SC/D06/J3

Examination of correction the effect of skip on the abundance
estimate for Antarctic minke whales in JARPA
Takashi Hakamada, Mutsuo Goto and Hajime Ishikawa
The Institute of Cetacean Research, 4-5, Toyomi-cho, Chuo-Ku, Tokyo, 104-0055, Japan
Contact email: hakamada@cetacean.jp

Abstract
There are four kinds of skip in JARPA survey: Type (A) which is caused by night steaming to the start point ofnext day; Type (B) which is due to catch up with the schedule of survey; Type (C) which is caused by closing
and chase a targeted minke whale and Type (D) which is caused by bad weather condition. Hakamada et al.,(2006) suggested that there was a significant correlation with minke whale density for skip type (A) and (C). The
bias of abundance estimate due to type (C) was corrected in SC/M06/J6. This paper deals with bias correction
due to skip type (A) by using a modified method of Burt and Borchers (1997). Corrected abundance estimate in
Area IV obtained from SSV data were 32,630 (CV=0.142) in 1989/90 and 34,982 (CV=0.171) in 1991/92. Thosein Area V were 108,457 (0.124) in 1990/91 and 84,813 (CV=0.162) in 1992/93. Abundance estimates werelarger after the correction and therefore we considered that the effect of skip (A) was corrected. The annual rateof change estimates are -1.10% [-4.25%, 2.02%] in Area IV and -2.16% [-4.83%, 0.44%] in Area V. Bothestimates are not significantly different from 0. It was shown that neither significant increase nor decrease inabundance at the 5% level was detected during 1989/90- 2004/05 in Areas IV and V even if we consider theeffect of the skip type (A)KEY WORDS: ABUNDANCE ESTIMATE, ANTARCTIC MINKE WHALESINTRODUCTION
At JARPA review meeting in 1997, possible bias of abundance estimate due to under-surveying in higher density
area was pointed out (IWC, 1998). Burt and Borchers (1997) attempted to correct the bias by extrapolatingskipped interval during night from encounter rate of the day. Hakamada et al., (2006) classified type of skip andexamined if each type of skip cause bias of abundance. They showed that skipping distance after the end of thesurvey of the day (skip type (A) defined later) correlate to encounter rate of the day from 1989/90 to 1992/93 andthat skipping distance that occurs after detection (skip type (C) defined later) could cause bias of abundance
estimate while other types of skip didn’t cause bias.
It was shown that skip type (C) caused underestimate of abundance and corrected by estimating correction factor
between survey mode in case of IWC-IDCR (Haw, 1991). The correction the bias of abundance due to skip type(C) in JARPA, was dealt with in paper SC/M06/06 presented at this meeting.
The IWC Scientific Committee recommended that since skip type (A) occurred only during the first four years of
JARPA, the resulting potential negative bias in estimates for these years should be accounted for before
including these estimates when examining trends in abundance (IWC, 2006). In order to address thisrecommendation, this paper attempt to correct abundance due to skip type (A).
MATERIALS AND METHODSSkip of sighting surveys during JARPA surveys
Process of sighting surveys in a day
Fig. 1 illustrates movement of a SSV in a day. SSV started from point A in the morning. It had planned toproceed to point C in the day. A school was detected and sighting survey was interrupted at point D1. SSV closed
to the detected school to confirm species and school size. If the detected school was identified as Antarctic minke
whales, SSV chased targeted minke whale to sample it. After SSV sampled it, SSV transport it to Research Base
Vessel, returned to point E1 on the trackline and resumed sighting survey. As a result, trackline between D1 andE1 was skipped. The same situation occurred between D2 and E2 and between D3 and E3. However, sometimes
the trackline wasn’t skipped as in the case of trackline between D2 and E2. In this case, D2 and E2 are the same
position. When the time to end the daily survey came, SSV arrived at the point B. If SSV didn’t reach point C,
SSV moved without surveying from B to C until the beginning of the survey next day. Conversely, if SSV

