPNII
surveys. The numbers are to be used for input of ecosystem modeling of the western North
Pacific. Given that the area is a migration corridor of the whales, the numbers were estimatedfor early season (May-June) and late season (July-Sep.). The estimates were 11,459 (in 2009)
and 11,652 (in 2011 and 2012) in the early and 10,843 (in 2008) in the late season for the sperm
whales. It is important to note that these estimates should not be used for assessment because theestimated figures represent only a part of the population considered.
INDTRODUCTION
It is important to estimate prey consumption and to develop ecosystem models. The number of whales inthe study area can be used for prey consumption estimates and ecosystem modelling. From the previous
results, prey species are different between early and late seasons (Tamura et al., 2009) and therefore theecosystem in the JARPN II survey area may be different in the early and the late seasons. For this reason,
the number of whales distributed are estimated in the early (May - June) and late (July – September) seasons,respectively.
MATERIALS AND METHODS
Sighting data used in this study
Dedicated sighting surveys were conducted during 2008-2014. Among the surveys, survey data thatcovered the JARPN II survey area (i.e. east of Japanese coast, west of 170oE, north of 35oN, south of
Russian and US EEZ) were used for this analysis. Survey period and vessels for these surveys are shownin Table 1. The numbers of whales distributed in the JARPN II survey are were estimated in early (MayJune) and late season (July-Sep). Considering the survey period and survey area, there are three data sets
to estimate the number of the whales in the JARPN II survey area. For the early season, the numbers were
estimated for the 2009 survey, and 2011 and 2012 1st surveys combined. For the late season, the numbers
were estimated for the 2008 survey. Figures 1 shows plots of primary effort and sightings for the sperm
whales in the early and late seasons. Primary sightings of the sperm whales were distributed uniformly in
the JARPN II survey area in the early and the late seasons.
Abundance estimation
Analytical procedures are similar to Hakamada and Matsuoka (2015).
For this analysis it is assumed that g(0)=1. Detections are truncated at 3.0 n.miles for sperm whales.
Abundance and its CV were estimated based on a Horvitz-Thompson like estimator of abundance expressedby formula (1) and (2), respectively.

P==

A n si∑
2WL i =1 p i ( z i )A n ˆ∑ s i f (0 | z i )2 L i =1

(1)

where P is abundance estimate, A is area size of the surveyed area, W is truncation distance (3.0 n.miles),1

L is searching effort, n is the number of schools detected within perpendicular distance of W, si is school
size of ith detection, pi(zi) is the probability that school i is detected given that it is within the perpendiculardistance W and given the covariate zi. f(0|zi) is conditional probability density function of distance 0 given
covariates zi
2
2
K
r
r
 PCk PC 
∂PC ∂PC −1 1 A  
−+var(P ) = l
H jm (θ ) (2)
 
∑k
∑∑
L 
 2WL   L( K − 1) k =1  l k
j =1 m =1 ∂θ j ∂θ mwhere K is the number of transect, lk is searching distance in kth transect, PCk is abundance estimate incovered region (within 3 n.miles from track line surveyed) in kth transect, PC is abundance estimate in the
covered region, Hjm-1(θ) is the jmth element of inverse of Hessian matrix of detection function for covariateθ.
Multiple Covariate Distance Sampling (MCDS) Engine in DISTANCE program was used (Thomas et al.,2010). Given previous discussions at the IA sub-committee on detection function (IWC, 2015), Half Normaland Hazard Rate models were considered as candidate models for the detection function. Full model of thedetection function was provided by
−b

 
g ( x) = 1 − exp−  x
a exp(Size + Beaufort + Year ) 
 

 2

g ( x ) = exp − x
2

2
a
exp
{
2
(
Size
+
Beaufort
+
Year
)
}


(3)

(4)

where x is perpendicular distance, a and b (b≧1) are parameter, Size is observed school size, Beaufort iscategorical variable for Beaufort sea state (good: 0-3, bad: 4-5) and Year is categorical variable for year. To
estimate detection function, all primary sightings occurred during 2008-2014 were used.
AIC was used to select the best model to estimate detection probability of 1/Wf(0|zi).
Smearing was not conducted on running MCDS because MCDS doesn’t deal with smearing. Perpendiculardistance was not binned on fitting detection function because selection of cut point could affect results ofmodel selection and coefficient estimates of detection function different from previous analysis.
Sensitivity analysis
Effect of including/excluding covariates in the detection function such as Beaufort sea state, school size
and year were examined. If difference in AIC of detection function is not substantially different among
the models, weighted average by Akaile weight (Buckland et al, 1997; Burnham and Anderson, 2002)
would be estimated.
Averaged abundance
Average of abundance estimates base case and in sensitivity analysis were also estimated. By using
Akaike weight, weight is larger as the model is better. Akaike weights are defined as follows;exp(− ∆AICi 2 )wi = 16∑ exp(− ∆AIC j 2)

(5)

j =1

The weighted average of the abundance estimates Pw and their standard errors were estimated byequations as follows.

