SC/F16/JR29

Predation impacts on sandlance population by
consumption of common minke whales off Sanriku
regionTOSHIHIDE KITAKADO1, HIROTO MURASE2 AND TSUTOMU TAMURA3
1 Tokyo University of Marine Science and Technology, 1-5-7 Konan, Minato-ku, Tokyo 108-0075, Japan
2 National Research Institute of Far Seas Fisheries, Fisheries Research Agency (FRA), 2-12-4 Fukuura,
Kanazawa, Yokohama, Kanagawa 236-8648, Japan
3 Institute of Cetacean Research, 4-5 Toyomi-cho, Chuo-ku, Tokyo 104-0055, Japan
Contact e-mail: kitakado@kaiyodai.ac.jp

ABSTRACTA statistical analysis was conducted to assess predation impacts of the common minke whales on the sandlance
population off Sanriku region. A state-space delay-difference model, which is a two-stage population dynamics modelwith a stock-recruitment relationship, was used for the sandlance population to employ two independent time series
indices for the juvenile and mature population sizes as well as catch and age-composition data. Predation impacts on thesandlance were assessed through minke whales’ consumption expressed as a functional response. To take into accountseveral stochastic flexibilities such as process errors, a Bayesian method was used to estimate the parameters and latentvariables in the model. The results showed that the predation by the common minke whales accounts for a certain
proportion of the current adult biomass for the sandlance population although the level of proportion is sensitive to themodel assumption.
KEWWORDS: COMMON MINKE WHALES, DELAY-DIFFERENCE MODEL, PREDATION, SANDLANCEINTRODUCTION
The sandlance off Sanriku, which is the western North Pacific region of Japan, is one of commerciallyvaluable fishery populations in that area. The sandlance is also one of prey species for the western North
Pacific common minke whales, and therefore an interaction between fishery and predation by thecommon minke whales is of interest for better understanding of the sandlance population.
The life history of sandlances is illustrated in Figure 1. The peak spawning season is an early period in thecalendar year, and then the fishery by dip nets starts in February for adult sandlances, which continues
until June, and that for juvenile sandlances comes next from March to May. As an atypical ecological life
history of this species, they have an aestivation period after the fishing season, and a sampling experimenthas been conducted to collect its size-distribution, which is converted to the age-composition data.
Fishery for this species has a long history but the data of catch and population index are poor until 1960.
Also, stock indices are available only since mid-1990 although separate indices are available for juvenile
and adult sandlances. To exploit this merit and also to employ a moderate complexity of model, we will
use a delay-difference model (e.g. Hilborn and Walters, 1992; Meyer and Millar, 1999). A state-spacemodel is constructed to take account for both the observation and process errors.

MATERIALS AND METHODS
Data1) Catch series of juvenile sandlances by lift nets with light fishery from 1960-2015 (Figure 2)
2) Catch series of adult sandlances by dip nets fishery from 1960-2015 (Figure 2)
3) CPUE series of juvenile sandlances by lift nets with light fishery from 1994-2015 (Figure 3)4) CPUE series of adult sandlances by dip nets fishery from 1994-2015 (Figure 3)5) Time series data for age composition from 2002-2013
6) Consumption of sandlances by common minke whales in 2005, 2006 and 2012 (Table 1; see Tamura etal., 2016: SC/F16/JR17 for more details)
7) Time series of abundance estimates in Sanriku region for the common minke whales in 2004, 2005,

1

SC/F16/JR29

2006 and 2012 (Table 2; see Hakamada et al., 2016: SC/F16/JR11 for more details)
Notation
Parametersr
KJ

Definition

Note

Resilience
Recruitment at carrying capacity
Carrying capacity of adult abundance(1000ton)
Depletion level in 1960
Exponent of density dependence
Fecundity at the carrying capacity

U(0.01, 2)
f KA

Juvenile survival rate

U(0.01, 0.99)

SA

Adult survival rate

U(0.01, 0.99)

qJ

Juvenile survival rate

U(0.00001, 0.99)

qA

Adult survival rate

U(0. 00001, 0.99)

FJ

Exploitation rate for juveniles

U(0.01, 0.99)

FA

Exploitation rate for adultU(0.01, 0.99)

Residuals

U(0.001, 1) for all SDs

Growth intercept
Growth slope
Weight at age 0
Weight at age 1
Per capita maximum consumption
Parameter in functional response

Fixed at 9.519
Fixed at 0.234
Fixed at 3.264 (g)Fixed at 10.33 (g)U(0.001,100)
U(1,1000)

N J ,tJuvenile sandlance abundance in year t

Log normal process error

N A,tAdult sandlance abundance in year t

Log normal process error

BJ ,tJuvenile sandlance biomass in year t

BA ,tAdult sandlance biomass in year t

I J ,tObserved CPUE for juvenile sandlances

Log normal

I A ,tObserved CPUE for adult sandlances

Log normal

C J ,tObserved CPUE for juvenile sandlances

Log normal

C A ,tObserved CPUE for adult sandlances

Log normal

Neff

Effective sample size

AssumedAge composition adjusted by Neff

MultinomialPˆt

Number of migrant minke whales off Sanriku

Log normal

Yt

Consumption of sandlances by minke whales

Log normal

KA
DA
z

f
SJ

 J ,  A etc.


