SC/F16/JR43

Fitting to catch-at-age data for North Pacific common minke
whales in the Pacific side of JapanTOSHIHIDE KITAKADO1 AND HIKARI MAEDA2
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Tokyo University of Marine Science and Technology, 5-7, Konan 4, Minato-ku, Tokyo 108-8477, Japan
National Research Institute of Far Seas Fisheries 2-12-4, Fukuura, Kanazawa, Yokohama, Kanagawa 2368648, Japan

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ABSTRACTThe catch-at-age data for common minke whales in the western North Pacific provided by the
JARPN/JARPNII program are used to refine existing RMP Implementation Simulation Trials (ISTs) in a simple
way, so as to investigate the relative plausibility of the single- and two (Ow and Oe) stock hypotheses for theO whales in the Pacific side of Japan. While the single stock scenario seems consistent with these age data, it
is difficult to reconcile the two stock hypothesis with these data because of the relative absence of particularly
younger whales in a supposedly separate discrete Oe stock. The analysis demonstrates the importance formanagement purposes of obtaining age data for the minke whales in the western North Pacific, which in turnnecessitates lethal sampling. Such age data need to be incorporated in the conditioning of revised RMP ISTs
for common minke whales in this region.

INTRODUCTION
Despite considerable investment in the analyses of genetic and non-genetic data, different views remain in the
IWC Scientific Committee (IWC SC) on the plausibility or otherwise of sub-structure within the O stock ofcommon minke whales in the Pacific side of Japan. In terms of the RMP trials for common minke whales in thewestern North Pacific, there could be only one stock (hypothesis A), or there could be two: a coastal (Ow) and an
offshore (Oe) stock (hypothesis C) (IWC, 2014). This distinction has important implications for management,
particularly as regards sustainable catches of O minke whales in coastal regions in the Pacific side of Japan, as
these could be set much higher if the two-O-stock scenario of hypothesis C could be refuted. In the trials, most ofthe ‘Unacceptable Trials’ were under the stock scenario of the hypothesis C (IWC, 2014).
The recent availability of age data from the JARPN and JARPNII catches of these whales (see Maeda et al., 2016;
SC/F16/JR53) provides a basis to improve the accuracy of the RMP Implementation Simulation Trials (ISTs) of
IWC (2014) for these minke whales through taking these data into account when conditioning these trials. This
document provides a first step in this direction by using these new data in a simple way to examine the plausibilityof the Ow-Oe stock scenario, through use of a Statistical-Catch-At-Age (SCAA) assessment approach.
MATERIALS AND METHOD
The data used for these analyses are listed in Appendix A.
The SCAA methodology applied is described in detail in Appendix B. Essentially this methodology takes inputs
from the hypotheses A and C for the baseline MSYRmat 1% and 4% trials, conditions on their 2000 estimates ofmature female abundance, and fits to the historical catch and JARPN/JARPNII catch-at-age data to determine preexploitation abundances and selectivity-at-age vectors over the period of these research permit catches. Note thatfor the Hypothesis A of a single O stock, it is necessary to allow for different selectivity-at-age vectors for thecoastal and offshore regions, given the catch-at-age composition differences between the two (for the earlier
period of commercial catches, the assumptions made for the ISTs (IWC, 2014) are retained).
RESULTS AND DISCUSSION
Four runs have been carried out, corresponding to trials A01_1, A01_4 (one O stock, MSYR mat of 1% and 4%,
respectively) and trials C01_1, C01_4 (Ow and Oe stocks, MSYRmat of 1% and 4%, respectively). Results forthese four runs are presented in Table 1 and Figures 1 to 4.