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16

Pw = ∑ wi Pi

(6)

i =1

∑ w var(P ) + 2∑ w w cov(P , P )2i

CV ( Pw ) =

i

i =1

i

j

i≠ j

Pw

i

j

(7)

where

∆AICi = AICi − AIC min (8)RESULTSThe number of the whales distributed in JARPN II survey area
Table 2 shows AIC for each model of detection functions for sperm whales. Hazard rate model with
Beaufort and Year as covariate was selected. Figure 2 shows plot of the selected detection function for
sperm whales. Figure 3 shows QQ-plot of the detection function for the sperm whales. These figuressuggests the fit of the detection function good. Table 3 shows the estimated number by strata for sperm
whales. Table 4 shows abundance estimate in the early season for sperm whale. The numbers of the whalesin the early season were estimated for 2008 and 2011+ the 1st survey in 2012 combined in each stratum.
Table 5 shows the estimated number of the whales distributed in the late season for sperm whales. The
numbers in the late season were estimated for 2009. The numbers in the JARPN II survey area are similar
to each other in the early and the late seasons.
Sensitivity analysis
Table 6 shows that the number of the whales distributed shown in Tables 4 and 5 would change when
applying detection functions other than the best model. For comparison, the estimated number applying thebest detection function is also included in the table. Table 7 shows weighted averages using Akaike weight.
CVs are under-estimates because variances of AIC are not taken into account. The difference in point
estimate is small. The estimated number in 2011+ the 1st survey in 2012 combined is less robust than othertwo estimates. This is because the difference in the estimate between hazard rate model and half normal
model is larger for 2011+ the 1st survey in 2012 combined than the other two estimates.
DISCUSSION
Assumption that g(0)=1 causes underestimation of the number for the sperm whales. Barlow and Sexton(1996) estimated g(0) for sperm whales is 0.87 with CV = 0.09 based on synchronously diving whales
with a 30-min dive cycle (25-min dives followed by 5 min at the surface). Whitehead (2002) derived thatg(0) for the sperm whales depends on the time period for which a sperm whale at the surface on the trackline of the survey vessel is visible considering diving behavior. The time period can be estimated using
the distance that the observer can detect the sperm whales and vessel speed. The estimate of g(0) couldchange if the Beaufort sea state and school size affects the detectability of schools. Investigation of g(0) is
necessary in the future to provide for unbiased estimates of the number of sperm whales.
The estimated number of sperm whales is similar for the early and the late seasons while the estimatednumber is different between the early and the late seasons for large baleen whales (Hakamada andMatsuoka, 2016a: SC/F16/JR12; 2016b: SC/F16/JR13). In previous analysis the abundance was estimatedas 15,929 in the early and 20,292 in the late seasons assuming g(0)=0.64 (Hakamada et al., 2009), whichcorresponds to 9,592 and 12,279 under the assumption that g(0)=1. The difference between these two
estimates is larger than that of present study. Whether these results imply that the number of sperm whales
doesn’t change from the early season to the late season cannot be confirmed at this stage and should befurther investigated.
ACKNOWLEDGEMENTS
Authors thank all researchers and crews involved in the JARPN II dedicated sighting surveys. Doug
Butterworth is thanked for his comments to improve the manuscript of an earlier version of this paper.

