FISHERIES SCIENCE 2002; 68: 963–971

INTRODUCTION

In the Pacific Ocean, chub mackerel (Scomberjaponicus) is one of the most important resources.The size of the chub mackerel stock in the PacificOcean off Japan declined during the 1980s andearly 1990s and remained at a low level through the1990s (Fig. 1).1,2 The yearly egg production in year t is donted by Et. The fluctuation of pelagic fish,including chub mackerel, is thought to be affectedby environmental fluctuations, as well as intra-species or interspecies competition.4

A cohort analysis of the chub mackerel stock2

revealed that recruitment-per-spawning (RPS) washigh in 1992 and 1996 (Fig. 1), despite a low level ofspawning stock biomass. The number of stock atage a in year t is denoted by Na,t, which is estimatedat the beginning of July. N0,t does not imply yearlyegg production (Et) but, rather, implies the number

of recruits in year t. Fish aged 0 years during thesetwo years and 1 years in the following years wereheavily fished before the age of maturity,2 as sug-gested in Fig. 1. The chub mackerel stock has notrecovered.

The ratio of immature chub mackerel in landedcatches shows yearly fluctuations (C Watanabe,unpubl. data, 1999) for numbers and by weight of67 and 53%, respectively, in the 1970s, 58 and 41%,respectively, in the 1980s and 84 and 71%, respec-tively, in the 1990s. For the period from 1993 to1999, the ratio of immature chub mackerel inlanded catched increased to 87% for numbers and77% by weight.

The present paper investigates the effects offishing on stock dynamics from 1970 to 1999 andthe effects of conserving immature fish or strongyear classes on future stock trends, as well as thefuture catch, with special attention to the differ-ence in fishing impact between the 1970s/1980sand the 1990s. We create three fishing policies forrecovering stock and discuss the practicability ofthese policies. Using year-dependent RPS and the

Recovery policy for chub mackerel stock usingrecruitment-per-spawning

Hiroaki KAWAI,1 Akihiko YATSU,2 Chikako WATANABE,2 Takumi MITANI,3 Toshio KATSUKAWA1

AND Hiroyuki MATSUDA1*

1Ocean Research Institute, University of Tokyo, Nakano, Tokyo 164-8639, 2Marine BioecologyDivision, National Research Institute of Fisheries Sciences, Kanazawa, Yokohama 236-8648 and3Kuroshio Research Division, National Research Institute of Fisheries Sciences, Kouchi,Kouchi 780-8010, Japan

ABSTRACT: The stock abundance of chub mackerel (Scomber japonicus) in the Pacific Ocean offJapan declined in the 1980s and remained at low levels through the 1990s. There were recruitmentsuccesses in 1992 and 1996. However, the cohorts born in these years were heavily fished beforethe age of maturity and chub mackerel has not begun to recover. To investigate the effects of con-serving immature fish, we created four recovery policies: (i) policy 0, actual fishing mortality duringthe 1990s; (ii) policy 1, conserve strong year classes; (iii) policy 2, apply the average fishing mortal-ity in the 1970s–1980s after 1992; and (iv) policy 3, a 55% reduction of the mortality adopted bypolicy 2. Policy 3 was considered to be the best in terms of final stock abundance and total catchfrom 1992 to 1999. We also calculate the future projection of stock and catch under these three poli-cies as well as using average fishing mortality from 1993 to 1999. Using average fishing mortalityfrom 1993 to 1999, the stock will not be recovered within the next 20 years. Even under the bestpolicy, the risk that the final stock is not recovered to 3 million tons within the next 10 years is 40%.

KEY WORDS: recovery probability, Scomber japonicus, simulation model, spawning potential ratio, virtual population analysis.