reached to C or proceed over the point C, SSV stayed there until the next morning. As far as the pre-determined
distance per day is concerned, it was applied until 1992/93.
The skips occurred during JARPA are classified into three types as follows.
(A) Skip occurring after end of daily survey (proceeding along the trackline in the night without sighting
surveys), in order to fulfill the pre-determined distance per day.
(B) Skip due to catch up with the schedule within a stratum. When time shortage occurred in a stratum, vessel
skipped some part of planned trackline.
(C) Skip accompanied a detection of whales due to closing to a detected school and chasing a targeted minke
whale.
(D) Skip due to bad weather conditions.
Skip type (A)The pre-determined distance per day is a task on daily movement on the research track line. It was applied to
JARPA from the 1989/90 to the 1992/93 seasons. The SSVs had to steam during the night to the start point ofnext day, when they did not achieved pre-determined distance during the daytime. This type of skip was causedby shortage of searching distance in a day due to bad weather conditions and/or sampling activity in the highdensity area of the minke whales. The concern was that such skip might cause biased population estimate
because SSV tended to skip over high-density areas of whales after sampling activity of a day (IWC, 1998).
However, pre-determined distance per day was abolished from the 1993/94 season because total distance ofplanned trackline in one survey was reduced. The survey in the Areas IV and V was conducted once in the peakmigration season of the minke whales from the 1992/93 season whereas SSV surveyed whole of Area IV/V twice
in a year before then. Type (A) skip is represented as segment BC which is illustrated as blue dotted line in Fig. 1.
Pre-determined distance is less in south strata than in north strata because it was expected that whale density ishigher in south strata than in north strata.
Skip type (B)After 1993/94, pre-determined distances were not set. Even if a survey vessel covered a shorter distance than
expected, it would not skip the sighting survey in the night. However, in the case that it became difficult tofinish the survey in a stratum within the planned schedule, planned trackline would be skipped during night tocatch up with the schedule. Compared with skip type (A), daily distance of this skip tends to be much less asshown in Table 1 (Hakamada et al., 2006).
Skip type (C)This type of skip occurs accompanied with the detection of the minke whales. In the case of SV, it is caused byonly closing to confirm species and school size of the detected school. In the case of SSVs, it is caused byclosing, chasing and sampling of a targeted minke whale. Type (C) skip is the union of the segment D1E1 andD3E3. It should be noted that type (C) skip is same kind of skip examined in Haw (1991), which occurred in the
IDCR/SOWER surveys.
Skip type (D)Clearly, skip due to bad weather is independent of the density of the minke whales. Therefore, skip type (D)would not affect the abundance estimate and is not examined in this study. This type of skip would occur during
surveys other than JARPA.
Methods
In correction method in Burt and Borchers (1997), it was assumed that effective half search width and estimatedmean school size were not biased due to skip type (A) and that sighting survey was conducted whole ofscheduled trackline and that encounter rate in the skipped trackline is same as that surveyed trackline in the day.
Original correction method in Burt and Borchers (1997) used estimate corrected encounter rate by following
formula;

⎧

n
=
l

⎫

ni

∑ ⎨n + l d (k − 1)⎬
i

⎩

i

i

i

i

∑ {l + d (k − 1)}
i

i

⎭

(1)

i

i

where di is proceeding distance on the ith day, ni is the number of sighted school on the ith day, l i is searching
distance on the ith day, k i is ratio of proceeding distance to pre-determined distance on the ith day. Illustration ofli , di and ki is given in Fig. 2. Notations and formulation were slightly modified from Burt and Borchers (1997)2

so as to make easier to describe modified formulas.
Modified method is described as following. There are two differences between our method and that in Burt andBorchers (1997). One is that we assumed skip type (C) would occur as sighting survey in the day and the next
day whereas they extrapolated encounter rate to whole of skipped trackline. We corrected the bias due to skip (C)by Haw’s correction method later. Another is that they extrapolated encounter rate of the day but we did averageof encounter rates of the day and the next day. Corrected encounter rate is estimated by∑i ni k in=l∑ li k i(2)iwhere if survey vessel proceed more than it had planned, we defined k i=1. In special case of l i =d i for all i (i.e.
vessels didn’t approach to detected schools), encounter rate estimated by formula (1) would equal to that byformula (2). Formula (2) assumes that encounter rate in skipped trackline was equal to encounter rate of the day.
But formula (2) can be modified as follows under the assumption that encounter rate in the skipped trackline isaverage of the encounter rate of the day and the next day taking into account that the method of Burt andBorchers (1997) could cause overestimate of corrected abundance because whole of skipped trackline was notalways higher density area.

