SC/J09/JR22

A minimum realistic model in the JARPN II offshore survey area
Shigeyuki Kawahara
National Research Institute of Far Seas Fisheries, Fisheries Research Agency, 5-7-1, Orido,
Shimizu, Shizuoka 424-8633 JAPANABSTRACTA minimum realistic model (formerly called Mult-spec type model) is under construction for theoffshore survey area of JARPN II (The Second Phase of the Japanese Whale Research Program
under Special Permit in the western North Pacific) with the system dynamics software that uses
difference equations. The final objectives of the model are to forecast the effect of various
management options for cetaceans and to make management recommendations including fisheryresources that take into account the effect of consumption by cetaceans (minke, sei and Bryde’s
whales). Pella-Tomlinson model was applied to the cetaceans under MSYR(1+) = 0.02, 0.04 (basecase) and 0.06. The abundance values of cetaceans prior to exploitation (K) and at present were
estimated on a yearly basis with abundance estimates from sighting surveys and catch series data.
Two main prey species of the cetaceans, that were also commercially important (Japanese
anchovy and Pacific saury) were age-structured with information from domestic stock assessment.
Other supplementary preys (krill, copepoda and others) were included in the model as they had
constant biomass with no seasonality. Feeding season of cetaceans was set in May-September andthe daily predation was assumed to be equal over the all individual cetaceans to the necessaryenergy. The proportion of each prey taken by cetacean was calculated from product of the preybiomass, overlap of distribution between prey and cetacean, and prey preference of the cetacean.
The overlap of distribution between prey and cetacean was estimated from JARPN II sighting
surveys. The estimates of prey preference of the cetaceans were obtained from the JARPN II
cooperated whale and prey surveys. Based on the data from 2001 to 2006, the proportion of thepreys taken by each cetacean was used for adjusting the parameters of the model. Natural deathof Japanese anchovy and Pacific saury was separated into the two parts: the consumption by
these cetaceans and the residual natural death. The preliminary results of the model exercises
showed that the effect of consumption by the cetaceans to the preys was large for Japanese
anchovy, especially in age 0, and limited for Pacific saury.

INTRODUCTION
Historical drastic fluctuations of the pelagic fisheries resources in a process called “species
replacement” and severe depletions of many groundfish stocks have occurred in the waters
around Japan (Yatsu et al., 2001; Fisheries Agency of Japan, 2008). While these fluctuations
and depletions could be attributed to the environmental factors and the effects of fisheries,
however, the effect of consumption by cetaceans may not be neglected. Most cetacean
resources continue to increase after the introduction of the moratorium on commercial
whaling (Hakamada et al., 2004). The usefulness and the need for the multi-speciesmanagement approaches are discussed in the international organizations (Plagányi, 2007.).
Ecosystem modelling is one of the main objectives of the JARPN II. Three different
approaches to the development of the ecosystem modelling are in progress (Kawahara andHatanaka, 2007); Ecopath with Ecosim (Christensen et al., 2000; Mori and Hakamada, 2007;
Mori et al., 2009) and minimum realistic model (former Multspec-type model: Bogstad et al.,
1997; Kawahara, 2007) for the offshore region, and a new Bayesian assessment of the effectof marine mammal consumption for the coastal region (Okamura, 2007; Okamura et al.,2009). The minimum realistic model is objective-orientated and is considered to be superior
to the other models for providing management advices (NAMMCO, 2003; Punt andButterworth, 1995). Following the basic minimum realistic model developed with EXCEL
VBA by Kawahara and Hosho (2004), a more practical model is under construction using thesystem dynamics software that utilizes data from the JARPN II. The final objectives of themodel are to forecast the effect of various management options for cetaceans and to makemanagement recommendations including fishery resources that take into account the effectof consumption by cetaceans. This document describes the specification of the model andreports the recent progress with some preliminary results. To show the overview of the modelfor the Review, assumed values are used for some parameters in the model.
METHODS
The modelling area is the whole JARPN II survey area except for the bottom layer on thecontinental shelf. The software used for modelling is STELLA (version 8, Japanese). STELLA
is based on difference equations (http://www.iseesystems.com) and has been applied to theecosystem modelling, for example, in the coastal area off northern Japan (Yamamura, 2004).
The basic structure of the minimum realistic model is specified in Appendix 1. The time
duration (dt) was set as one month to keep efficiency in calculation and to capture
seasonality in the model. An example of the model, which is used for calculating the
proportion among preys taken and for separating the consumption by cetaceans from theprey’s natural death, is shown in Fig. 1. The most parts around the basic structure are fornumerical calculation to check the model behavior.
Pella-Tomlinson model was applied to all baleen whales sampled during the JARPN II(minke, sei and Bryde’s whales) with MSYR(1+) = 0.02, 0.04 (base case) and 0.06. The
abundance of minke, sei and Bryde’s whales prior to exploitation (K) and at present were
estimated for each MSYR from fitting to the abundance estimate for the whole stock. The
summary of abundance estimates of minke, Bryde's and sei whales in the western North
Pacific is shown in Table 1 (Hakamada et al., 2009). The estimates with better coverage thanothers were selected as the abundance for the stock (Table 2). For sei whale, however,estimate of 28369 in 1999 (Hakamada, 2002) was adopted as the base case for the analysis.
Other abundance estimates were used to estimate the migration that represent the
proportion of animals of the stock in the modelling area by season (Table 3). Catch series ofcetaceans are shown in Appendix 2. The first year of catch series was treated as the year forK (1930 for minke whale, 1946 for sei whale and 1911 for Bryde’s whale).
2