w0
w1
cmax
BH

U(1,100)
U(0.01, 0.99)
Fixed at 1
Derived by (4)Estimated in the modelDatant  (n0,t , n1,t , n2 ,t )2

SC/F16/JR29

State-space Population Dynamics Models for sandlances (Model I)
We employ a delay-difference model with juvenile and adult stages. The list above summarizes notations
used in this paper. The number of juvenile sandlances is assumed to be expressed as a density dependent
stock-recruitment model with a process error as follows:  N  z  u
N J ,t  f N A,t 1  r 1   A,t    e J ,t , u J ,t ~ N (0,  J2 ) .
  K A  





(1)

The number of adult sandlances is expressed as a sum of survived juveniles and adults as follows: uA,t , u A,t ~ N (0,  A2 ) (2)N A,t  (1  FA, period (t 1) )S A N A,t 1  (1  FJ , period (t 1) )S J1/2 S 1/2
A N J ,t 1  e
As in other population dynamics models, a simultaneous equation for the equilibrium conditions at thecarrying capacity (say K J and K A ),
 K  
 K J  f K A 1  r 1  A   K A   ,

1/2 1/2
 K A  S A K A  SJ S A K J(3)produces an explicit solution for the fecundity, f , as

f 

1 SA
.
1/2
S 1/2
J SA

(4)

The biomass of juvenile and adult sandlances can be given by the following formulas:

BJ ,t  w0 N J ,t
BA,t  w1 N A,t(5)

Using a relationship

BA,t  w1 N A,t  w1 (1  FA,t )S A N A,t  w0 (1  FJ ,t )S J1/2 S 1/2
A N J ,t(6)

and Ford-Brody

w1 N A,t   N A,t   BA,t ,(7)which is derived from a general assumption of growth for fish of age a

wa Na,t  (   wa 1 ) Na,t   Na 1,t   wa 1 Na 1,t  (1  Fa )Sa ,(8)

the following recursive formula is obtained:
1/2
BA,t  ( N A,t 1   BA,t 1 )(1  FA, period (t ) )S A  w1 (1  FJ , period (t ) )S 1/2(9)
A S J N J ,t 1 .

3

SC/F16/JR29

State-space Population Dynamics Models for sandlances with whale consumption (Model II)
In case that the morality by the minke whale predation is taken into account, then the following model is
proposed, where g is a function for functional response: u A,t
1
N A,t  (1  FA, period (t 1) ) S A N A,t 1  g ( BA,t 1 ) Pt  (1  FJ , period (t 1) ) S J1/2 S 1/2, (10)A N J ,t 1  ew1
where the functional response is generally given byg ( BA,t ) cmax BAm,t
BHm  BAm,t

,

(11)

though we here assume only m=1 (Type II functional response).

Observation models
CPUE data (tons/vessel) are available for juvenile and adult sandlances. Here, neither of hyperstability
nor hyperdepletion is considered for both the fisheries.

log I J ,t ~ N (log(qJ , period (t ) BJ ,t ), J2 )(12)

log I A,t ~ N (log(q A, period (t ) BA,t ), A2 )The total catch and age-composition data are also available for estimation of parameters as follows:

log CJ ,t ~ N (log( FJ , period (t ) BJ ,t ),  J2 )(13)

log C A,t ~ N (log( FA, period (t ) BA,t ),  A2 )andnt  (n0,t , n1,t , n2,t ) ~ Multinomial ( Nt ,( p0,t , p1,t , p2 ,t )) ,

(14)

where

p0,t  (1  FJ ,t ) S 1/2
J N J ,tp1,t  (1  FA,t ) S A (1  FJ ,t 1 ) S 1/2
J N J ,t 1(15)

p2  ,t  (1  FA,t ) S A (1  FA,t 1 ) S 1/2
A N A,t 1
andnt  (n0,t , n1,t , n2 ,t )isavectorfortheage-compositionofsampledindividuals( Nt  n0,t  n1,t  n2  ,t ). We here assume an effective sample size (Neff) as 100 for all the years.
The total consumption of sandlance by the common minke whales and the population size of minke
whales contributed to the likelihood in Model II.

ˆ 2)
log Pt ~ N (log Pt , CVtlog Pt ~ (iid ) N (log P ,  2 )(16)

log Yt ~ N (log( g ( BA,t ) Pt ), cvt2 )

(17)

4

SC/F16/JR29

Statistical estimation
Due to a large number of parameters are included in the model, achievement of convergence might bedifficult when the likelihood is tried to be maximized. Also, usually it is hard to distinguish the processerror variance from observation error variance. Therefore, when the process error is estimated, a Bayesian
method is applied. Also in theory the Bayesian method has a benefit when a hierarchical structure such assmooth changes in the fishing mortality is incorporating into the model.
A Markov Chain Monte Carlo method (e.g. Gelman et al., 2013) was employed for generating posterior
distribution. A software WinBUGS (Speigelhalter, 2003) was used for this computation.