*Corresponding author: Tel: 81-3-5351-6494. Fax: 81-3-5351-6492. Email: matsuda@ori.u-tokyo.ac.jp

Received 23 May 2001. Accepted 12 February 2002.

from catch-at-age data and relative stock index(e.g. catch per unit effort):2 we denote catch-at-agea in year t by Ca,t, the natural mortality coefficientby M and the fishing mortality coefficient in year tat age a by Fa,t. Yatsu et al.2 estimated that thefishing mortality coefficients of immature fish werelarger in the 1990s than in the 1970s/1980s (Table1) for a wide variation in the natural mortality coef-ficient (M = 0.3–0.5 /year). In the 1970s and 1980s,the fishing mortality coefficient F for immature fishwas lower than F for mature fish, whereas F for fishaged 1–2 years was not lower than F for mature fish in the 1990s.

To calculate RPSt, we used time series for therecruitment number, denoted by Rt, and thespawning stock biomass at the end of the spawn-ing season in year t, denoted by SSBt. These wereestimated using cohort analysis.2 The age atrecruitment is 0 years and Rt = N0,t. The followingequations were used to define RPSt and SSBt in year t:

(1)

(2)

where tmax is lifetime, Wa,t is weight and ma,t is therate of maturity at age a in year t.6,7

In order to investigate the trend of fisheriesimpact, we calculated the static %SPR and projected foregone reproduction (PFR) in year t,8

which are defined as by the following equations:

SSB N W mt at at ata

t

==

 , , ,

max

0

RPS R SSBt t t=

stock-recruitment relationship, we calculate stockand catch dynamics starting from stock size in1992 under the three differenct policies and usingthe actual catch. We also calculate these dynamicsstarting from stock size in 1999 under the three differenct policies and using average fishing mortality from 1993 to 1999.

MATERIALS AND METHODS

Evaluation of fishing impact on the basis of RPS

We estimated percent spawning per recruitment(%SPR)5 to compare fisheries in the 1970s withthose after 1993. The %SPR refers to the ratio ofspawning per recruitment (SPR) with actual fishingto SPR without fishing, where the SPR is theexpected number of eggs spawned by a female atthe age of recruitment until she dies.

We used catch-at-age data, average body weightand estimated stock in number during the period1991–1999.2 We considered the chub mackerelfishing season to start in July and end in June thefollowing year. We assumed that spawning onlyoccurs at the end of June and that fishing onlyoccurs at the end of December. We also assumedthat fish are recruited just after the end of thespawning season with survival rate in year t givenby N0,t/Et.

From cohort analysis, the stock abundance Na,t

and fishing mortality coefficient Fa,t is obtained

964 FISHERIES SCIENCE H Kawai et al.

Fig. 1 Catch-at-age data (bars;compiled by Yatsu et al.2), esti-mate of yearly egg production(compiled by the Japan Ministryof Agriculture, Forestry, and Fish-eries3) and the recruitment-per-spawning (RPS; �) for chubmackerel in the Pacific Ocean offJapan.

(3)

(4)

where

(5a)

(5b)

and

(5c)V m W M y aat x t a x x t a xx a

t

, , ,* expmax

= - -( )[ ]- + - +=

Â

V m W F Mat x t a x x t a x y ty a

x

x a

t

, , , ,expmax

= - +( )ÈÎÍ

˘˚̇

- + - +==

ÂÂ

s F M s a Mat x t a xx

a

at, , ,exp , * exp= - +( )ÈÎÍ

˘˚̇

= - -( )[ ]- +=

-

Â0

1

1

PFRN V

N Vt

at ata

t

at ata

t= - =

=

Â

Â1 0

0

, ,

, ,

max

max

*

%

*

, , ,

, , ,

max

maxSPR

W m s

W m st

at at ata

t

at at ata

t= =

=

Â

Â0

0

where sa,t is survival rate of age a from recruitmentuntil year t, Va,t and Va,t* are the reproductive valuesat age a in year t if the fishing mortality rate in yeart continues in the future and without any fishingmortality, respectively. The difference between100% and static %SPR represents foregone repro-duction per recruit due to sustained fishing at aconstant rate over time. The PFR represents fore-gone reproduction in the future at a constantfishing mortality rate on the observed cohorts inthe population.8 The %SPRt and PFR are usefulindices related to the degree of recruitment overfishing.9,10

To investigate environmental effects on therecruitment of chub mackerel, we estimated therelationship between stock and recruitment,applying the Beverton–Holt model:11