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Hajime Nakamichi is thanked for his help in data preparation and running the DISTANCE program.
REFERENCE
Barlow, J. and Sexton, S. 1996. The effect of diving and searching behavior on the probability ofdetecting track-line groups, g0 , of long-diving whales during linetransect surveys. NOAA National
Marine Fisheries Service, Southwest Fisheries Center Administrative Report LJ-96-14. 21pp.
Buckland, S. T., Burnham, K. P. and Augustin, N.H. 1997. Model selection: an integral part of inference.
53: 603-618.
Burnham, K.P. and Anderson, D.R. 2002. Model selection and multimodel inference -A practical
Information Theoretic approach-. Second Edition. Springer. New York. i-xxvi+488pp.
Hakamada, T., Matsuoka, K. and Miyashita, T. 2009. Distribution and the number of western North
Pacific common minke, Bryde’s, sei and sperm whales distributed in JARPN II Offshore component
survey area. Paper SC/J09/JR15 presented to JARPN II review meeting. January 2009.
(unpublished). 18pp.
Hakamada, T. and Matsuoka, K. 2015. Abundance estimate for sei whales in the North Pacific based onsighting data obtained during IWC-POWER surveys in 2010-2012. Paper SC/66a/IA12 presented to
IWC Scientific Committee, May 2015. (unpublished). 11pp.
Hakamada, T. and Matsuoka, K. 2016a. The number of western North Pacific common minke, Bryde’s andsei whales distributed in JARPN II Offshore survey area. Paper SC/F16/JR12 presented to the
JARPNII special permit expert panel review workshop, Tokyo, February 2016 (unpublished). **pp
Hakamada, T and Matsuoka, K. 2016b. The number of blue, fin, humpback, and North Pacific right whalesin the western North Pacific in the JARPN II Offshore survey area. Paper SC/F16/JR13 presented to
the JARPNII special permit expert panel review workshop, Tokyo, February 2016 (unpublished). **pp.
International Whaling Commission. 2015. Report of the IA sub-committee. Annex G of the Report of the
IWC Scientific Committee. J. Cetacean Res. Manage. (Suppl.) 16: 176-95.
Tamura, T., Konishi, K., Isoda, T., Okamoto, R. and Bando, T. 2009. Prey consumption and feeding habitsof common minke, sei and Bryde’s whales in the western North Pacific. Paper SC/J09/JR16 presented
to JARPN II review meeting. January 2009. (unpublished). 36pp.
Thomas, L., Buckland, S.T., Rexstad, E.A., Laake. J.L., Strindberg, S, Hedle, S. L., Bishop, J. R.B., T. A.
Marques, T.A., and K. P. Burnham. 2010. Distance software: design and analysis of distance sampling
surveys for estimating population size. Journal of Applied Ecology 47: 5-14.
Whitehead, H. 2002. Estimates of the current global population size and historical trajectory for sperm
whales. Mar Ecol Prog Ser 242: 295–304

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Table 1. Summary information on dedicated sighting survey under JARPN II during 2008-2014.
Year

Vessels

PeriodSurvey area

2008

KK1, KS2

2Jul.-29Aug.

SA7, 8, 9

2009

KK1, YS1

23May-23Jun.

SA7, 8, 9

2011

YS1, YS2,YS3

5May-5Jun.

SA8,9

2012 1st

YS3

18May-29Jun.

SA7CS,7CN,7WR,7E

Table 2. AIC for each model of detection functions for base case. For selected model, AIC is indicated bybold letters. HR: Hazard Rate and HN: Half Normal.
Sperm whale
Model

HR

HN

School size+Beaufort+Year

1155.51156.4

School size+Beaufort

1160.41159.1

School size+Year

1160.91163.4Beaufort+Year

1153.51155.2

School size

1166.21165.9Beaufort

1158.41158.5Year

1158.91161.5

No covariate

1164.21164.5

Table 3. Abundance estimates for the sperm whales and their CV’s for each stratum based on 2008, 2009,2011 and 2012 JARPN II cruises for the best model of detection function. A is area size of the surveyed
area, ns and nw are the number of schools detected and the number of individuals detected withinperpendicular distance of 3.0 n.miles, L is searching distance, P is abundance estimate and CI isabbreviation for confidence interval.
Year

Stratum

A

L

ns

nw

n w /L

CV(n w /L )

P

CV(P)