Two main prey species of the cetaceans, that are also commercially important (Japanese
anchovy and Pacific saury) are age-structured with information on catch, abundance,
recruitment, growth etc. cited from the most up-to-date domestic stock assessment (Fisheries
Agency of Japan, 2008: Appendix 3). Because the stock assessment was restricted to thecoastal part of Japanese anchovy stock, the stock size was expanded to the modelling areafrom multiplying the correction factor (3.54) based on the data of acoustic surveys under
JARPN II in 2004-2006. The virtual coastal stock was introduced in the model to reflect thestock assessment and management in the coastal area. Supplementary preys (krill, copepoda
and others) were included in the model as they had the constant biomass with no seasonality.
Others were mackerels, sardine, squids etc.
The daily consumption by cetaceans was assumed to be equal over the all individual
cetaceans to the necessary energy (Tamura et al., 2009). The daily necessary energy perweight (kcal kg-1) was assumed to be 206.25M^0.783 (Sigurjónsson and Víkingsson, 1997).
The average weight (M in the equation) for minke, sei and Bryde’s whales were 4.5, 20.4 and14.0 tons, respectively as in Mori et al. (2009). The energy per weight of the preys is shown in
Table 4. The feeding season of cetaceans was set from May to September as JARPN II
offshore survey has covered the period. The same correction factor of feeding season (2.02) tothat in Lockyer (1981) was used for our model as in Tamura et al. (2009). The proportion ofeach prey taken by cetacean was calculated from product of the prey biomass, overlap of
distribution between prey and cetacean, and prey preference of the cetacean. The overlap of
distribution between prey and cetacean was estimated monthly from dividing the survey
area into the 1*1 degree blocks (see Appendix 4). The monthly distribution patterns ofcetaceans and preys were constructed from the JARPN II sighting survey data and the roughfigures on the distribution described in Fishery Agency of Japan (2008), respectively. The
initial values of prey preference of cetaceans in the model were set with reference toestimates obtained from the JARPN II cooperated whale and prey surveys (Murase et al.,2009; Table 5).
Adjustment of the parameters of the model was made mainly with two points: Proportion
among preys taken by each cetacean and separation of consumption by the cetaceans fromprey’s natural death. The period used for adjustment was 2001-2006 as the abundance of
cetaceans in the period did not differ among MSYR and the data for the stock assessment of
the main preys were improved in the period. For example, the information on the offshore
abundance became available for Japanese anchovy from the acoustic surveys under JARPN
II after 2004 and for saury from the mid-water trawl survey by the Fisheries Research
Agency after 2001. For adjustment with the proportion among preys (and ages in Japanese
anchovy and Pacific saury) taken by each cetacean, the comparison between the results
obtained from the model and the real stomach contents was made. The diet composition
matrix used as the real stomach contents was the same as in Mori et al. (2009). The
proportion in the model was calculated from summing the consumption of each prey (andages in Japanese anchovy and Pacific saury) by cetaceans for the five years from 2001-2006.
Adjustment was repeated mainly on the prey preference by cetaceans until the proportion3

among preys by each cetacean became similar to the real stomach contents. For separating
the consumption by cetaceans from the prey’s natural death, comparison between the natural
death with and without consumption by cetaceans was made for Japanese anchovy andPacific saury by age. The residual natural death was adjusted to be equal to the difference
between the original natural death and the consumption by these cetaceans.
RESULTS AND DISCUSSION
The estimates of K and present abundance of cetaceans are shown in Table 2. Examples offitting the abundance estimates under MSYR(1+) = 0.02, 0.04 and 0.06 are shown in Fig 2.
The stock depletions at present (2006) were 0.88-0.95, 0.65-0.97 and 0.81-0.99 for minke, sei
and Bryde’s whales, depending on MSYR(1+).
For each cetacean, the proportion of preys in the feeding season (May-September) calculated
from the model could be well coincided with that in the real data by adjusting mainly theprey preference by cetaceans (Fig. 3). The adjusted final values of prey preference aresometimes different considerably from the initial values from the cooperated whale and preysurveys (Table 5). This is partly due to the problem in the biomass estimates of the preys. For
both Japanese anchovy and Pacific saury, the natural death could be separated to theconsumption by cetaceans and the residual natural death (Fig. 4). The preliminary results
showed that the consumption by three species of cetaceans was more effective for Japanese
anchovy, especially age 0, and less effective to Pacific saury.
Although the model exercise showed the large effect of consumption by the cetaceans toJapanese anchovy, there are several uncertainties for the information related to both
cetaceans and Japanese anchovy. For example, the correction factor of feeding season (2.02),
especially for Bryde’s whale, might not be appropriate value to be used in our case. The stock
size of Japanese anchovy in the modelling area was expanded from that of the coastal area
using the correction factor because the domestic stock assessment was restricted to thecoastal area. Furthermore, at present the information on the distribution and migration ofpreys is incomplete to precisely estimate the overlap with the cetaceans. Similarly, there is apossibility that the consumption of Pacific saury by the cetaceans is underestimated as thefeeding season of cetaceans is set short from May to September. In addition to that, the
JARPN II surveys did not cover the northern area along the Aleutian Islands and theKamchatka Peninsula where Pacific saury is distributed in summer. The data for the prey
preference are not yet adequate, too. For example, the initial values of preference to krill andcopepoda by sei whale were adjusted substantially by the model. Therefore, JARPN II survey
should be continued to acquire better data set than we have now to improve the model andthen the model will improve the survey to achieve its final objectives. Also, sensitivity
analyses should be conducted to forecast the effect of various management options forcetaceans, for example, in the biomass estimates of cetaceans in the modelling area.