(6)

where a and b are parameters with positive valuesand Ñ0,t is the expected value of N0,t from the following best-fit model. Parameter a means the

˜,N

SSBt

t0

1=

+a

b

Recovery policy for mackerel FISHERIES SCIENCE 965

Table 1 Fishing mortality coefficients (Fa,t) at age a in year t.2

Age a (years)Year t 0 1 2 3 4 5 6

1970s–1980s 0.10 0.29 0.50 0.77 1.06 1.72 1.720.023 0.051 0.068 0.080 0.086 0.105 0.105

1993–1999 0.33 0.85 0.77 0.71 0.67 0.46 0.460.052 0.110 0.100 0.101 0.101 0.078 0.078

1990 0.06 0.14 0.19 0.18 0.19 0.70 0.700.018 0.034 0.049 0.041 0.043 0.132 0.132

1991 0.06 0.08 0.24 0.27 0.14 0.09 0.090.012 0.020 0.049 0.057 0.024 0.016 0.016

1992 0.15 0.06 0.18 0.55 0.65 1.23 1.230.018 0.008 0.031 0.102 0.135 0.208 0.208

1993 0.32 1.72 1.48 0.97 0.59 0.29 0.290.054 0.138 0.155 0.163 0.111 0.062 0.062

1994 0.27 0.58 0.92 0.80 0.38 0.42 0.420.056 0.079 0.097 0.117 0.073 0.079 0.079

1995 0.59 0.78 0.71 0.93 0.63 0.42 0.420.091 0.161 0.087 0.096 0.097 0.069 0.069

1996 0.54 0.71 0.38 0.98 1.34 0.68 0.680.070 0.110 0.087 0.117 0.159 0.104 0.104

1997 0.32 1.04 0.68 0.40 1.22 0.95 0.950.054 0.128 0.110 0.087 0.195 0.167 0.167

1998 0.08 0.67 0.73 0.46 0.14 0.15 0.150.014 0.096 0.103 0.074 0.025 0.028 0.028

1999 0.20 0.48 0.46 0.44 0.38 0.29 0.290.025 0.061 0.058 0.056 0.049 0.036 0.036

Data from 1990 to 1999 and average fishing mortality coefficients at age a during the 1970s–1980s and from 1993 to 1999, assuming that M = 0.4 /year (bold numbers) with sensitivities (bold numbers + italic numbers when M = 0.3 /year; bold numbers–italic numbers when M = 0.5 /year).

sidered a policy that conserves immature fish inthe year following recruitment success (1993 and1997). Under this policy, we reduce the fishingmortality coefficients of fish at F

–a, averaged over

the 1970sto 1980s (Table 1). Policy 2 applies thefishing mortality coefficient, F

–a, averaged over the

1970s to 1980s, to Fa,t in all years after 1992. Policy3 is a 55% reduction in the fishing mortality rate ofpolicy 2.

To estimate the effect of conserving immaturefish in the 1990s, we used the estimated stockabundance in 1991, Fa,1991 (Table 3), and at in the1990s (Table 2). Let na,t, rpst, ssbt, ca,t and fa,t be Na,t,RPSt, SSBt, Ca,t and Fa,t, respectively, under policies1–3. When the fishing mortality coefficients (Fa,t)after 1992 (Table 1) are determined by each policy,we can simulate the stock and catch dynamics ofchub mackerel after 1991.

The stock abundance (na,t) and catch (ca,t) innumbers in the next year t can be calculated by thefollowing equations:

(9)

(10)

(11)

