FISHERIES SCIENCE 2002; 68: 87–94

INTRODUCTION

Shellfish resources in coastal areas are overex-ploited easily because of their lesser mobility.Neptune whelk Neptunea arthritica is a commer-cial gastropod distributed around Hokkaido. Thisspecies is an important target of trap fishery inShiriuchi and fishery management of the species isrequired.

Reproduction and mortality are important para-meters of fishery management. Growth and repro-duction of N. arthritica have been well studied,1–8

but published information about its mortality isavailable only in a study by Fujinaga and Nakao.9

They estimate the mortality rate of each age classfrom the density of individuals; however, there isno distinction between natural mortality andfishing mortality in their study, which is important

for evaluating the effect of fishing on the whelkpopulation. To estimate fishing effect, an analysisof age distribution is usually used.10 But the agecharacteristics of N. arthritica have not yet beeninvestigated.

Tag and recapture experiments are also used for mortality estimation.11–13 Sudden death afterrelease is a major problem in the case of fishtagging studies.14 For gastropods, a tagging experi-ment is more suitable because their sudden deathafter marking occurs less frequently. In studies ofwhelk Dicathais orbita,15 nodulose reef creeperCerithium nodulosum,16 abalone Haliotis laevigataand Haliotis ruber,17 successful tagging experi-ments and estimates of mortality have beenreported.

The aim of the present paper is to estimate thenatural mortality and exploitation rate of commer-cial fishing on N. arthritica in the Shiriuchi fish-ing ground. We developed a statistical model todescribe multiple tag-and-recapture data. Accord-ing to the model, we estimate the mortality coef-ficient as a constant and exploitation rates asvariables, which depend on every sample group.

Original Article

Estimation of natural mortality and exploitation rates of whelk Neptunea arthritica by

multiple tagging experimentKengo SUZUKI,*a Tomonori HIRAISHI, Katsutaro YAMAMOTO AND Katsuaki NASHIMOTO

Hokkaido University, Graduate School of Fisheries Sciences, Division of Marine Environment and Resources, Laboratory of Fishing Production System, Hakodate, Hokkaido 0410-8611,Japan

ABSTRACT: To estimate the natural and fishing mortality of whelk, Neptunea arthritica, a multipletagging experiment was carried out in Shiriuchi, Hokkaido between August 1991 and March 1994.Whelks collected by trapping surveys were used in tagging experiments. All recaptured whelks werereleased back again so that a statistical model based on binomial distribution could be developed.Maximum likelihood estimator of the natural mortality coefficient and that of exploitation rate weredetermined numerically. Analysis of the recovery data show: (i) no size-dependent mortality wasobserved in whelks larger than 40 mm in shell height; (ii) the daily natural mortality coefficient was1.438 ¥ 10-3, thus annual natural mortality rate was 41%; and (iii) the exploitation rate of commercialfishing in 1994 was approximately 77.3%. At least 53% of the total mortality was attributable to fishingin the exploited area.

KEY WORDS: exploitation rate, maximum likelihood estimator, multiple tagging experiment,natural mortality, Neptunea arthritica, trap fishing, whelk.

*Corresponding author: Tel: 81-175-71-1410. Fax: 81-175-71-1401. Email: skengo@ies.or.jp

aPresent address : Institute for Environmental Sciences, 1-7Ienomae, Obuchi, Rokkasho, Aomori pref. 039-3212, Japan

Received 25 December 2000. Accepted 23 July 2001.

marked with numbered plastic tags to identifyindividuals. A tag was set in a 2 mm hole drilled atthe upper growing edge of the shell, and fixed withhot-melt adhesive (Fig. 2). After marking, the shellheights of all of the whelks collected were mea-sured before being released at the sampling point.

Prior to the field experiment, the effect ofmarking on the survival of a whelk was examinedin an aquarium. In this experiment, marked andunmarked whelks were kept in the same tank for3 weeks and none of the marked whelks diedduring the period; hence, we concluded that theeffect of marking on survival was negligible.