4

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5

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271-287
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Paper SC/J09/JR16 presented to the JARPN II Review Workshop, Tokyo, January 2009
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of catch and stock abundance of dominant small pelagic fishes and common squid withsome related environmental indices around Japan. PICES Sci. Rep., 18: 175-8.
6

7

10N -43N ,130E-180;
25N -43N, 180-155W .

JA R PN II (Area 7-9)

B ryde's w hale
W estern N orth P acific

1:B uckland,S .T ,C attanch, K.L.and M iyashita,T .1992.M inke w hale abundance in the N orthw est P acific and the O khotsk S ea,estim ated from 1989
and 1990 sighting surveys.R ep.int.W hale.C om m on 42:387-392.
2.H akam ada T., M atsuoka,K.and M iyashita,T .2008.A ppendix :N um ber of w estern North P acific com m on m inke,B ryde's,sei and sperm w hales
distributed in JA R P N II (O ffshore com ponent) survey are for estim ation of prey consum ption by the w hales.D ocum ent
3.M iyashita,T.2008 (in prep.).C om m on m inke w hale abundance in the O khotsk Sea, east of K urilIs and the K am chatka P eninsula assum ing g(0)=1,
estim ated from 2003 and 2005 sighting surveys.A ppendix to H akam ada's paper of assessm ent of catch effect press w hale estim ated from the sighting data
4.S him ada,H .and M iyashita,T. 1997. Population abundance of the w estern N orth Pacific B rydeʼ
collected from 1988 to 1996.D oc.IW C /SC /49/N P 4.9 pp.
5.S him ada,H ., O kam ura,H .,K itakado,T.and M iyashita,T .2008.A bundance estim ate of w estern N orth Pacific Bryde's w hales forthe estim ation of additional variance and C LA application.D ocum ent SC /60/PF12. 34pp.
s w hales and6.Kitakado, T., Shim ada, H.,O kam ura,H .and M iyashita,T .2008.C LA abundance estim ates for w estern N orth Pacific B rydeʼ
their associated C V s w ith taking the additionalvariance into account.D ocum ent SC /60/P FI3.27pp.
7.H akam ada,T.,M atsuoka,K .and N ishiw aki,S. 2004. Increase trend and abundance estim ate of seiw hales in the w estern N orth P acific. D ocum ent
S C /56/O 19.9pp.

972
68,0007,744
5,406
21,901
20,501
1,677
9,797
0.52
0.418
0.27
0.812
0.188
0.366
0.893
0.311
2005 2002-2003
1988-1996 1998-2002
2006-2007
2006-2007
Aug-Sep M ay-June July-Sep
A ug-S ep
M ay-June July-Sep
3
7
2
2
4
5,6
2
2

East of
KurilIs(R ussian
O khotsk
Pacific
EE Z) andJA R PN II(A rea 7（
R ussian(30N -55N,
east of
9)
EEZ)
145E-180)
Kam chatka
P en.(R usssi
an EEZ)A bundance
25,04928,436
7,338*
2,976*
CV
0.315
0.712
0.517
0.185
Y ear
1989-1990
2003
2006-2007
S easonA ug-S ep M ay-June July-S ep
A ug-S ep
12
2
3
R eference*:assum ing g(0)=0.732 (C V =0.309) (O kam ura et al.2008)

A rea

O khotsk（Russian
EEZ), Eastof K rill Is（Russian
JA R PN Ⅱ(A rea 7-9)
EEZ) andhigh seas(north of
40N, w est of170E)

T able 1.S um m ary of abundance estim ates of m inke,sei and B ryde's w hales in the w estern N orth Pacific.
Species
C om m on m inke w hale
Sei w hale
S tockO -stockW estern N orth P acificTable 2. Estimated K and abundance of minke, sei and Bryde’s whales.