(12)

where rpst is given by eqns (1) and (8), ssbt is givenby eqn (2) and fa,t is the fishing mortality coefficientgiven by each policy. We assumed that na,1991 =Na,1991 and fa,1991 = Fa,1991 in Table 3 and started thesimulation from the year 1992. Therefore, ca,1991 =Ca,1991 for all a; M is the natural mortality coefficientand is assumed to be constant at 0.4 for all cohortsand ages. Quantities ca,t, na,t, rpst and ssbt after 1992

c n eat atM

, ,= ◊ - 2

n n n e c c et t tM

t tM

6 5 1 6 1 5 1 6 12

+ - + --

- + --= +( ) ◊ - +( ) ◊

+( ), , , , ,

for ages 6

n n e c eat a tM

a tM

, , ,= ◊ - ◊ ( )- --

- --

1 1 1 12 for ages 1– 5

n ssbt t t0 1, = +( )a b

survival rate from egg to recruitment when therecruitment is given by Ñ0,t, when the stock is sosmall that the density effect is removed. However,the recruitment N0,t differs from Ñ0,t and is alsodetermined by environmental conditions. The par-ameters a and b are obtained by the minimum squ-are sum method using the quasi-Newton method(Microsoft Excel for Windows 95, Version 7.0):

(7)

where S is the sum of squared differences.We assumed that the distance between N0,t and

Ñ0,t is a process error caused by environmental conditions. We ignored measurement errors in the cohort analysis. To describe the process error, we replaced a with the time-dependentparameter at:

(8)

where at and b are used irrespective of recoverypolicies (Table 2).

Effects of conserving immature fish on futurestock and catch

We investigated the effect of conserving immaturefish on stock recovery. We considered four policiesfor the recovery of chub mackerel fisheries andcompared the performance of these four policiesby simulation. Policy 0 means an actual fishery asin the 1990s. Policy 1 conserves immature fish bornin years of recruitment success (1992 and 1996).The idea behind this policy is effective use of dominant year classes for stock recovery. However,the existence of a strong year class can be notedonly after fishing the year class. Therefore, we con-

a bt t tSSB N= +( ) ¥1 0,

S N Nt tt

= -( )=Â 0 0

2

1970

1999

, ,˜

966 FISHERIES SCIENCE H Kawai et al.

Table 2 Results for the number of recruits in year t (N0,t;million individuals), spawning stock biomass at the endof the spawning season in year t (SSBt; thousand tons),recruitment-per-spawning in year t (RPSt; /kg) and sur-vival probability of egg until the age at recruitment (at;/kg) when M = 0.4 /year

t N0,t SSBt RPSt at

1991 1027.5 68.6 149.8 160.81992 2764.7 80.6 342.8 372.41993 574.0 100.1 57.4 63.51994 594.9 95.4 62.4 68.81995 1151.2 69.3 166.2 178.51996 4495.4 54.4 826.7 874.81997 629.6 61.9 101.7 108.41998 441.1 118.7 37.2 41.91999 809.1 121.2 66.8 75.4

Table 3 Chub mackerel stock abundance in terms ofnumbers (million individuals) in 1991 and 1999, fishingmortality coefficient (/year) in 1991 and catch in termsof numbers (million individuals) in 19912

Age a(years) Na,1991 Ca,1991 Fa,1991 Na,1999

0 1027.5 48.0 0.06 380.81 205.1 13.2 0.08 159.52 60.4 10.4 0.24 62.13 32.0 6.1 0.27 74.84 31.0 3.3 0.14 9.85 19.9 1.4 0.09 5.16+ 2.8 0.2 0.09 0.9

Na,1991, Na,1999, number of recruits in 1991 and 1999, respec-tively; Ca,1991, catch-at-age a in 1991; Fa,1991, fishing mortalitycoefficient in 1991.

depend on fa,t, which is determined by each policy.In addition, we assume that the recruitment is not larger than that in 1977 or N0,t £ 12.2 billionindividuals.