Marked whelks were then recaptured inresearch surveys and during commercial fishing.Recaptured whelks caught during research surveyshad their shell heights measured and were thenreleased back at the sampling point. Duringresearch surveys, newly marked and unmarkedwhelks were also released. Commercial whelkfishing operated on the offshore side of the fishingground in 1992 and 1994, and on the inshore sidein 1993. More than 120 fishery households wereallowed to operate whelk fishing in Shiriuchi. Eachfishery used 90 traps (three sets of gear). Fishingperiods lasted approximately 20 days and fisher-men soaked their traps every day. In 1992, we rec-ommended that operating near the sampling pointbe avoided because we released marked whelksjust before the fishing started. Therefore, thefishing effort on the marked whelks may be differ-ent throughout these 3 years. Recaptured whelkscaught during commercial fishing were kept in a breeding tank at Shiriuchi Fisheries NurseryCenter until the end of the fishing period to avoidany duplicate recapture. After the fishing period,

MATERIALS AND METHODS

Field studies

A marking and recapture experiment was carriedout from August 1991 to March 1994 at the whelkfishing ground in Shiriuchi, Hokkaido. During thisperiod, six marked groups were released and ninesamples were collected by research surveys and by commercial fishing. The fishing ground was ashallow area (< 30 m in depth) along the coast (Fig.1). The fishing ground was divided into two sides:inshore and offshore. The sampling point was posi-tioned on the offshore side. Each side of the fishingground was exploited alternately every other year.

Research surveys were repeated seven times andnew markings were performed six times. Whelksused for marking experiments were caught by trap2 km off Shiriuchi. The sampling operation was the same as that for ordinary whelk fishing.18 A set of fishing gear which comprised 30 traps andmain rope (200 m) was used. Traps were soaked for19–23 h in research surveys. Collected whelks were

88 FISHERIES SCIENCE K Suzuki et al.

Fig. 1 Map of fishing ground. Commercial fishing wascarried out on the offshore side in 1992 and 1994, and onthe inshore side in 1993. ( ) Area used for mariculture. Fig. 2 Position of tag.

they were measured and released back at the sam-pling point.

Mathematical methods

Whelk fishing lasted for quite a short period –approximately 20 days and it was treated as impul-sive. For convenience, we assumed that all whelksrecaptured during commercial fishing were caughton March 10 every year. Because all of the re-captured whelks were released back again, thesampling procedure of marked whelks used was sampling with replacement. Therefore, weassumed that the number of recaptured whelksfollows binomial distribution. The binomial distri-bution model for sighting data analysis has beenreported elsewhere.19,20 We expand this model todescribe multiple tagging data. A statistical modelfor the multiple tagging experiment of whelks wasthen developed on the assumptions that:1. Natural mortality is constant in any size classesand tagging group;2. All of the recaptured whelks are reported andthen released back again;3. There is no fishing gear selectivity;4. Effects of marking and recapture on survival arenegligible;5. Wild and marked whelks were distributed ran-domly and each of them was captured equally nearthe sampling point; and6. Population was closed.

We defined these variables following Iwao,21 inwhich M is the natural mortality coefficient; Ei isthe exploitation rate of sample i; Pji is the proba-bility of capture in sample i for a whelk marked insample j; mi, is the number of marked whelksrecaptured in sample i; ni is the total number ofwhelks caught in sample i; yj is the number ofwhelks newly marked and released in sample j; cji

is the number of whelks recaptured in sample i firstmarked in sample j; tji represents the time intervalfrom release at sample j to recapture in sample i.

Probability of recapture Pji is a product of prob-ability of survival and probability of being recap-tured, and is defined as follows:

(1)

Suppose sampling and release was performed ktimes, the likelihood function of the field data Lcan be written as:

(2)

whereby is the number of combinations to get

cji from yj. We call this model the binomial model.

y

cj

ji

ÊË

ˆ¯

Ly

cP P

j

jii j

k

j

k

jic

jiy cji j ji= Ê

ˈ¯ -( )

= +=

--’’

11

1

1

P Mt Eji ji i= -( ) ¥exp

We also examined the normal approximation ofthe binomial model so as to consider overdisper-sion.19,20,22,23 From equation 2, we get the followingnormal distribution model:

(3)

whereby f is the dispersion parameter.The following four types of models were exam-

ined:Model 1: binomial model; all of the exploitation

rates in research surveys were the same, and theexploitation rates during commercial fishing weredifferent each year.

Model 2: binomial model; the exploitation ratesduring research surveys were different each time,and the exploitation rates during commercialfishing were also different.

Model 3: normal distribution model; theexploitation rates during research surveys were dif-ferent each time, and the exploitation rates duringcommercial fishing were also different, withoutoverdispersion (f = 1).

Model 4: normal distribution model; theexploitation rates in research surveys were differ-ent each time, and the exploitation rates duringcommercial fishing were also different, withoverdispersion (f π 1).