⎧⎧⎛ ni + ni +1 ⎞⎫⎟⎟⎬⎪⎨ni + d i (k i − 1)⎜⎜∑i ⎩⎝ d i + d i +1 ⎠⎭⎪n(i ≤ N − 1)
⎪l =
⎧
⎫
⎞
⎛
l
l
+
i
i
+
1
⎪⎪
∑i ⎨li + d i (k i − 1)⎜⎜ d + d ⎟⎟⎬⎨i +1 ⎠ ⎭⎝ i⎩⎪⎪∑i ni k in
⎪ =(i = N )⎪lli k i∑⎪⎩i(3)where di is proceeding distance in the ith day.
Derivation of formula (3) is as follows. After the end of the survey on the ith day, skipped distance can be
expressed as di(ki-1). Searching distance in the skipped trackline is calculated as⎛ l +l ⎞d i (k i − 1)⎜⎜ i i +1 ⎟⎟⎝ d i + d i +1 ⎠(4)

under the assumption that ratio of proceeding distance and searching distance equals in the skipped trackline toaverage of those in the day and the next day. Average of encounter rate of the day and the next day is⎛ ni + ni +1 ⎞⎜⎜⎟⎟⎝ l i + li +1 ⎠(5).

From formulas (4) and (5), the estimated number of detected school in the skipped trackline is⎛ n + ni +1 ⎞⎟⎟d i (k i − 1)⎜⎜ i⎝ d i + d i +1 ⎠(6).

In the case of the last day of the survey, there was no searching effort and detection in the next day (i.e. nN+1 =0、
lN+1 =0), formula (3) would be same as formula (2).
CV of the corrected encounter rate was estimated by bootstrap. We took resamples 100 times under condition
that sampling unit is a day.
Abundance trend
To estimate abundance trend, we should correct the bias due to skip type (C). We applied Haw (1991)’s
correction method to the abundance estimates after correction by the formula (3). Estimates are shown in Table 3.
Abundance trend are estimated by linear regression model weighted by inverse-variance. For more details ofthese methods, see SC/D06/J6.
RESULTS

3

Table 2 shows that comparison uncorrected abundance and corrected ones and their CV’s. Corrected abundance
estimate are more than uncorrected. This suggested skip type (A) caused underestimate of abundance but degreeof underestimate was not substantial. Corrected abundances using formula (3) is smaller than those using
formula (2) in most of the cases.
Table 3 shows that abundance series obtained by applying Haw(1991)’s method to the corrected abundance byformula (3) in order to estimate abundance trend in Areas IV and V. Estimated annual increase rates and theirCV’s are shown in Table 4. The estimates are -1.10% [-4.25%, 2.02%] in Area IV and -2.16% [-4.83%, 0.44%]
in Area V. Both estimates are not significantly different from 0.
DISCUSSION
Comparison of corrected abundance by formula (2) and (3)Corrected abundance estimate are more than uncorrected. Hakamada et al., (2006) showed that positive
correlation between distance of skip type (A) and density was observed. It can be thought that underestimate ofabundance was occurred due to skip type (A), and as seen in Table 1, abundances corrected by formula (2) are
more than those corrected by formula (3) in most of the cases, as expected. This is due to that the whole ofskipped trackline after the end of daily survey is not always high density. This means the assumption that density
in skipped trackline was same as that in surveyed trackline of the day was not appropriate. Tanaka (1999)
estimated the length of higher density areas to be 10-20 n.miles and assumed this in his simulation study, basedon the geographical distribution of detected minke whales in southern strata observed during 1992/93 JARPA
surveys. He showed that abundance estimate derived from Burt and Borchers (1997) was overestimated (Tanaka,1999). By adopting the assumption that density in skipped area is average of density in the day and next day (i.e.
using formula (3) instead of formula (2)), overestimate of corrected abundance would be improved.
Abundance trend using corrected abundanceComparing to abundance trend in Table 5, abundance trend was not substantially different. Even if we consider
the correction of bias due to skip type (A), it was shown that neither significant increase nor decrease was
detected during 1989/90- 2004/05 in Areas IV and V.
Skip type (D) (skip due to bad weather condition)
We couldn’t examine correlations between the density and the distance of skip of type (D). It is impossible to do
because we didn’t conduct sighting survey under such bad weather conditions and we don’t have data to estimate
density under such bad weather condition as sighting survey was suspended. We can assume that the effect ofskip type (D) on abundance could be small as there is no clear reason why we would expect minke whale density
to be correlated with changes in weather conditions because this type of skip didn’t occur intentionally.
ACKNOWLEGMENT
We thank all the researches and crew involved JARPA. We also thank Drs. Hiroshi Hatanaka and Doug
Butterworth (University of Cape Town) for their valuable comments to improve earlier manuscripts.
REFFERENCES
Burt, M. L. and Borchers, D. L. 1997. Minke whale abundance estimate from the 1991/92 and 1992/93 JARPA
sighting surveys. Paper presented to the JARPA review meeting, May 1997 (unpublished). 16pp.
Burt, M L. and Hedley, S. L., Hakamada, T. and Matsuoka, K. 2005. Comparison of abundance estimates of
JARPA survey data in Area V from standard line transect analysis and density surface fitting. Paper
SC/57/IA18 presented to the IWC Scientific Committee, May 2005 (unpublished). 14pp.
Hakamada, T., Matsuoka, K., Nishiwaki, S. (2005) An update of Antarctic minke whales abundance estimatebased on JARPA data including comparison to IDCR/SOWER estimates. Paper JA/J05/JR4 presented to
JARPA review meeting January 2005, Tokyo. (unpublished) 33pp.
Hakamada, T., Goto, M. and Ishikawa, H. (2006) Examination of the effect of skip on the abundance estimate for
Antarctic minke whales in JARPA. Paper SC/58/IA6 presented to Scientific Committee, May 2006
(unpublished). 18pp.
Haw, M.D. 1991. An investigation into the differences in minke whale school density estimates from passing
mode and closing mode surveys in IDCR Antarctic assessment cruises. Rep. int. Whal. Commn 41: 313–30.
Hedley, S.L., Buckland, S.T. and Borchers, D.L. (1999) Spatial modelling from line transect data. Journal of
Cetacean Research and Management 1(3): 255-264.