Future projections

We calculated future projections of stock and catchstarting from stock in 1999 (Table 3), using thenumbers of individuals in 1999.2 at is randomlychosen from at from 1990 to 1999 permitted mul-tiple choosing. In the same way as described ineqns 8–12, except that at was chosen randomly, wecalculated stock and catch within the next 20 yearsfor 1000 simulated runs under policies 1–3 andunder a fishery as in the 1990s (policy 0). Underpolicy 0, we assumed that the fishing mortalitycoefficient at age a in year t is equal to averaged F

–a

over 1994, 1995, 1996 and 1998 if at – 1 < a1992 or isaveraged F

–a over 1993 and 1997 if at – 1 = a1992 or if

at - 1 = a1996 (1 year after a strong year classappears). Under policy 1, the fishing mortalitycoefficient at age a in year t is equal to F

–a under

policy 0 if at - 1 < a1992 or is equal to policy 2described in the previous section if at - 1 ≥ a1992.Because we ignore variation in body weight, rate of maturity and any other parameter values infuture projections, the catch amount after stockrecovery is probably overestimated. Therefore, we investigated the frequency distribution of thecatch in 2009. From these simulated runs, weobtained a probability that the final stock biomass(SB) is larger than 3 million tons and a frequencydistribution for the catch in 2009 under eachpolicy.

RESULTS

The degree of overfishing, measured by PFR and‘100% – %SPR’, as shown in Fig. 2, represented amore than 80% loss of reproduction in 1984–1989and 1993–1997. Less than 30%SPR is usually recognized as recruitment overfishing.12 Projected foregone reproduction was larger as the naturalmortality coefficient became smaller (Fig. 2). ThePFR during the period 1990–1992 was smaller thanin other years, because the fishing mortality coef-ficients during these years were smaller than thosein other years (Table 1).

We obtained a minimum S of 1.93 ¥ 1010, when b = 1.07 ¥ 10-6 (/ton) and a = 13 500 (/ton) when M = 0.4 /year. Using the a and b values obtained, we describe a best-fit curve for the recruitment–SSB relationship (Fig. 3).

For all policies, when M = 0.4 and 0.5 /year, theSB in 1999 was higher than the actual SB in thatyear (Fig. 4). The SB when M = 0.5 /year is smallerthan that when M = 0.4 /year. When M = 0.3 /yearunder policy 3, the SB in 1999 could be 79% of theSB in 1977, although this may be unrealistic. Underpolicy 1, the level of SSB in 1999 was approximatelyfivefold larger than the actual level in 1999. Underpolicies 2 and 3, the SSB recovered rapidly and theSB in 1999 reached a level six- and 10-fold larger,respectively, than the actual level in 1999 when M = 0.4 /year. The levels of the SB in all policieswere approximately the same until 1993. After1994, the SB under policy 3 recovered more rapidlythan under the other policies. The trend of spawn-ing SB was similar to that of SB. Under policy 3, thefinal stock was almost half the maximum stocklevel in 1977.

Recovery policy for mackerel FISHERIES SCIENCE 967

Fig. 2 Estimated projected fore-gone reproduction (PFR; M = 0.3,0.4 and 0.5 /year) and static per-cent spawning per recruitment(%SPR; M = 0.4 /year) of chub mac-kerel in the Pacific Ocean off Japan(1970–1999).

Under policies 2 and 3, the catch recoveredslowly until 1995 (Fig. 5). After 1995, the catchrecovered rapidly and reached 0.6 million tons.Catch under all policies was smaller than the actualcatch in 1992, but soon increased due to stockrecovery. Under all policies, the projected catcheswere larger than the actual catches, except in 1993and 1996 when M = 0.3 and 0.4 /year.

The dynamics of SB and catch differed amongthe three policies (Figs 4,5). The results are sum-marized in Table 4. To restore SB, policy 3 seemsbetter than the actual and other two policies. If therecruitment in 1996 reaches the maximum level inthe 1970s, the stock abundance in 1999 reaches themaximum level in the 1970s, as shown in Fig. 4.This projection may be too optimistic, because weignored density effects on the growth rate and ageat maturity. We investigated the effects of thesepolicies on future stock and catch starting from the

968 FISHERIES SCIENCE H Kawai et al.

Fig. 3 Relationship between the number of recruits in year t (N0,t) and spawning stock biomass at the end of the spawning season in year t (SSBt) from 1970 to 1999 (circles) and the regression curve (Ñ0,t) from theBeverton–Holt model (eqn 5).

Fig. 4 Projected stock abundance starting from stock in1991 for the actual catch and under the three policies.Bold lines and filled symbols indicate cases where M =0.4 /year, whereas thin lines and open symbols representcases where M = 0.5 /year.

