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SC/O05/BWI7

Estimation of some biological parameters of western North
Pacific Bryde’s whales by age distributions
TAKEHARU BANDO1), TOSHIYA KISHIRO2) AND SEIJI OHSUMI1), RYOKO ZENITANI1),
HIDEHIRO KATO3)
1) The Institute of Cetacean Research, 4-5, Toyomi-cho, Chuo-ku, Tokyo, 104-0055, Japan.
2) National Research Institute of Far Seas Fisheries 5-7-1 Orido, Shimizu, Shizuoka 424-8633, Japan3) Department of Ocean Science, Faculty of Marine Science, Tokyo University of Marine Science andTechnology, 4-5-7 Konan, Minato-Ku, Tokyo 108-0075, Japan
Contact e-mail: bando@cetacean.jp
ABSTRACTThis paper estimates several kinds of biological parameters of the western North Pacific Bryde’s whale byuse of biological data especially age distributions obtained by Japanese pelagic whaling in 1971-79 andJARPN II in 2000-03 to confirm the most reliable biological parameters which will be used for the IST ofthe whale stock. The values of biological parameters obtained by the present study are as follows: Total
mortality rate is 0.091 (Z=0.095), natural mortality rate is 0.076 (M=0.078), fishing mortality rate is 0.015(F=0.017), age at sexual maturity of males and females is 8 and 6 years old, respectively, full recruitment
age in males and females is 11 and 8 years old, respectively, and average recruitment age in males andfemales is 9 and 6 years old, respectively.
KEYWORDS: AGE DISTRIBUTION, AGE AT RECRUITMENT, AGE AT SEXUAL MATURITY,
BRYDE’S WHALE, FISHING MORTALITYRATE, NATURAL MORTALITY RATE, WESTERNNORTH PACIFICINTRODUCTION
The biological parameters are needed for the studies of population dynamics of biological resources.
Among them some parameters such as natural mortality rate, fishing mortality rate, age at recruitment,
and age at sexual maturity can be estimated by use of age distribution. These biological parameters for thewestern North Pacific Bryde’s whale were examined at the work on the comprehensive assessment of thiswhale stock in 1995 and 1996 (IWC, 1997). However, the age distribution seems to have not yet been
examined fully in recent years.
The First Intercessional Workshop for the IST for this whale stock will examine on the conditioning ofbiological parameters, and it will be needed to re-examine these biological parameters at this chance.
This paper will re-estimate some biological parameters by use of age and other biological data whichwere collected by Japanese pelagic whaling and JARPN II.
MATERIALS AND METHODS
Materials
The numbers of age data which were collected by Japanese pelagic whaling (it will be called byʻwhalingʼ later parts) during 1971-1979 and by JARPN II during 2000-03 are shown in Table 1. The
pelagic whaling was not conducted in sub-area 1 west (SA 1W), and the data from sub-area 2 (SA 2) wereonly collected by the whaling, and they are smaller in number compared with those in sub-area 1 east (SA1E). Although the materials were collected from both SA 1W and SA 1E by JARPN II, the number of age
materials which were collected by JARPN II (total) has been still smaller than those by whaling (total),and they are used only for estimation of age at sexual maturity.