4

International Whaling Commission. 1998. Report of the Intersessional Working Group to Review and Resultsfrom Special Permit Research on Minke Whales in the Antarctic, Tokyo, 12-16 May 1997. Rep. Int. Whal.
Commn, 48, 377-411.
International Whaling Commission. 2006. Report of the Scientific Committee. Journal of Cetacean Researchand Management 9(suppl.).
Tanaka, S. 1999. Bias in density estimates when the speed of whale sampling vessels is reduced in high density
areas. Paper SC/51/CAWS12 presented to the IWC Scientific Committee, May 1999 (unpublished). 18pp.

5

Table 1. Skipping distance of type (A) for 1989/90 and 1990/91 and type (B) for 1993/94, 1994/95, 2000/01 ineach stratum (Hakamada et al., 2006)

stratum
NW
NE
SW
SE
PB

1989/90
Type (A)
397.6
314.3
167.4
225.6
15.6

1993/94
Type(B)
0.0
158.4
61.8
76.6
0.0

2001/02
Type(B)
0.0
0.0
0.0
0.0
0.0

stratum
NW
NE
SW
SE

1990/91
Type (A)
284.3
369.0
295.3
286.0

1994/95
Type(B)
126.6
4.8
64.4
0.0

2000/01
Type(B)
69.2
368.8
0.0
152.9

Table 2. Uncorrected abundance estimate and corrected ones using formula (2) and (3). Formula (2) is
extrapolating encounter rate of the day and (3) is extrapolating average encounter rate of the day and the next day.
Numbers in the parentheses are CV’s.
Area IV
strataNorth-West (NW)
North-East (NE)South-West (SW)South-East (SE)Prydz Bay (PB)
total

uncorrected8,334 (0.336)
10,521 (0.222)
2,463 (0.184)
6,494 (0.230)
2,181 (0.357)
29,993 (0.135)

1989/90
Formula (2)9,765 (0.289)
12,421 (0.301)
2,645 (0.189)
6,856 (0.152)
2,193 (0.306)
33,881 (0.144)

Formula (3)9,614 (0.292)
11,822 (0.291)
2,583 (0.184)
6,446 (0.160)
2,165 (0.311)
32,630 (0.142)

strataNorth-West (NW)
North-East (NE)South-West (SW)South-East (SE)Prydz Bay (PB)
total

uncorrected
12,894 (0.191)
2,809 (0.443)
2,700 (0.250)
2,171 (0.270)
12,097 (0.567)
32,670 (0.228)