Fig. 5 Projected catch starting from stock in 1991 underthe four policies. Filled and open symbols representcases where M = 0.4 and 0.3 /year, respectively.

Table 4 Total catch (1992–1999) and stock biomass averaged over 1996–1999 under the four policies

Total catch Stock biomass averaged over1992–99 1996–1999

Policy M (million tons) Vs actual (%) (million tons) Vs 1977 (%)

0 0.3 1543 100 410 60 0.4 1543 100 348 70 0.5 1543 100 301 71 0.3 2028 131 1464 231 0.4 2369 154 1536 301 0.5 2705 175 1561 372 0.3 2173 141 1724 272 0.4 2639 171 1821 352 0.5 3168 205 1895 453 0.3 1782 115 2711 423 0.4 2309 150 3016 583 0.5 2967 192 3331 79

For stock biomass, percentages are relative to the years when the stock biomass was highest in 1977.

age distribution in 1999. The results indicated thatthe final SB is larger than 1 million tons under eachpolicy from 2000 to 2019 (Fig. 6). Only two of the1000 simulated runs in policy 0 resulted in stockrecovery. In contrast, 40% of runs under policy 3succeeded in stock recovery within the next 10years. We also obtained a frequency distribution ofcatch in 2009 under each policy (Fig. 7). More than50% of runs under policy 0 resulted in less that 200thousand tons of catch. Under policy 3, fewer than10% of runs resulted in less than 200 thousand tonsof catch.

DISCUSSION

We have considered process error in the SSB–recruitment relationship. The reproductive successof spawners depends on local conditions of theoceanographic environment. The area of spawning

ground will increase as the SSB increases. If goodspawning grounds vary with year and if spawnersrandomly choose a spawning ground, recruitmentmay be determined by a stochastic process, suchas Poisson distribution. If the mean and varianceof N0,t are approximately proportional to SSBt, vari-ance of RPSt (= Rt/SSBt) decreases as SSBt increases.In fact, the mean and variance of N0,t from 1970 to1984 are, respectively, 6193 ¥ 106 and 11 ¥ 1012,whereas those from 1985 to 1999 are 1383 ¥ 106 and2.3 ¥ 1012, respectively. The variance in R from 1970to 1984 is significantly higher than the variance inR from 1985 to 1999 (F test; P ª 0.3%). In contrast,the mean and variance of RPS from 1970 to 1984are 7.9 and 22, respectively, whereas those from1985 to 1999 are 17.8 and 659, respectively. Thevariance in RPS from 1970 to 1984 is significantlylower than the variance in RPS from 1985 to 1999(F ; P < 1 ¥ 10-6). This suggests that the RPS at highstock levels is more stable than at low stock levels.Therefore, we investigated the recovery probabilityin future projections rather than the average stockabundance.

According to estimates from the cohort analysis,the fishing mortality coefficient F on immature fishfrom 1993 to 1999 is larger than F on mature fish inthese years. Wintering immature fish distribute inmore northern regions than wintering maturefish.13 Therefore, we expected that F on immaturefish was actually larger than F on mature fish. Incontrast, fishermen could conserve immature fishin the 1990s, at least like in the 1970s.

Conserving immature fish is an effective way ofavoiding recruitment overfishing. As shown above,all the policies that we considered would haverestored the SB of chub mackerel by 1999. In addition, the total catch in the 1990s would

Recovery policy for mackerel FISHERIES SCIENCE 969

Fig. 6 Probability that the projected stock biomassfrom 2000 to 2019 is larger than 0.5 million tons underthe four policies.

Fig. 7 Frequency distribution ofthe projected catch (thousandtons) in 2009 under the four poli-cies.

chub mackerel stock. We need to elucidate theeffects of community or ecosystem-based fisheriesmanagement policy on stability and stock abun-dance in non-equilibrium stocks, such as chubmackerel and other small pelagic fishes.