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In the Figures, the top row plots shows the trajectories of mature females, followed by total numbers and thecatches by gender and region/stock. The second row of plots shows the estimated selectivities for eachregion/stock. The third and fourth rows show the fit to the catch-at-age data, first aggregated over the years forwhich data are available and then as bubble plots of the standardised residuals.
The key results from these analyses are the selectivity vector estimates shown in Figures 1-4. For hypothesis A in
Figures 1 and 2 (the single O stock scenario), the coastal region (corresponding to that assigned to the postulated
Ow stock) selectivity is virtually independent of age, and reflects the presence of the youngest animals in thestock. However these animals are generally absent offshore, where the selectivity vector rises slowly to asymptote
only once reaching ages of 20 and greater. This is compatible with the concept of a single stock that is nothomogeneously distributed in terms of age, with the younger animals more concentrated in the coastal region. Of
course, future revised ISTs, which take explicit account of age-specific movement patterns, would need to seek
selectivity curves which were all closer to uniform over ages, which might in turn necessitate modifications to thenatural mortality-at-age vector that is adopted at present for these trials.
For hypothesis C in Figures 3 and 4, the selectivity curves estimated are very similar to those for hypothesis A,
but their interpretation is different, which is important. The near flat selectivity curves for the Ow stock are notproblematic – all age groups within a supposedly discrete population are represented. In contrast though, theslowly increasing selectivity curves for the supposedly discrete Oe stock are very difficult to explain. Certainly
the youngest whales are missing, and furthermore females up to about age 20 are more heavily under-represented
than males. While this might in part be explained by some mature females having entered the Okhotsk Sea before
the JARPN/JARPNII sampling further to the southeast took place, the overall under-representation of younger
animals is hardly possible to reconcile with the associated hypothesis of a separate Oe stock which would need toreflect reasonable proportions of all age components of the stock.
CONCLUDING REMARKS
These “missing” younger whales from the Oe stock in the two-O-stock hypothesis C scenario raise serious
questions about the plausibility of this hypothesis. In future RMP ISTs, the conditioning needs to take age-structure
data into account to better reflect the underlying dynamics of this population.
This analysis demonstrates the importance for management purposes of obtaining age data for the whales in theregion concerned, which necessitates lethal sampling.
ACKNOWLEDGEMENTS
We thank Doug Butterworth and Rebecca Rademeyer for advice related to SCAA on conducting this analysis,
and Cherry Allison (IWC Secretariat) for providing the RMP trial outputs used.
REFERENCES
IWC. 2014. Report of the Scientific Committee, Annex D1. J. Cetacean Res. Manage. 15 (Suppl): 112-188.
Maeda, H., Bando, T., Kishiro, T., Kitakado, T. and Kato, H. 2016. Basic information of earplug as age
character of common minke whales in western North Pacific. Paper SC/F16/JR53 presented to the
JARPNII special permit expert panel review workshop, Tokyo, February 2016 (unpublished).10pp.

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Table 1: Results for the four SCAA runs

*These contributions are zero because very small values are input for the standard errors of the abundance
estimates to force trajectories to hit the abundance value given.

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Figure 1: Results for A01_1.

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Figure 2: Results for A01_4.

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Figure 3: Results for C01_1.

6Figure 4: Results for C01_4.

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Appendix A - The data

The catches assumed by regions/stocks for males and females separately are given in Table A1 (Cherry Allison,pers. commn). These catches are median outputs from trials A01_1/4 and C01_1/4 which are detailed in IWC(2014). For the one stock hypotheses, the catches for males and females have been split by region corresponding
to OW and OE (see details given below), assuming the same OW:OE proportions as those in the corresponding
C01_1 and C01_4 trials.
The numbers assumed for mature females in 2000 are provided in Table A2. They correspond to deterministic
values for the associated trials, kindly provided by Cherry Allison.
Table A3 gives the males and females catches-at-age from JARPN surveys for the regions corresponding to OW
and OE (Luis Pastene, pers. commn). Catches in sub-areas 8, 9 and 7E have been assigned to region/stock OE.
Catches in sub-areas 11, 7CN and 7CS have been assigned to region/stock OW. Catches in sub-area 7WR havebeen assumed to come from region/stock OE if taken east of 145E and OW otherwise.
Table A4 lists the life history parameters used (IWC, 2014), taken to be the same for both stocks in the two-stocks
hypothesis.

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Table A1: Male and female minke catches assumed for each run (see above for source).

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Table A2: Number of mature females in 2000 (Cherry Allisson, pers. commn).

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Table A3: Catch-at-age data from JARPN surveys for regions corresponding to OW and OE.

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Table A4: Life history parameter values (as defined for the trials detailed in IWC(2014)).