M inke w hale
M S YR
0.02
0.04
0.06

K（1930） S urvey(1990)
30300
25049
27400
26400

2001
26800
26400
25900

2006
26700
26000
25400

2007
26700
25900
25300

M S YR
0.02
0.04
0.06

K（1946） S urvey(1999)
46200
28369
35200
28900

2001
28100
27900
26700

2006
30000
30600
27900

2007
30400
31000
28000

M S YR
0.02
0.04
0.06

K（1946） S urvey(2003)
77300
68000
69000
68100

2001
69000
68200
68000

2006
70900
68400
67900

71200
68400
67800

2001
20700
20400
20500

2006
21800
21100
20600

2007
22000
21200
20600

Sei w hale

B ryde's w hale
M S YR
0.02
0.04
0.06

K（1930） S urvey(2000)
27000
20501
22200
20900

Table 3. Proportion of animals of the stock in the modelling area*

Ｍｏｎｔ
ｈ
M ay
June
m inke w hale
0.293
0.293
Sei w hale(28369)**
0.273
0.273
Sei w hale(68000)**
0.114
0.114
B ryde's w hale
0.082
0.082
*"M igration" is used in the m odel**():abundance estim ates for the stock

8

July
0.158
0.191
0.080
0.478

A ug.
0.158
0.191
0.080
0.478

S ep.
0 .1580 .191
0 .0800 .478

Table 4.

Energy per weight of preys (kcal/kg).

Prey species
Japanese anchovy

kcal/kg
1320
1530
Pacific saury
1260
3140
Krill
850
C opepoda
920
O thers1000(M odified from Tam ura et.al)

Table 5.

A ge
0
1 and 201Prey preference of minke, sei and Bryde’s whales
Above: estimated initial values from cooperated whale and prey surveys
Below: Final adjusted values

Estim ated values
Krill C opepoda O thers
Japanese anchovy
P acific saury
Year 0Year 1+
Y ear 0Year 1
*
*
*
0.61
0.09
0.00
0.05
M inke w hale
0.61
1.00
*
*
Sei w hale
0.73
0.73
0.31
1.00
0.05
0.49
*
*
*
*
0.49
B ryde's w hale
1.00
1.00
0.06
0.00
0.05
*tentative value as the estim ate is not available in the cooperative w hale and prey suveys
m ainly due to the unoverlapped distribution betw een the cetacean and the prey
A djusted values
Japanese anchovyYear 0Year 1+
M inke w hale
0.00
1.30
Sei w hale
3.00
0.70
B ryde's w hale
0.27
4.00

P acific saury
Y ear 0Year 1
0.40
0.70
0.005
0.005
0.00

9

Krill

C opepoda

O thers

0.012
0.007
0.004

0.005
0.007
0.00

0.60
0.05
0.03

Minke K

Minke MSYR

Minke catchMinkeswitchMinkeweightAnchovy
consumption
weightMinkeenergy per day

Minkebiomass

Anchovy annual
consumption weightMinkenecessaryenergyAnchovy
natural deathsum upAnchovy
offshorecorrection+

Anchovy annual
consumption total

Anchovy
consumption

Anchovy
recruit~Anchovy
biomass

Anchovy
pre M Anchovy coastal
natural death

Brydesenergh pre day

Anchovymonthly M~

Saury
migration

Anchovytotalbiomass

Saury
total
biomass++

Anchovy
Anchovy catch
aging minus
Anchovy
Anchovy coastal catch

Anchovy
total catchSaury
total catch++

BrydesswitchBrydesweightBrydesenergy prer day

Othersconsumption
weightAnchovy
migration

Brydesmigration

Brydesbiomass

Others annual
consumption
calculation

Copepoda annual
consumption
calculation

Saury annual
consumption weight
Brydespredation
calculation

Krill Copepod Others
Saurybiomass biomass biomass biomass

Anchovy
numberAnchovy
aging plus

SeiswitchSeienergy per day

~

Saury
consumption
sum upSaury
natural death
Saury annual
natural death weightSaury
natual death
initialize
Saury
Fseason~Saury
weight~Saury
consumption
Saury
natural deathSaury
recruit~Saury
natural deathsum upSaury
monthly M

Anchovy coastal
Anchovy annual total Saury annual toal
monthly M
catch calculation catch calculation
Anchovy
Anchovy
coastalAnchovy annual
monthly F Anchovy
catch weight
Anchovy coastal number
catch
recruitment
Anchovy
Anchovy
coastalcatch~ annual F
Anchovy coastal
Anchovy coastal
aging plus
Anchovy
Anchovy
aging minus
Anchovy ~annual catchannual catch
Anchovy coastal
weightsum upinitialize
Anchovymonthly M
monthly F

+

Saury
catch

Saury
aging plus

Saury
FseasonSaury
aging minus

Saury
monthly M~

Saury annual natural
death totalSaury
monthly F

Saury annual
catch weight

Saury
catch

Saury
weight+Saury annual
consumption tatal

Saury
recruitment

monthly M~

Saury
weightSaury
number

Saury
pre M

Saury
consumption
weightSaury
consumption
initialize

Saury
consumption
weight~Anchovy
natural death

Brydes decrease

Brydes number
in survey areaSei
predation
calculation

Anchovy
weight+Brydes increase

Anchovy
consumption
weightAnchovynatual death
initialize

Anchovy
recruitment

Anchovy annual
natural death total

CopepodKrillconsumption
consumption
weightweightMinke
predation
calculation

natural death weight~Sei
necessaryenergy~Brydes number

Sei decreaseSeibiomass

Brydes catch

Brydes K~

Sei number
in survey area~SeiweightKrill annual
consumption
calculation

Anchovy
Anchovy
consumption
consumption
sum upinitialize
Anchovy
natural death
Anchovy annual

Anchovy
weightSei
migration

Brydes MSYR

Sei catch

Sei increase

Minke number
in survey area

~

Sei K
Sei number

Minke decrease

Minke increaseMinkemigration

Sei MSYR~

Minke number

~

Saury
annual catch
initialize

Saury
annual catchsum upFig. 1. The structure of the minimum realistic model for calculating the proportion among
preys taken and separating the consumption by cetaceans from natural death.