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The method of catch of whales is different between the whaling and JARPN II. In the case of thewhaling there were many operation restrictions based on the Schedule of the ICRW and Japanese
domestic law such as catch quota, whaling ground, whaling season, size limit, prohibition of catch of cowand calf, etc. Related to the biological parameters, the size limits for the coastal and pelagic whaling of
the Bryde’s whale are set to be 10.7 and 12.2 m, respectively, by the ICRW, and the western limit ofJapanese pelagic whaling ground was set at 158 degree East to protect coastal whaling by Japanese
Government (Ohsumi, 1995). The restriction measures by the ICRW are not applied for the JARPN II,and whales were become a target of sampling in the waters west of 170 degree East. However, since
2002, the sampling of cow and calf has not been carried out.
The biological data which will be used in this paper are date and position of whales caught, sex, age,weight of testes, number of corpora lutea and albicantia in ovaries, for each whale.
MethodThe materials are divided by position caught into the sub-area 1 west (west of 155 degree East, SA 1W),
sub-area 1 east (between 155 degree East and 180 degree Longitude, SA 1E) and sub-area 2 (between 180
degree Longitude and 160 degree West, SA2) following the IWC/SC.
The age was determined by earplug annual layers. The sexual maturity of the male is identified by larger
testis weight of 0.8 kg and over in the commercial whaling, and combined testes weight of 1.5 kg andover in JARPN II. The sexual maturity of the female is determined by the existence of corpus luteum orcorpus albicans in ovaries.
RESULTSAge distribution
Table 1 shows number of whales in each age class by sub-area and by sex in whaling, and in JARPN II
number of whales in SA1W and SA1E combined by each age class, by sex and by sexual maturity.
Sexual difference of total mortality rate
Fig. 1 shows the age distribution of males and females, respectively, in all sub-areas combined by use ofdata obtained by pelagic whaling. The patterns of the age distribution are almost the same between sexes
with a peak is at about 10 years old, although the maximum age is 68 years old in females, and that is 53years old in males. The total mortality coefficient of males is 0.080, and that of females is 0.084, whenage data are used in the range between 10 and 40 years old. This means that the values of mortality
coefficient are almost the same in both sexes. Then, age data of both sexes combined are used for later
analyses.
Total mortality rate
Fig. 2 shows the comparison of age distributions of both sexes combined in SA1E and SA 2 which wereobtained by the whaling. Although it is difficult to compare the age distributions in pelagic whaling
between SA 1E and SA 2, because sample numbers in SA 2 (210) are smaller than those in SA 1E (436),
some difference may be estimated between them. The relatively sharp peak age in SA 1E is at 10 years
old. On the other hand, gentle peaks are at 15 years old in SA 2. Although further examination will beneeded to confirm, this phenomenon may indicate the difference of distribution pattern of Bryde’s whales
between SA 1E and SA 2, caused by the difference of operational strategy for both sub-areas. There areseasonal difference of catch in both sub-areas, and catch in SA 1E was mainly in early season from Mayto July, whereas it was mainly in later season from June to August in SA 2.
However, the total mortality coefficient which was calculated by use of age range of 10-40 years old in
SA 1E is 0.095, and those calculated by use of age range of 15-40 years old in SA 2 is 0.096. Then, both
figures are almost the same. This means that there is a possibility of the same stock in SA1E and SA2.
Fig. 2 shows also age distributions of Bryde’s whales of both sexes in SA1W by JARPN II. Althoughsample size in SA 1W (110) are still too small to compare the age distributions in other sub-areas, thepeak of age distribution in SA 1W is at about 6 years old which is about 4 years younger than that of2

THIS PAPER CAN NOT BE CITED WITHOUT PERMISSION FROM THE AUTHORSwhaling. This phenomenon indicates the difference of collection methods, and there is a size limit ofcatch in the case of whaling, whereas this management measure is not applied for JARPN II.
Estimation of natural mortality rate and fishing mortality rate
From above examination, the total mortality coefficient (M) of the western North Pacific Bryde’s whale isestimated to be 0.095 as the average of those in SA 1E and SA 2. Then, total mortality rate (D) iscalculated to be 0.091.
An ideal age distribution of whales caught is shown in Fig. 3. Total mortality coefficient (Z) includes M
and fishing mortality coefficient (F) in years between age at full recruitment (tr) and the year when theexploitation started. This age shows a transition point (tc) in the age distribution. And, the value of Z is
the same as M in older than the age (tc).
However, it is difficult to estimate the transition point of the age distribution in this paper. This means
the sample size is too small to find the point, or the fishing mortality coefficient is too small to have thepoint.
Ohsumi (1995) describes the catch history of the western North Pacific Bryde’s whale. The average
number of whales caught annually during years 1945-1970 is 179.2 whales, although yearly fluctuation
occurs during the years. The annual catch increased rapidly from 1971 when USSR and Japanesepelagic whaling started. The annual catch was 940.2 whales including coastal whaling during years
1971-79. Then, the average annual catch during 1945-1979 is 380.6 whales. As the population size of
this stock is estimated to be 26,000 (Kitakado et al., this meeting) and if the figure is used as the base of
population size, the fishing mortality rate was about 0.007 in 1945-70, and 0.015 during 34 years of
1945-79. If 0.015 is considered to be the average fishing mortality rate (fishing mortality coefficient:0.017) during 1945-1979, the natural mortality coefficient is calculated to be 0.095-0.017=0.078. Then,natural mortality rate (D) is calculated to be 0.076.
Age at sexual maturity:
The data of whaling are not used for this purpose, because the size limit (12.2 m) which was set for thepelagic whaling by the IWC, and it is near the body length at sexual maturity (around 12 m), so that bias
may occur in the sexual maturity ratios in the age near the sexual maturity.
Although the sample size of JARPN II is still small, the age at sexual maturity is estimated by use ofdata of JARPN II in which samples are collected without size limit.
Fig. 4 shows relation between age and sexually mature ratios of males and females, respectively. From
this figure, the age at sexual maturity is estimated by the 50 % mature age. They are 8 and 6 years old inmales and females, respectively.
Age at recruitment:
From Fig. 2, the age of full recruitment is determined as the peak of the age distribution, and it isestimated to be 11 years old in males and 8 years old in females. The average of both sexes is 10 years
old.
The average age at recruitment is calculated to be the average age of the age before the age at fullrecruitment, and it is estimated to be 9 and 6 years old in males and females, respectively.
DISCUSSION
The biggest problem in use of data of the commercial whaling is the catch restrictions by the regulation ofwhaling (Ohsumi, 1995). These regulation measures are possible to give some bias on the data. This
paper used the data of the pelagic whaling, and the size limit in the pelagic whaling (12.2 m) is different
with that of coastal whaling (10.7 m). Then, the age at recruitment must be different each other, but thisbiological parameter for the coastal whaling was not used in this paper. When we assess the populationof coastal and pelagic whaling combined, this matter must be discussed and confirmed.