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Appendix B - The Statistical Catch-at-Age Model

The text following sets out the equations and other general specifications of the SCAA followed by details of thecontributions to the log-likelihood function from the different sources of data available. Quasi-Newton
minimization is then applied to minimize the total negative log-likelihood function to estimate parameter values(the package AD Model BuilderTM (Fournier et al. 2011) is used for this purpose).
B.1. Population dynamics

B.1.1 Numbers-at-age
The resource dynamics are modelled by the following set of population dynamics equations:Ng, jy 1,a
0.5b yj1g, j
N y ,a 1  C yg,,aj1 S a 1
 N g, j  C g, j S  N g, j  C g, j S
y ,m 1
m 1
y ,m
y ,m
m
 y ,m 1

where
N yg,,aj

C

g, j
y ,a

b yj













if a  0
if 1  a  m(B1)

if a  mis the number of animal of gender g and age a in stock j at the start of year y,is the catch (in number) of animal of gender g and age a in stock j during year y,is the number of calves born to females from stock j at the start of year y,is the survival rate  e  M where M a is the instantaneous rate of natural mortality (assumed to be
independent of stock and gender),m  20 is the maximum age (treated as a plus-group).
Saa

B.1.2. Births
Density-dependence is assumed to act on the female component of the mature population.
zb yj  B j N yf , j 1  A j 1  N yf , j K f , j  

 





where
Bj



j

(B2)

Aj
zj

is the average number of births (of both genders) per year for a mature female in stock j in the pristine
population,is the resilience parameter for stock j (see Table A4),
is the degree of compensation for stock j (see Table A4),

N yf , j famis the age-at-first parturition (see Table A4);

f af , jis the proportion of mature female of age a in stock j,f,ja

N yf,,aj is the number of mature' females in stock j at the start of year y,

a

K

f,j

is the number of mature females in stock j in the pristine population.

B.1.3. Total catch and catches-at-age
The catch-at-age is given by:13

C yg,,aj  Fyg , j v yg,,aj N yg,,aj

(B3)

where
C yg,,aj

is the catch-at-age, i.e. the number of animal of gender g and age a in stock j caught during year y,v yg,,aj

is the commercial selectivity of an animal of gender g and age a in stock j for year y; when v y ,a  1 , theg, jage-class a is said to be fully selected,
C yg , jis the proportion of a fully selected age class that is caught , andFyg , j 
 v yg,,aj N yg,,ajaB.1.4. Initial conditions
For the first year (y0) considered in the model (here 1930), the numbers-at-age are taken to be at unexploitedequilibrium, i.e.:

0.5B j K f , j
N yg0,,ja   N yg0, ,ja 1 S a 1
 g, j N y 0,m 1 S m 1 /(1  S m )for a  0
for 1  a  m  1(B4)

for a  m

B.2. The likelihood function
The model is fitted to estimates of mature female numbers and catch-at-age data to estimate model parameters.
Contributions by each of these to the negative of the log-likelihood (- nL ) are as follows.

B.2.1 Estimates of mature female numbers

 

2

 yj   n 
2 
2  
j 



(B5)



 yj  n I yj   n  f af , j N yf,,aj 
a




(B6)

 n L

abund

with

where
I yj

  0.01

is the estimate of mature female numbers in year y and stock j, and(i.e. sufficiently low to force an exact fit to I yj )B.2.2. Commercial catches-at-age
The contribution of the catch-at-age data to the negative of the log-likelihood function under the assumption of amultinomial error distribution is given by: pˆ yg,,aj  n LCAA    p yg,,aj ln
g, j 
j, y,g a  pˆ y ,a ' 
 a'


(B7)

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wherep yg,,aj

is the observed number of whale of age a and gender g caught in year y in stock j,pˆ
is the model-predicted number of whale of age a and gender g caught in year y in stock j,
wherepˆ yg,,aj  Fyg , j v yg,,aj N yg,,aj
g, j
y ,a

(B8)

The standardised residuals are computed as: yg,,aj pp yg,,ajg, jy ,a '

 pˆ yg,,aj

a'

 pˆ

g, j
y ,a 'a'(B9)

 yg,,aj

with

p




pˆ yg,,aj 1 pˆ yg,,aj'   pˆ yg,,aj' 

a'
a'


g, j
p
 y ,a 'pˆ yg,,aj

g, j
y ,a

 yg,,aj 

(B10)

a'

B.3. Harvesting selectivity
Fishing selectivities-at-age are estimated using a logistic form:v aj  1  e (  a ) 
j

j



1

(B11)

The selectivities are taken to be the same for males and females. Pre-1988, the selectivities are taken to be thesame for the two regions/stocks, with the parameters fixed:  j  4 and  j  1.2 (i.e. as for the trials detailed in
IWC (2014)). Post-1988, the selectivities are estimated separately for the two regions/stocks.

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