Substituting equation 1 and the recapture datafor equations 2 and 3, we estimated M, Ei(i = 2 . . .k) and f, which gives the maximum value of thelikelihood function. In actual calculations, we took the logarithm of likelihood function, and minimized negative log likelihood function forconvenience. A simplex minimization program24

was used to obtain a numerical solution. Standarderrors of estimates were calculated from Fisher’sinformation matrix.25

RESULTS

The result of the mark–recapture experiment issummarized in Table 1. The total catch weightduring the research surveys ranged between 18.4 kgand 74.2 kg, and ranged between 33.9 ton and134 ton during commercial fishing. As shown inTable 1, we caught 1646 whelks during the firstresearch survey, of which 1328 were marked.Among the marked whelks caught during the firstresearch survey, 33 were recaptured in the secondsurvey and 14, 6, 1, . . . 214 whelks were caught sub-sequently. We also caught 1725 whelks during the

L y P P

c y Py P P

j ji jii j

k

j

k

ji j ji

j ji ji

= -( ){ }

- -( )-( )

ÏÌÓ

¸˝˛

-

= +=

-

’’ 2 1

2 1

1 2

11

1

2

pf

fexp

Mortality of whelk FISHERIES SCIENCE 89

second survey and marked 1597 new whelks.Among the marked whelks in the second survey, 36,20, 3, . . . 373 whelks were recaptured during subse-quent surveys and commercial fishing. Althoughmarked whelks were recaptured during sevenresearch samplings and three commercial fishingoperations, the greatest portions of the recoverywere seen during the commercial fishing in 1994(16.1–58.3%). In comparison, recapture rates weremuch lower in 1992 and 1993.

To examine the relationship between recapturerate and size of whelks, shell height distributions ofwhelks were compared between released samplesand recaptured samples at the release time (Fig. 3),and no significant differences were found (Kol-mogorov–Smirnov’s two samples test; P > 0.05). Wehave already shown in a previous study that thereis no selectivity between whelk size and fishinggear used during tagging experiments;26 hence, weconclude that there is no difference in survivalrates among size classes larger than 40 mm in shellheight.

Natural mortality and exploitation rates wereestimated using the data shown in Table 1. Toexamine the robustness of this estimate, a widerange of initial values was set in order to calculatethe maximum likelihood estimator. But the resul-tant estimator converged well on a unique valueand no dependence on the initial condition wasobserved.

The estimated value of parameters and standarderrors of each models are shown in Table 2.Although the fishing effort of each research surveywas the same, Akaike’s Information Criterion(AIC)27 value of Model 1 is the largest of the fourmodels. The resultant estimators and AIC value ofModel 2 and 3 were similar to each other. The resul-tant estimators of Model 4 were similar to that ofModel 3, but the standard errors were estimated to be approximately 1.7 times larger than that ofModel 3 and the value of dispersion parameter wasestimated to be 2.86. This result shows that therecaptured number was overdispersed. The AICvalue of Model 4 was the smallest of all the models;therefore, it is concluded that Model 4 gives thebest estimates of parameters. From Model 4, thedaily natural mortality coefficient was estimated as1.438 ¥ 10-3 (0.5249 annual mortality coefficient);that is, the annual survival rate of the natural pop-ulation was calculated to be 59%. The exploitationrates of research surveys ranged between 1.0% and7.3%, whereas the exploitation rates of commercialfishing in 1992, 1993 and 1994 were estimated as0.1%, 11.7% and 77.3%, respectively. Exploitationrates of commercial fishing in 1992 and 1993 werevery small. This result reflects the fact there wereno commercial fishing operations near the sam-

90 FISHERIES SCIENCE K Suzuki et al.

Tab

le1

Mar

k–re

cap

ture

dat

a fo

r a

seri

es o

f 10

sam

ple

s o

f w

hel

k N

eptu

nea

art

hri

tica

po

pu

lati

on

in t

he

Shir

iuch

i fish

ing

gro

un

d

Tota

l cat

chN

o. t

ota

l N

o. n

ewly

N

o. m

arke

d w

hel

ks c

augh

t in

sam

ple

i fi

rstl

y m

arke

d in

sam

ple

j(c

ji)

Tota

l D

ate

wei

ght

(kg)

cau

ght

(ni)

rele

ased

(y i

)an

d r

ecap

ture

rat

e in

par

enth

eses

(%

)m

arke

d (

mi)

j=1

23

45

67

89

Au

g. 5

199

160

.816

4613

28i=

1–

––

––

––

––

0Se

p. 2

562

.117

2515

972

33 (

2.5)

––

––

––

––

33D

ec. 1

725

.161

448

13

14 (

1.1)

36 (

2.3)

––

––

––

–50

Mar

. 4 1

992

18.4

428

303

46

(0.5

)20

(1.