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THIS PAPER CAN NOT BE CITED WITHOUT PERMISSION FROM THE AUTHORSIn this study, the maximum age was 53 in males and 68 years old in females. Ohsumi (1963) estimatedthe longest life span of the North Pacific Bryde’s whale to be 63 years old from the interspecies
relationship. Present study supports the result. The average ages which were calculated from the age
distribution are 18.7 years old in males and 16.4 years old in females. Considering the scarcity ofjuveniles in catch, the average life span of this stock should be younger than these figures.
In the past several papers tried to estimate mortality rates of the North Pacific Bryde’s whale. Doi,Nemoto and Ohsumi (1967) estimated total mortality coefficient (Z) by use of growth curve and size
distribution of whales caught to be 0.059-0.085. Ohsumi (1977a) estimated Z was 0.091 from age
distribution and it was 0.080 from ovulation distribution and annual ovulation rate. Ohsumi (1977b)
estimated M to be 0.085 from age distribution, and Ohsumi (1979) estimated M to be 0.074 frominterspecies relationships. IWC/SC agreed that M is 0.07 at the comprehensive assessment workshop in1996.
We estimated in this paper from age distribution that Z is 0.095, natural mortality coefficient M is 0.078,
and fishing mortality coefficient F is 0.017. These figures are close to the past figures, Then, we propose
to use 0.08 for the value of M instead of 0.07.
The value of the natural mortality coefficient in 0 years old was not estimated from the age distribution
in this paper. We expect that this biological parameter will be estimated in accordance of developmentof JARPN II.
It was difficult to estimate age at sexual maturity (tm) from age and maturity data of the commercial
whaling, because of the bias from size limit of catch. However, it could be estimated by use of JARPN II
data, although sample size is still small. This paper estimates the age at sexual maturity is 8 years old formales and 6 years old for the females. Ohsumi (1977a) estimated this parameter by means of threemethods, and he indicates that it is 8-10 years old in males and 7-8 years old in females. IWC agreed theparturition age (tm+1) of females is 9 years old. However, this figure will be better to change to 7 years
from the present result.
Two sets of the age at recruitment were estimated in this paper. Both the full and average recruitment
ages are older than the age at sexual maturity, and the average recruitment age. In the case of making apopulation dynamics model, this phenomenon should be considered.
ACKNOWLEDGEMENTS
We are also indebted to researchers who engaged in the collection of various kinds of materials whichwere used in this paper during pelagic whaling period and in JARPA Ⅱ.
LITERATURES CITED
Doi, T., Nemoto, T. and Ohsumi, S. 1967.Thierd memorandum on results of Japanese stock assessment ofthe whales in the North Pacific. Rep. Int. Whal. Commn 17: 89-92.
IWC.2005. Report of the Workshop on the pre-implementation assessment of western North PacificBryde’s whales, Tokyo, Japan, 21-24, March 2005. Paper SC/57/REP3 presented to the IWC
Scientific Committee, May, 2005 (unpublished). 30ｐｐ.
Kitakado, T., Shimada, H., Okamura, H. and Miyashita, T. (this meeting). Update of additional varianceestimate for the western North Pacific stock of Bryde’s whales. SC/O05/BWI
Ohsumi, S. 1977a. Bryde’s whales in the pelagic whaling ground of the North Pacific/ Rep. int. Whal.
Commn. (Special Issue 1):140-150.
Ohsumi, S. 1977b. Further assessment of population of Bryde’s whales in the North Pacific. Rep. Int.
Whal. Commn 27: 156-160.