Sei whale

Minke whale
Stock size: 1 - 2 - 3 -Stock size: 1 - 2 - 3 1:

50000

1:

50000
1
1

1
2
1:

2

1
2

3

3

1

2

3

1

2

1

3

2

3

25000

2

3
1:

25000

1
3
1

1

2

1:

0

1:
1.00

Page 1

16.40

31.80

47.20
Years

62.60
78.00
17:18
2008年 10月 22日

Trend of the tock size of minke whale

3
2

3

13.20

25.40

37.60
Years

49.80
62.00
17:02
2008年 10月 22日

Untitled

Fig. 2. Examples of estimation of K and present abundance of cetaceans fitting theabundance estimates under MSYR=0.02, 0.04 and 0.06 (left: minke whale,
right: sei whale ).
10

3

0
1.00

Page 1

2

Minke whale
100%
80%

Others
Copepod
Krill
Saury age 1
Saury age 0
Anchovy age 1+
Anchovy age 0

60%
40%
20%
0%
Model

Real

Sei whale
100%
80%

Others
Copepod
Krill
Saury age 1
Saury age 0
Anchovy age 1+
Anchovy age 0

60%
40%
20%
0%
Model

Real

Bryde’s whale
100%
80%

Others
Copepod
Krill
Saury age 1
Saury age 0
Anchovy age 1+
Anchovy age 0

60%
40%
20%
0%
Model

Fig. 3.

Real

Comparison of proportion of preys taken by cetaceans between the model andthe real data (above: minke whale, middle: sei whale, below: Bryde’s whale).
Saury in the real data is not divided into the age group.

11Japanese anchovy

C atch age 2
C atch age 1
C atch age 0
N atural death age 2
N atural death age 1
N atural death age 0

100%

100%

80%

80%

60%

60%

40%

40%

20%

20%

C atch age 2
C atch age 1
C atch age 0
C onsum ption age 2
R esidual natural death age 2
C onsum ption age 1
R esidual natural death age 1
C onsum ption age 0
R esidual natural death age 00%0%
B efore separation

After separation

Pacific saury

C atch age 1
C atch age 0
N atural death age 1
N atural death age 0

100%

100%

80%

80%

60%

60%

40%

40%

C atch age 1
C atch age 0
C onsum ption age 1
R esidual natural death age 1
C onsum ption age 0

20%

20%

0%

0%
B efore separation

Fig. 4.

R esidual natural death age 0

A fter separation

Separation of natural death into consumption by cetaceans and residual
natural death (above: Japanese anchovy, below: Pacific saury)12Appendix 1. Specification of the minimum realistic model for JARPN II
The software used is STELLA (version 8, Japanese). STELLA is the intuitive icon-basedgraphical interface where difference equations are automatically generated, results are
shown

in

figure/tableandsensitivity

analyses

can

be

made

readily(http://www.iseesystems.com). The basic structure of the model is shown in Fig. 1.
AREA AND TIME DURATION
The modelling area is the whole JARPN II survey area except for the bottom layer on thecontinental shelf. Calculation is made monthly (dt = one month).
CETACEANS
Pella-Tomlinson model is applied to all baleen whales sampled during JARPN II (minke, sei
and Bryde’s whales). The example for minke whale is shown below.
Minke_number(t) = Minke_number(t - dt) + (Minke_increase - Minke_decrease) * dt
Minke_increase =Minke_number*Minke_MSYR*1.42*(1-(Minke_number/Minke_K)^2.389)
Minke_decrease = Minke_catch(in April)(in July)

Minke_biomass = Minke_number_in_the survey_area*Minke_average weight
Minke_necessary_energy = Minke_biomass*Minke_energy_per_day*30
Minke_number_in_the survey_area = Minke_number*Minke_migration
MAIN PREYS
An age-structured model is applied to the two main preys of commercial importance(Japanese anchovy and Pacific saury). The life-span is three and two years for Japanese
anchovy and Pacific saury, respectively. The example for Pacific saury is shown below(a=age).
Saury_number[a](t) = Saury_number[a](t - dt) + (Saury_recruitment- Saury_natural_death[a] - Saury_catch[a] - Saury_consumption[a]) * dt
Saury_recruitment = Saury_recruit*100*exp(Saury_pre_M*3)(in April)

Saury_natural_death[a] = Saury_number[a]*Saury_monthly_M[a]/(Saury_Fseason[a]+Saury_monthly_M[a)*(1-exp(-Saury_Fseason[a]-Saury_monthly_M[a]))Saury_catch[a] = Saury_number[a]*Saury_Fseason[a]/(Saury_Fseason[a]+Saury_monthly_M[a])*(1-exp(-Saury_Fseason[a]-Saury_monthly_M[a]))Saury_consumption[a] = Saury_consumption_weight[a]/Saury_weight[a]Saury_biomass[a] = Saury_number[a]*Saury_migration[a]*Saury_weight[a]13