3)2

(0.4

)–

––

––

–28

Mar

. 10*

No

dat

aN

o d

ata

No

dat

a5

1 (0

.1)

3 (0

.2)

1 (0

.2)

1 (0

.3)

––

––

–6

Jul.

8N

o d

ata†

772

916

35 (

2.6)

35 (

2.2)

18 (

3.7)

20 (

6.6)

––

––

–10

8Se

p. 1

674

.216

730

739

(2.

9)64

(4.

0)37

(7.

7)25

(8.

3)–

4 (4

.4)

––

–16

9M

ar.1

0 19

93*

134

000

No

dat

aN

o d

ata

872

(5.

4)88

(5.

5)34

(7.

1)20

(6.

6)–

0 (0

)–

––

214

Sep.

235

.470

645

39

4 (0

.3)

4 (0

.3)

7 (1

.5)

2 (0

.7)

–0

(0)

––

–17

Mar

. 10

1994

*33

900

No

dat

aN

o d

ata

1021

4 (1

6.1)

373

(23.

4)14

5 (3

0.1)

80 (

26.4

)–

17 (

18.7

)–

–26

4 (5

8.3)

1093

*Co

mm

erci

al fi

shin

g.† In

Ju

ly 8

199

2 o

nly

tag

ged

wh

elks

wer

e m

easu

red

.

pling point in 1992 so as to avoid catching whelksjust after release, and that in 1993 commercialfishing operated in the inshore fishing ground,where the release point was not situated.

DISCUSSION

In the present study, whelks were collected by trap.Although the fishing effort of each research surveywas the same, the exploitation rates varied widely.There are two considerable causes for this varia-tion: (i) the patchy distribution of marked whelks;and (ii) changes in environmental conditions. Theefforts of commercial fishing were much greaterthan that of research surveys, but commercialfishing in 1992 and 1993 recaptured fewer markedwhelks. Commercial fishing during these yearsoperated beyond the sampling point. Conversely,many marked whelks were recaptured in commer-cial fishing in 1994, which operated on the offshoreside, which includes the sampling pint. This result

shows that released whelks had less mobility andthat they did not spread throughout the fishingground. The sampling effort of the present study’sresearch was too small to cover this patchy distri-bution and may be a cause of overdispersion.Overdispersion in mark and recapture data hasbeen reported previously in other fish taggingstudies,28,29 and was observed in the present whelktagging experiment. Changes in environmentalconditions (e.g. water temperature, tidalcurrent,30,31 and substratum)32 might also be thecause for the wide variation in exploitation rates.From the result that Model 2 gives a better AICvalue than Model 1, it is thought that the effect ofthese environmental factors varied in each surveybut might be the same in different release groupscaught during the same survey.

Estimated value of the natural mortality coeffi-cient of N. arthritica (0.5249/year) was smallerthan that of Buccinum tsubai (0.9281/year)33 and B.tenuissimum (0.961/year).34 Conversely, the resultshows the high exploitation rate of whelk fishing in

Mortality of whelk FISHERIES SCIENCE 91

Fig. 3 Comparison of shellheight distributions betweenreleased and recaptured whelks.Whelks were released in: (a)August 1991; (b) September 1991;(c) December 1991; (d) March1992; (e) July 1992; and (f) Sep-tember 1993 and recaptured inMarch 1994. (––) Recapturedgroup; (----) released group. Theshell height of both is that at thetime of release.

92F

ISHE

RIE

S SCIE

NC

EK

Suzu

ki etal.

Table 2 Estimated parameters of whelk population in Shiriuchi fishing ground according to the four model types

Model 1 Model 2 Model 3 Model 4

Daily natural CV (%) Daily natural CV (%) Daily natural CV (%) Daily natural CV (%)mortality 4.9 mortality 4.9 mortality 4.9 mortality 8.3coefficient (± SE) coefficient (± SE) coefficient (± SE) coefficient (± SE)

1.406 (0.0694) ¥ 10-3 1.442 (0.0707) ¥ 10-3 1.438 (0.0702) ¥ 10-3 1.438 (0.1194) ¥ 10-3

Sampling date Sample* Exploitation rate Exploitation rate Exploitation rate Exploitation rate in % (± SE) in % (± SE) in % (± SE) in % (± SE)