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THIS PAPER CAN NOT BE CITED WITHOUT PERMISSION FROM THE AUTHORSOhsumi, S. 1979. Interspecies relationships among some biological parameters in cetaceans andestimation of natural mortality coefficient of the Southern Hemisphere minke whale. Rep. int. Whal.
Commn 29: 397-406.
Ohsumi, S. 1995. A review on population studies of the North Pacific Bryde’s whale stocks (Revised).
Paper SC/47/NP14 presented to the IWC Scientific Committee, May, 1995 (unpublished). 35pp.

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Table 1. Age and sexual maturity status of Bryde's whales collected during 1971-1979 commercial
whaling and 2000-2003 JARPN II surveys.
FemaleMaleAge0123456789101112131415161718
1920
21
222324
25
26
27
28
2930
31
32
33
34
35
36
37
38
39
40
41
42
45
46
47
49
52
53
58
68
Total

Whaling
Sub-area Sub-area
1E
2

1348
10
1115
16
20
10
13
91416
71115
54
984443921232
1212231212334223453415345933631332191121211311211262

1211115

Total

3671212131820251317101919111624871511577510112352242354
121121112
11377

JARPN II
Maturity
Imm Matrate(%)
10.0
10.0
10.0
60.0
50.0
50.0
3
350.0
20.0
1
150.0
2100.04100.01100.02100.010.0
4100.01480.01100.02100.011111112731

100.0
100.0
100.0

100.0100.0100.0Whaling
Sub-area Sub-area
1E225115911111269557981027257563111132118353755752816345223322Total

2513610191417916101014141018
3135912582614

JARPN IIMaturity
Imm Matrate(%)
10.0
10.0
10.0
20.0
40.0
1100.0
2
250.0
2
250.0
1480.04100.06100.06100.03100.04100.03100.01100.06100.02100.0
3100.013331212223
12100.0
50.0
100.0

1100.03100.01100.0

58

79.5

100.0

53.4

174

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100MaleFemale
Male; regression curve

Frequency

Female; regression curve

Male: Y=51.7e-0.0803X
Female: Y=38.8e-0.0838X

101
1

6

11

16

21

26

31

36

41

46

51

56

61

66

Age (years)

Fig. 1. Age distribution and mortality rate of male and female Bryde's whales collected during 1971-1979
commercial whaling.

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Frequency

100

Sub-area 1E
Whaling
Regression curve:
Y=74.8e10-0.0945X

1
1611162126

3136414651

56

6166

Age (years)

Frequency

100

Sub-area 2
Whaling
Regression curve:
Y=47.8e10-0.0960X

1
1

61116

21

26

313641

4651

56

61

66

Age (years)

Frequency

100

Sub-area 1E and 2
Whaling
Regression curve:
Y=108.5e10-0.0904X

11611162126

3136414651

566166Age (years)
100

Frequency

Sub-area 1W
JARPN II10116111621263136414651

Age (years)

Fig. 2. Age distribution and mortality rate of Bryde's whales in each sub-area.

8566166

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log nFrequency (n)Z =M+FM

tratrtc

Fig. 3. Schematic diagram of age distribution and mortality rate.

9Age (years)

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10120.0
Male100.0

8Mature8.2

680.0

Maturity rate (%)
Regression curve

60.0

4Y=100/{1+e40.0(4.25-0.517X)}

2Maturity rate (%)

Frequency (n)Immature

20.0

3530252015

1050.000Age (years)

10Female

120.0

100.0

8680.0Mature

5.9

Maturity rate (%)
Regression curve

4Y=100/{1+e60.0(2.86-0.482X)

}

240.0

20.0

3530

2520

15

10

50.000Age (years)

Fig. 4. Age at sexual maturity of Bryde's whales collected during 2000-2003 JARPN II surveys.

10Maturity rate (%)

Frequency (n)Immature