SUPPLEMENTARY PREYS
A simple model with constant biomass (no seasonality) is used for preys of less commercial
importance. The biomasses are 110,000 (krill), 60,000 (copepoda) and 3,000 (others:mackerels, sardine, squids etc.) thousand tons, same as Mori et al. (2009).
CONSUMPTION
The consumption by cetaceans is assumed to be equal to the necessary energy. The monthly
total consumption of a prey is calculated by summing the consumption to the prey by eachcetacean. The example of the consumption by minke whale is shown below.
First, total monthly requirement of preys by minke whale is calculated as follow,
Minke_requirement = Minke_necessary_energy/Σ(Minke prey_energy*Minke_prey_%)
Minke_necessary_energy = Minke_biomass*Minke_necessary energy_per_day*30
The proportion of each prey taken by minke whale, for example, in the case of anchovy [age a],
is calculated as follows.
Minke_anchovy_%[a] = Minke_anchovy_biomass[a]*Minke_anchovy_preference[a]*Minke_anchovy_overlap[a]/Minke_all
Minke_all =Σ(Minke_prey_biomass[a]*Minke_prey_overlap[a]*Minke_prey_preference[a])Minke_anchovy_overlap[a] is the degree of distributional overlap between minke whale andanchovy[a] (see the Appendix 3). Minke_anchovy_preference[a] is the preference to anchovy[a] by minke whale (see the text).
Finally, the consumption of anchovy [a] by minke whale is calculated as follows,
Minke_anchovy_predation[a] = Minke_requirement*Minke_anchovy_%[a]Migration is the proportion of animals of the stock in the modelling area

14

Sei whale

Minke whale
Minke K

Minke MSYR

Minke catchMinkeweightSei increaseSeimigration

Minke number
in survey area

~

Minke
energy per day

Minkebiomass

MinkenecessaryenergyBrydes number

Brydes increase

Sei decrease

Sei
necessaryenergyCopepodKrillconsumption
consumption
weightweightBrydesenergh pre day

Seienergy per day

Anchovy
offshorecorrection

Brydespredation
calculationSei
predation
calculation

Saury
consumption
weightAnchovy
recruitment~

Anchovymonthly M

Anchovy
natural death

Pacific saury

Saury
Krill Copepod Others
Saurybiomass biomass biomass biomass weight

Anchovy
biomass

Anchovy
migration

Saury
migration~

Saury
consumption
Saury
natural deathSaury
recruitAnchovy
number~Anchovy
aging plus
Anchovy
recruitAnchovy
Anchovy catch
aging minus

Anchovy
pre M
Anchovy coastal
natural death~

Anchovy coastal
recruitment
Anchovy coastal
aging plus

Consumption~~

Anchovy
weightAnchovy
consumption

Brydesbiomass

Brydesenergy prer day

Othersconsumption
weightAnchovy
consumption
weightJapanese anchovy

Brydesmigration~

BrydesweightOthers annual
consumption
calculation

Copepoda annual
consumption
calculation

Minke
predation
calculation

Brydes decrease

Brydes number
in survey areaSeibiomass

SeiweightKrill annual
consumption
calculation~~

Sei number
in survey area~

Brydes catch

Brydes K

Brydes MSYR

Sei catch
Sei number

Minke decrease

Minke increase

Bryde’s whale

Sei K

~

Minke number

Minkemigration

Sei MSYR

Anchovymonthly M

Saury
recruitment
Saury
pre M

Anchovy
annual F
Anchovymonthly F

Anchovy
coastal catch

Saury
monthly M

Saury
numberAnchovy
coastal catch~

Anchovy
coastalnumberSaury
FseasonSaury
aging plus

Saury
catch
Saury
aging minus
Saury
monthly M

Saury
Fseason~Saury
monthly F

Anchovymonthly M
Anchovymonthly F

Anchovy coastal
aging minus

Virtual coastal part

Consumption calculation for minke whaleMinkeanchovy predation

Minkeanchovy energy

Minkekrill predation

Minkekrill energy

Minkecopepoda predation

Minkerequirement

Minke
copepoda energy

Stock
Minke
others predation

Minkeothers energy

Minkesaury predation

Minkesaury energyMinkeanchovy %Minkeanchovy overlap

~

Minke
copepoda overlap

~

Minke
others overlap

Minke
Minke
Minke
Minke
krill % copepoda % others % saury %~ConverterMinkesaury preference

~

Minke
krill overlap

Flow

Minke
others preference

Decision
Process DiamondMinkecopepoda preferenceMinkekrill preference
+

Minke
all

Fig. 1. The basic structure of the minimum realistic model for JARPN II.
.