Sep. 25 1991 R 2.67 (0.46) 17.2 2.64 (0.45) 17.0 2.57 (0.75) 29.2

Dec. 17 R 3.17 (0.17) 5.3 1.99 (0.28) 14.0 2.05 (0.28) 13.7 1.98 (0.46) 23.2

Mar. 4 1992 R 1.05 (0.20) 19.0 1.11 (0.20) 18.0 1.01 (0.31) 30.7

Mar. 10 C 0.20 (0.08) 40.0 0.20 (0.08) 40.0 0.16 (0.06) 37.5 0.10 (0.06) 60.0

Jul. 8 R 3.17 (0.17) 5.3 4.35 (0.42) 9.7 4.47 (0.42) 9.4 4.34 (0.70) 16.1

Sep. 16 R 7.27 (0.57) 7.8 7.51 (0.58) 7.7 7.33 (0.96) 13.1

Mar. 10 1993 C 11.61 (0.87) 11.82 (0.89) 7.5 11.90 (0.89) 7.5 11.68 (1.49) 12.8

Sep. 2 R 3.17 (0.17) 5.3 1.21 (0.30) 24.8 1.39 (0.30) 21.6 1.14 (0.42) 36.8

Mar. 10 C 75.50 (3.74) 5.0 77.20 (3.82) 4.9 77.48 (3.80) 4.9 77.33 (6.46) 8.4

Dispersion parameter f2.86 (0.74) 25.9

AIC AIC AIC AIC443.64 272.48 271.60 248.48

*Sample type: R, research survey; C, commercial fishing.AIC, Akaike’s Information Criterion.

Shiriuchi. The exploitation rate of commercialfishing in 1994 was 77.3%, and the annual naturalmortality rate was 41%. During that year, the totalmortality rate of fishing-sized whelk was estimatedas 86%. Assuming that fishing took place after allthe natural deaths occurred, the percent fishingmortality rate of total mortality is 53%. Thus, atleast 53% of whelks’ deaths were attributable tofishing in the exploited area. Although this result isapplicable only to the marked whelk population, itis obvious that the fishing intensity of commercialfishing was higher near the sampling point.Although the actual size of the exploited area hasnot been obtained, it can be estimated from thenumber of traps. Assuming that the number offishery households is 120, whereby each uses 90traps, and the effective range of each trap is 4.4 min radius,32 then the exploited area is estimated as approximately 0.66 km2 in one day. The area ofeach side of the fishing ground is approximately 18km2; therefore, approximately 3.6% of one side ofthe fishing ground is exploited in one day. Usuallyfishermen change their fishing gear position everyfew days, so it is assumed that not a small portionof the fishing ground was exploited during thefishing period in 1994.

Fujinaga and Nakao estimated adult mortalityas being 76.3% from May to August, 1980 in UsuBay.9 They proposed that natural deaths afterspawning and deaths by fishing were the cause of the high mortality rate. In the present study, we presume that fishing in Usu Bay has also seri-ously affected the whelk population. Although the lifespan of N. arthritica still remains unknown,it seems to be 6 years or more. The reason for thisinference is the fact that an 80 mm-sized whelk,which was thought to be ≥ 4 years old,1,2 was recap-tured 2.6 years after its release (Fig. 3). Assumingthat first maturation occurs at age 3 years,1,2,6

N. arthritica spawns at least three times during its lifetime. Neptunea arthritica spawns only 40–80 egg capsules, each of which bears only one juvenile.6 The regulated size of whelks caught in Shiriuchi is larger than 60 mm, which is the maturation size of a female; hence, the fishingpressure seems to reduce the chance of adultwhelks reproducing.

The Shiriuchi Fisheries Cooperative is reducingthe fishing effort by restricting the fishing periodand the number of traps allowed. But from thepresent study, we have shown that the exploitationrate under the present regulations is still ratherhigh. The Cooperative also regulates catch size and promotes annual alternative use of fishinggrounds. To examine the efficiency of these regula-tions, further studies will be necessary for clarify-ing the total life cycle of whelks.

ACKNOWLEDGMENTS

We thank Mr K Sunakoma and Shiriuchi FisheryCooperative for their valuable assistance in thefield; Dr O Yamamura and Mr H Ito (HokkaidoNational Fisheries Research Institute) for readingthe manuscript; and Dr K Hiramatsu (NationalResearch Institute of Far Seas Fisheries) for hishelpful suggestions on the numerical solutions.

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