ACKNOWLEDGMENTS

We thank T Matsuishi (Faculty of Fisheries,Hokkaido University), M Kato, I Mitani (KanagawaPrefectural Fisheries Experimental Station), TWada (Fisheries Agency of Japan), two anonymousreviewers and the members of the Fish Popula-tion Dynamics at Ocean Research Insitute (ORI),including former Professor Y Matsumiya, who suddenly passed away in April 2000. We also thankProfessor Y Watanabe and Japan Fisheries Agencyfor arrangement of this joint research between ORIand National Research Institute of FisheriesScience. This work was supported, in part, by aGrant-in-Aid from the Japan Ministry of Education,Science and Culture to HM.

REFERENCES

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2. Yatsu A, Mitani T, Watanabe C. Stock assessment and allowable biological catch of chub mackerel in the PacificOcean off Japan. Kaiyo Monthly 2002; 34: 280–283.

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have exceeded the actual catch if we had appliedany of these policies. This suggests that conservingimmature fish is important for sustainable fisheries.

Although the fisheries in the 1980s were betterthan those in the 1990s, the stock decreased in the1980s. Even under a better fishing policy than wehave considered herein, the chub mackerel popu-lation would have decreased in the 1980s.14 Thisdecline in the fish population was caused not onlyby fishing, but was also due to natural reasons. In the eastern Pacific, chub mackerel stock hasdeclined coincidently since 1984 due to poorrecruitment and heavy exploitation has resulted infurther population decline.15

Let us suppose that we had conserved strongyear classes. The 1992 cohort would have maturedin 1996 and could have spawned in 1996, produc-ing a large RPS. Therefore, the year class born in1996 would have been much larger than it was.Recruitment also succeeded in 1996. In otherwords, we lost two opportunities to help the chubmackerel population recover. Chub mackerel stockactually increased from 1955 to 1962. In theseyears, recruitment succeeded at least twice in 1955and 1962.16 More than two successes in recruit-ment, with several years interval, are needed forthe recovery of the chub mackerel population. Weneed to wait for another two or three opportunitiesof a good environment for recruitment that isaccompanied with a large RPS.

We have not investigated uncertainty in therecovery process. We need to incorporate mea-surement errors into our calculations in the future.In addition, we also ignored density effects ingrowth rate and age of maturity in future projec-tions, because density effects are negligible whenthe stock is sufficiently low. We did not explicitlyconsider physical, chemical or biological environ-mental effects, such as ocean currents, water temperature, changing habitat, density of prey andinterspecific competition with other pelagic fish.We expect that RPS depends on these environ-mental factors.

The present study considers fishing policies fora single species. The specie-replacement patternsuggests a negative correlation in the stock abun-dance between species. The optimal harvestingpolicy may depend on the stock abundance of other fish species. The Japanese large- andmedium-type purse seine fishery will be the targetof this discussion because this fishery occupied51–73% of the total catch of small pelagic fish,including sardine, chub mackerel, anchovy andjack mackerel,17 and because the current fishingpower of this fishery, which focused on sardines inthe 1980s, apparently prevented the recovery of

970 FISHERIES SCIENCE H Kawai et al.

ships for fisheries, and the construction of sustainable yieldcurves. J. Cons. Int. Explor. Mer. 1982; 40: 67–75.

10. Matsumiya Y. Case studies of fish stock management toavoid recruitment. Bull. Jpn. Soc. Fish. 1997; 61: 168–178.

11. Beverton RJH, Holt SJ. On the dynamics of exploited fishpopulations. Fish Fish. Ser. 1957; 11: 1–553.

12. Mace PM, Sissenwine MP. How much spawning per recruitis enough?. Fish. Aquat. Sci. 1993; 120: 101–118.

13. Kawasaki T. On the ecology of the young mackerel of thePacific population. Bull. Tokai Reg. Fish. Res. Lab. 1968; 55:59–113.

14. Matsuda H, Kishida T, Kidachi T. Optimal harvesting policyfor chub mackerel in Japan under a fluctuating environ-ment. Can. J. Fish. Aquat. Sci. 1992; 49: 1796–1800.

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Recovery policy for mackerel FISHERIES SCIENCE 971