95%LL

95%UL

2008

7

166,306

886.5

22

129

0.146

0.569

6,351

0.564

1,709

23,594

2008

8

162,789

1193.6

21

34

0.028

0.503

1,170

0.545

396

3,457

2008

9

499,235

3067.0

64

89

0.029

0.319

3,322

0.312

1,784

6,186
12,253

2009

7

166,306

1036.5

31

156

0.151

0.337

5,325

0.361

2,314

2009

8

162,7891084.5

22

41

0.038

0.347

1,532

0.390

631

3,718

2009

9

362,1132274.1

35

109

0.048

0.594

4,601

0.676

1,208

17,5302011

8

162,789

1101.5

26

51

0.046

0.411

2,906

0.370

1,106

7,637

2011

9N

208,660

1496.4

12

30

0.020

0.677

1,814

0.761

337

9,756

2011

9S

290,575

1492.8

17

30

0.020

0.426

2,204

0.503

721

6,739

2012

7CS

26,826

850.9

17

29

0.034

0.481

330

0.555

108

1,006

2012

7CN

16,171

649.2

1

2

0.003

1.014

14

1.020

2

100

2012

7WRN

6,874

175.7

7

14

0.080

0.366

195

0.306

76

503

2012

7WRS

66,117

750.1

45

121

0.161

0.471

3,837

0.448

1,443

10,1972012

7E

48,208

302.3

4

5

0.017

0.365

351

0.412

124

992

Table 4. Abundance estimate for sperm and killer whales in JARPN II survey area (i.e. sub-areas 7, 8 and9 excluding foreign EEZ) in early season for 2009 and 2011+1st survey in 2012 combined assuming thatg(0)=1.

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Sperm

Early

P

CV(P)

2009

11,4590.332

2011+2012_1st

11,652

0.266

Table 5. Abundance estimate for sperm and killer whales in the JARPN II survey area in late season for2008 assuming g(0)=1.
Sperm

Late
2008

P

CV(P)

10,843

0.358

Table 6. Abundance estimate for sperm whale in JARPN II survey area in the early and the late seasonsfor sensitivity test (i.e. applying alternative detection function other than the best model). Bold letter
indicates the estimate is based on the best model. It is assumed that g(0)=1.
Early (2009)
Model

Hazard Rate

Covariates

P

CV(P)

S+B+Y

11,187

0.298

Model

Covariates

P

CV(P)

S+B+Y

13,1340.255

S+B

14,4900.333

S+B

13,7000.287

S+Y

11,156

0.246

S+Y

11,1090.229

B+Y

11,4590.332

S13,9690.258

Half Normal

B+Y

10,9390.248

S12,9160.233

B14,3050.297

B12,0040.251

Y11,2200.229

Y10,808

0.221

None

13,809

0.226

None

11,8700.218

Early (2011+2012)
Model

Hazard Rate

Covariates

P

CV(P)

S+B+Y

11,578

0.267

Model

Covariates

P

CV(P)

S+B+Y

8,547

0.223

S+B

9,773

0.241

S+B

8,068

0.214

S+Y

10,496

0.277

S+Y

8,130

0.220

B+Y

11,652

0.266

S

8,705

0.248

Half Normal

B+Y

8,576

0.211

S

7,592

0.217

B

9,747

0.234

B

7,859

0.209

Y

10,512

0.263

Y

8,085

0.216

None

8,686

0.236

None

7,467

0.212

Late (2008)
Model

Hazard Rate

Covariates

P

CV(P)

S+B+Y

10,6420.164

S+B

13,895

S+Y

9,976

Covariates

P

CV(P)

S+B+Y

11,150

0.136

0.176

S+B

12,236

0.135

0.182

S+Y

9,832

0.145

B+Y

10,8430.358

S12,416

0.199

Model

Half Normal

B+Y

10,0680.127

S11,1790.140

B13,7640.134

B11,1230.116

Y10,014

0.155

Y

9,646

0.134

None

12,325

0.148

None

10,5950.125

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Table 7. Weighted average of abundance estimates in Table 6 by Akaike weight for sensitivity.
Early

Late
Sperm

Sperm
Early

P

CV(P)

2009

11,701

0.296

Change frombase case
2.1%

2011+2012_1st

10,3890.236-10.8%

Late
2008

P

CV(P)

Change frombase case

10,857

0.342

0.1%

Early (2011 and 2012)

Early (2009)

Late (2008)
Figure 1. Plot of actually surveyed track line (black lines) and position of the sperm whales (brown
triangles) for JARPN II surveys in early and late seasons in 2008, 2009, 2011 and 2012 (1st survey).

7

Figure 2. Plot of the estimated detection function fitted to the number of schools as a function of
perpendicular distance (n. miles) from the track line (Left panel) and QQ-plot of the detection function forthe best model for sperm whale (Right panel).

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