RESULTS AND DISCUSSION
Model Fitting and Parameter estimates
Figures 4 shows the posterior distributions of key estimated parameters in Model I, and Figure 5 presents
fittness in CPUE as well as the estimated population trajectories for juveniles and adults in that model.
Also, Figure 6 and 7 provide the same information for Model II. The posterior distributions are almost
unimodal except for some paratemers with bounds, but the original assumption of prior shapes and thegenerated posterior distributions indicated that all the parameters were well-updated using information ofobserved data. However, in most recent years, the predicted CPUEs tend to be greater than observed
values. This might be attributed to changes in the fishery; the less fishing efforts compared to theprequake level.
The total biomass level of sandlaces is estimated differently in Models I and II, respectively. The results
showed that the predation by the common minke whales accounts for a certain proportion of the current
adult biomass for the sandlance population although the level of proportion is sensitive to the model
assumption.
Potential sensitivity tests and extensions
We applied a Bayesian method for estimation parameters, but further analyses should be conducted to
examine sensitivities of the results to the assumption of prior distributions.
Regarding the modelling, we only consider a Type II functional response to link between preys andpredators in the model. Another functional form and/or multiple-prey functional response with krill andanchovy are worth investigation. Also, it is possible to extend the model by incorporating morehierarchical structures such as assumption of smooth changes in fishery coefficients. Bayesian methods
have benefits of these sorts of extensions.
How weights are allocated to likelihood components is a matter of interest these days especially in theforum of integrated models, which tend to use a multiple sources of information/data. Usually, due to anature of fishery population, the actual samples for age composition are not independent and therefore thereduced sample size, so-called the effective sample size (which is less than the original sample size), is
assumed to relatively down-weight the likelihood of age/size composition data to the CPUE data etc. A
more careful examination will be addressed in the future.

ACKNOWLEDGMENTS
The authors are grateful to Drs. Saeki and Onodera, scientists of Miyagi Prefectural Fisheries Researchand Development Center, for their valuable data of the sandlance population.

REFERENCES
Hakamada, T. Matsuoka, K., Kishiro, T. and Miyashita, T. 2016. The number of western North Pacific common minke whales(Balaenoptera acutorostrata) distributed in JARPNII coastal survey areas. Paper SC/F16/JR11 presented to the JARPNII special
permit expert panel review workshop, Tokyo, February 2016 (unpublished). 7pp.
Gelman, A., Carlin, J. B., Stern, H. S. and Rubin, D. B. 2013. Bayesian Data Analysis (3rd ed). Chapman and Hall/CRC.

5

SC/F16/JR29

Hilborn, R. and Walters, C. J. 1992. Quantitative Fisheries Stock Assessment. Chapman and Hall.
Meyer, R. and Millar, B. R. 1999. Bayesian stock assessment using a state–space implementation of the delay difference model.
Canadian Journal of Fisheries and Aquatic Sciences, 56(1): 37-52.
Okamura, H., Nagashima, H. and Yonezaki, S. 2009. Preliminary assessment of impacts on the sandlance population by
consumption of minke whales off Sanriku region. Paper SC/J09/JR14 presented to the JARPNII special permit expert panel review
workshop, Yokohama, January 2009 (unpublished). 20pp.
Speigelhalter, D. Thomas, A., Best, N. and Lunn, D. 2003. WinBUGS version 1.4 User manual.
Tamura, T., Kishiro, T., Yoshida, H., Konishi, K., Yasunaga, G., Bando, T., Saeki, M., Onodera, K., Mitsuhashi, M., Yamashita, Y.,
Funamoto, T. and Kato, H. 2016. Updated prey consumption by common minke whales and interaction with fisheries in coastal
areas. Paper SC/F16/JR17 presented to the JARPNII special permit expert panel review workshop, Tokyo, February 2016
(unpublished). 47pp.

6

SC/F16/JR29

Table 1. Consumption of sandlances by common minke whales.

Year
2005
2006
2012

Sandlance consumption (ton)
3,709
1,522
683

CV
0.16
0.18
0.22

Table 2. Time series of abundance estimates in Sanriku region for the common minke whales

Year
2004
2005
2006
2012

Minke whale abundance
260
401
216
124

CV
0.56
0.32
0.41
0.37

Sampling

Birth

Sampling
Adult Fishery

Juvenile FisheryJan

From March to May Aestivation
periodFigure 1. Life history of sandlance population.

7

Jan

SC/F16/JR29

Figure 2. Time series of catch for juvenile and adult sandlances.

Figure 3. Time series of CPUE for juvenile and adult sandlances.

8

SC/F16/JR29

Figure 4. Posterior distributions of key estimated parameters in Model I.

Figure 5. Fittness in CPUE and estimated population trajectories with 95% credible region for juveniles
and adults for Model I.

9SC/F16/JR29

Figure 6. Posterior distributions of key estimated parameters in Model II.

Figure 7. Fittness in CPUE and estimated population trajectories for juveniles and adults for Model II.

10