15

Appendix 2. Catch series of minke, sei and Bryde’s whales*
The catches are taken in sub-areas 7, 8, 9, 11 and 12 for minke whale, from the west of 180
for sei whale, and in sub-areas 1 and 2 for Bryde’s whale (IWC, 1996; 1997; 2004: Ohsumi,1971).
M inke w hale
Year C atch
Year C atch
1930
131970 3071931
131971 263
1932
13
1972 337
1933
141973 518
1934
241974 3661935
241975 328
1936
24
1976 339
1937
57
1977 246
1938
68
1978 400
1939
68
1979 392
1940
79
1980 364
1941
57
1981 358
1942
68
1982 309
1943 101
1983 279
1944
79
1984 367
1945
68
1985 319
1946
96
1986 311
1947 115
1987 304
1948 1681988
01949 1341989
01950 2021990
01951 233
1991
01952 293
1992
01953 234
1993
01954 273
1994
21
1955 374
1995 100
1956 456
1996
77
1957 357
1997 100
1958 516
1998 100
1959 281
1999 100
1960 257
2000
40
1961 333
2001 100
1962 239
2002 150
1963 220
2003 150
1964 289
2004 159
1965 312
2005 220
1966 360
2006 1951967 270
1968 214
1969 213

Sei w hale
Y ear C atch
Year C atch
1946 560
1986
01947 466
1987
01948 620
1988
01949 897
1989
01950 5001990
01951 638
1991
01952 1102
1992
01953 741
1993
01954 8581994
01955 644
1995
01956 989
1996
01957 700
1997
01958 1357
1998
01959 1543
1999
01960 1078
2000
01961 8662001
01962 1462
2002
39
1963 1701
2003
50
1964 2118
2004 100
1965 1656
2005 100
1966 2445
2006 100
1967 3661
1968 3606
1969 3128
1970 2768
1971 1822
1972 1414
1973 1073
1974 748
1975 302
1976
0
1977
0
1978
0
1979
0
1980
0
1981
0
1982
0
1983
0
1984
0
1985
0

16

Bryde's w hale
Year C atch
Year C atch
1911 1681959 263
1912
01960 4041913
01961 167
1914
62
1962 504
1915 162
1963 210
1916
90
1964
68
1917
71
1965
8
1918
84
1966
55
1919
78
1967
45
1920
74
1968 171
1921
95
1969
89
1922
84
1970 139
1923
74
1971 919
1924 112
1972 160
1925 120
1973 698
1926 138
1974 1323
1927 116
1975 1433
1928
77
1976 1459
1929
61
1977 946
1930
64
1978 596
1931 135
1979 1028
1932 101
1980 793
1933
92
1981 485
1934 101
1982 482
1935 100
1983 545
1936
96
1984 528
1937 147
1985 357
1938 1701986 317
1939 2041987 317
1940
49
1988
0
1941 151
1989
0
1942
21
1990
0
1943
49
1991
0
1944 121
1992
0
1945
11
1993
0
1946 1411994
01947 2031995
01948 197
1996
01949 2311997
01950 2701998
01951 304
1999
01952 486
2000
43
1953
57
2001
50
1954
70
2002
50
1955
89
2003
50
1956
24
2004
50
1957
39
2005
50
1958 254
2006
50

Appendix 3. Information on Japanese anchovy and Pacific saury
The fish stocks within the EEZ of Japan are assessed annually by Fisheries Agency with thesupport of Fisheries Research Agency. Following information on Japanese anchovy andPacific saury was referred from the latest report of the domestic stock assessment (Fisheries
Agency of Japan, 2008).
JAPANESE ANCHOVY
Pacific stock of Japanese anchovy is distributed from coastal to offshore waters (Fig. 1). The
fisheries are operated throughout the year but the fishing operations are limited to thecoastal waters. Recent catches range from 200 to 400 thousands tons. While spawning takes
place all the year round except for winter, the main spawning season is now early spring tosummer and the recruitment of age 0 fish to the fisheries occurs several months later. For
convenience the recruits in January were used in the stock assessment although therecruitment takes place essentially after April. In the model, the values were adjusted tothose in April by using the natural mortality rate of age 0 for three months (called pre_M).
The fish matures one year old and the life-span is 3 years (A fish gets older at January 1st
and lives just 3 years in the model).
Cohort analysis showed recruits and fishing mortality rates (Table 1: only recent years). The
stock was at high level but decreasing. Recommended yearly fishing mortality rate as
ABCtarget was 1.07 to age 1 for 2008 fishing year. After 5 years the fishing mortality ratewould support the lowest spawning biomass in the recent 5 years. In the stock assessment,
yearly natural mortality rates applied to were 1.0 for age 0-1 and 1.6 for age 2. Those were
estimated empirically with maximum length, growth parameter and water temperature(Pauly, 1980; Quinn and Deriso, 1999). Relationship between age in month and body weight(g): BW = 9.5762t + 3.4685. Recently the information on the offshore biomass became
available by the acoustic surveys under JARPN II.

Table 1.R ecruits in January and fishing m ortality rates
by age for Japanese anchovy.
Year

Recruits
10^6
127,952
160,838
154,941
90,294135,426
92,921

2001
2002
2003
2004
2005
2006
Fig. 1. Distribution of Pacific stockof Japanese anchovy.