1991/92
Formula (2)14,315 (0.203)
3,869 (0.595)
3,374 (0.248)
3,505 (0.291)
11,815 (0.393)
36,878 (0.165)

Formula (3)13,234 (0.223)
3,869 (0.503)
3,229 (0.219)
3,212 (0.341)
11,438 (0.406)
34,982 (0.171)

strataNorth-West (NW)
North-East (NE)South-West (SW)South-East (SE)total

uncorrected
28,692 (0.172)
26,342 (0.414)
6,416 (0.187)
39,296 (0.178)
100,745 (0.135)

1990/91
Formula (2)32,110 (0.178)
29,443 (0.331)
9,228 (0.194)
47,240 (0.204)
118,020 (0.127)

Formula (3)29,978 (0.184)
29,178 (0.329)
8,248 (0.188)
41,053 (0.183)
108,457 (0.124)

strataNorth-West (NW)
North-East (NE)South-West (SW)South-East (SE)total

uncorrected
15,525 (0.313)
13,746 (0.279)
6,879 (0.286)
29,997 (0.466)
66,147 (0.233)

199293
Formula (2)Formula (3)24,846 (0.360)
13,993 (0.331)
10,625 (0.307)
35,260 (0.289)
84,724 (0.174)

26,175 (0.289)
12,970 (0.338)
9,302 (0.302)
36,366 (0.282)
84,813 (0.162)

Area V

6

Table 3. Corrected abundance by applying Haw’s method to the abundance estimates using formula (3) in Table
1 in Areas IV and V. Correction factors R1=0.821 (CV=0.086) and R2=0.759 (CV=0.126) were used.
Area IV

year
1989/90
1991/92
1993/94
1995/96
1997/98
1999/00
2001/02
2003/04

Area VP
52,40256,18041,39842,36325,922
44,931
48,28044,564

CV
0.208
0.229
0.192
0.203
0.220
0.151
0.188
0.291

year
1990/91
1992/93
1994/95
1996/97
1998/99
2000/01
2002/03
2004/05P
174,176
150,123
166,830
145,021
184,914
164,789
201,883
91,819

CV
0.196
0.191
0.234
0.229
0.225
0.205
0.154
0.147

Table 4. Estimated annual increasing rate in Areas IV and V after the correction of the bias due to skip type(A).

Area IV
Area Vestimate 95%CILL 95%CIUL-1.10%-4.25%
2.02%-2.16%-4.83%
0.44%

Table 5. Estimated annual increasing rate in Areas IV and V not taking the correction of the bias due to skip
type (A) into account. (SC/D06/J6)
Area
Area IV
Area Vestimate-0.42%-1.54%

95%CILL 95%CIUL-3.58%
2.68%-4.01%
1.21%

7

●

●

▲

D1

A

E1

D2(E2)
▲

▲
D3

E3

B

C

●

A: Starting position of the day,
B: Ending position of the day
C: Starting position of the next day
D1,D2,D3: Sighting position of the 1st, 2nd and 3rd detection of the day, respectively.
E1,E2, E3: Position of restarting sighting survey after the 1st, 2nd and 3rd detection of the day, respectively.
In this case, point D2 and E2 are the same position.
Bold line indicates track line where sighting survey was actually conducted.
Dotted line indicates survey vessel proceeded without sighting surveys
Filled circle indicates point where both species and size of detected school were confirmed.
Filled triangle indicates point where a targeted minke whale was taken.

Fig. 1. Illustration of skip type (A) and (C).
Type (C) skip is the union of the segment D1E1 and D3E3. Type (A) skip is the segment BC. It had been planned sighting
survey on the segment AC. If there had been no detection on the day, survey vessel could be proceed to point C. Bold blackline represent actually surveyed, vessel go along dotted curves to close a detected school and chase a targeted whale. Bluedotted line indicates trackline skipped in the night.

A

B

C

D

E

Fig 2. Illustration for variables li , di , ki ,in formulas (1)-(7). A is the starting position on the i th day. B is
position where sighting survey was stopped due to detection of a school. C is position where sighting survey was
restarted. D is position at the end of daily survey. E is the starting position on the (i+1) th day. Bold line indicatestrack line where sighting survey was actually conducted. Dotted line indicates survey vessel proceeded without
sighting surveys

li = AB + CD
d i = ADk i = AE AD
AD indicates length of segment AD.

8