17

Fishing m ortality rate
A ge 0A ge 1
A ge 2+
0.02
0.65
1.75
0.03
1.33
2.24
0.02
1.39
3.47
0.03
1.30
3.02
0.01
1.08
2.59
0.02
1.26
3.03

PACIFIC SAURY
Pacific saury is distributed widely in the offshore waters (Fig. 1) and conducts the
anticlockwise seasonal migration. The fisheries take place during summer and autumn(Fishing season was set from July to December in the model as in the stock assessment).
Recent catches are around 400 thousands tons, half of them are taken by Japan. Main
spawning season is winter. As the abundance is available from the June/July mid-water
trawl survey, recruitment is treated to occur as the end of June in the stock assessment (Fullrecruitment was assumed to occur April in the model as predation begins in May). Some fish
matures at one year old and the life-span is 2 years (A fish gets older at January 1st in themodel).
Based on the June/July mid-water trawl survey, the stock assessment has been madeannually (Table 1). Recommended fishing mortality rate for 2008 6-month fishing season is0.298 to age 1 (multiplied by 0.438 to age 0). The ABCtarget was based on the SPR analysis.
The natural mortality rates were estimated as 0.0535 on average by tracing the year class aswell as the fishing mortality rates. Relationship between age in day and body weight (g): BW= 200.46(1-exp(-0.004(t+44.79)))^3.

Table1.R ecruits in July and m onthly fishingm ortality rate by age for P acific saury
Y ear
R ecruits Fishing m ortality rate
10^8
A ge 0A ge 1
2001(553)
0.00390.0168
2002
945
0.00420.01682003
329
0.00340.01102004
631
0.00370.02072005
481
0.00090.01892006
381
0.00730.0165( ):an average of 2002-2006

Fig. 1. Distribution of Pacific saury (2007 June/July mid-water trawl survey)

18

Appendix 4. Overlap of monthly distribution between cetaceans and preys
As one of the factors that decide the proportion of prey taken by a cetacean, the overlap of
distribution between cetaceans and preys were analyzed from May to September. The survey
area was divided into 1*1 degree blocks and relative density (low: 1, middle: 2, high: 3) was
assigned tentatively for cetaceans and preys in each block. Highest relative density (4) was
given to the blocks in the main fishing grounds of the preys. Due to the limited data, someextrapolation and assumption were made, for example, to unsurveyed area of cetaceans.
DISTRIBUTION OF CETACEANS
The monthly distribution pattern of cetaceans was estimated with the data from JARPN II
sighting surveys. Examples of determination of the pattern are shown in Fig.1. Three speciesof cetaceans showed the northward movement during the period (Fig. 2). Minke whale wasdistributed widely from the west to the east and reaches the northernmost part north of 46 N
in August/September. It is known that minke whales enter into the Sea of Okhotsk insummer. While the distribution pattern of sei whales was similar to that of minke whales,
the summer distribution was limited to the north-eastern part of the survey area. Some
Bryde’s whales appeared in the southernmost part of the survey area in May. The northern
limit of the summer distribution was around 42 N. Those results are well coincide with thepast information.
DISTRIBUTION OF PREYSFor Japanese anchovy and Pacific saury, rough figures on the distribution by feeding andspawning seasons are provided by Fishery Agency of Japan (2008). Since 2001 more detailed
information on saury has been provided through the June/July mid-water trawl survey
covering widely the most western part of North Pacific. The information on the seasonal
fishing grounds is available for both Japanese anchovy and Pacific saury. As the information
on seasonal movement was limited, the monthly distribution patterns of Japanese anchovy
and Pacific saury were assumed mainly with the constant northern sift (Fig. 3). For the
supplementary preys (krill, copepoda and others), even distribution was assumed in themodelling area except that relatively high density (middle: 2,) was assigned to krill andcopepoda in the coastal and northern areas.
OVERLAP OF DISTRIBUTION
An example of the monthly overlap of distribution between cetaceans and preys is shown for
June (Fig.4). The red and grey circles show overlapped and not overlapped blocks,
respectively. Minke whale was well overlapped with Pacific saury (age 0 and 1) and Japanese
anchovy (age 1+). Sei whale was relatively well overlapped with Pacific saury (especially age0). Bryde’s whale was well overlapped with Japanese anchovy (age 0) but not with Japanese
anchovy (age 1+) or Pacific saury. As the input for the model, the degree of overlap was
weighted with the assigned density of prey.
19

Minke whale

AugustJune

Fig. 1.

Sei whale

Bryde’s whale
July

Examples of determination of the monthly distribution pattern with the datafrom JARPN II sighting surveys.

Minke whale

Sei whale

Bryde’s whale

August/September

July

June

May

Fig. 2.

Monthly distribution pattern of three cetacean species (the size of circle shows
the relative density assigned to the block).
20Anchovy age 0
May-September

Saury age 1

Saury age 2
September

Anchovy age 1
AugustAugustJuly/September

July

June

June

May

May

Fig. 3.

Monthly distribution pattern of Japanese anchovy and Pacific saury (the sizeof circle shows the relative density assigned to the block).

21

Minke whale

Sei whale

Bryde’s whale

Japanese anchovy age 1+

Japanese anchovy age 0

Pacific saury age 1

Pacific saury age 0

Krill and Copepoda

Fig. 4.

Examples of the overlap of distribution between cetaceans and preys in June (redcircle: overlapped, grey circle: not overlapped). The size of circle shows relative density
assigned to the block.
22