Environ Biol Fish (2009) 85:127–137 DOI 10.1007/s10641-009-9471-x

Growth and mortality of bigeye tuna Thunnus obesus (Scombridae) in the eastern and central tropical Pacific Ocean Guoping Zhu & Yingqi Zhou & Liuxiong Xu & Xiaojie Dai

Received: 22 January 2008 / Accepted: 31 March 2009 / Published online: 30 April 2009 # Springer Science + Business Media B.V. 2009

Abstract Biological parameters such as age, growth and age (or size) at maturity are vital for stock assessment and management. Aging is essential in yielding such information. However, limited aging studies have been conducted for large tropical pelagic species in the eastern and central tropical Pacific Ocean. The objective of this study is to conduct a length frequency analysis for estimating growth and mortality of bigeye tuna in the eastern and central tropical Pacific Ocean using samples from the Chinese longline fishery during February to November 2006. The von Bertalanffy growth parameters of asymptotic fork length L∞ and growth coefficient k were estimated at L∞ = 207.4 cm fork length, k = 0.23 year-1, and theoretical age at zero length t0 = −0.40 year. The total mortality rate (Z) was estimated to be 0.60; the fishing mortality rate (F) and the natural mortality rate (M) were 0.25 year-1 and 0.35 year-1, respectively. The exploitation rate (E) was 0.16. This study provides the estimates of growth and mortality rate for bigeye tuna in the eastern and central tropical Pacific Ocean, which G. Zhu : Y. Zhou : L. Xu (*) : X. Dai The Key Laboratory of Shanghai Education Commission for Oceanic Fisheries Resources Exploitation, College of Marine Sciences, Shanghai Ocean University, Shanghai 201306, China e-mail: [email protected] G. Zhu : Y. Zhou : L. Xu : X. Dai The Key Laboratory of Sustainable Exploitation of Oceanic Fisheries Resources, Ministry of Education, Shanghai Ocean University, Shanghai 201306, China

can be used as biological input parameters in further stock evaluations in this region. However, age analysis, further validation of the age composition and stock structure are needed for future studies. Keywords Bigeye tuna . Thunnus obesus . Growth . Mortality . Eastern Pacific Ocean . Size frequency analysis

Introduction Bigeye tuna (Thunnus obesus Lowe 1839) is a fish species of great commercial importance in the tropical and subtropical waters of the Atlantic, Indian, and Pacific Oceans (Sun et al. 2001; Farley et al. 2006). It is intensively exploited by longline fisheries of many Asian countries and regions, and US and European purse seiners at various stages of its life cycle (Stéquert and Conand 2000) and is exploited at an overfishing level for the Eastern Pacific Ocean (Aires-da-Silva and Maunder 2007). Bigeye tuna are the principal target species of the large ‘distant-water’ longliners from Japan and Korea and Taiwan, and of the smaller ‘fresh sashimi’ longliners based in several Pacific Island countries. Bigeye tuna is sold as sashimi and sushi, as loins, as canned tuna, in foil pouches and as specialty products such as steaks (Hampton et al. 1998). In 2006, imports into the Japanese market were worth $649 million. Frozen products dominated, representing as much as 84 percent in volume and 81 percent in value.

128

Most of the world landings of bigeye tuna from 1963 through 2005 occurred in the Pacific Ocean. While more than 43 nations that reported bigeye tuna catches in Pacific Ocean in 2005, Japan and Indonesia harvested majority of the catches of bigeye tuna in this area -approximately 22 and 11 percent, respectively. Since 1980, the Pacific-wide longline catch of bigeye varied between 90 000 and 165 000 metric tones (t). Japanese longline vessels contribute over 80% of the catch. Longline catch in the eastern Pacific Ocean (EPO), the area east of 150°W, varied from 50 000 – 115 000 t since 1980, whereas the catch was typically 40 000 – 60 000 t in the western and central Pacific Ocean (WCPO), the area west of 150°W. Reported catch of bigeye tuna peaked at 455 000 t in 2002 according to Food and Agriculture Organization (FAO) data. The total catch of 403 000 t in 2005 was the lowest recorded catch in the past decade. China began to develop the distant water tuna longline fishery in the late 1980 s. Most small scale tuna longliners were mainly operating inside the Exclusive Economic Zone (EEZ) waters of Palau, Tonga, Micronesia, Marshall Islands (targeting bigeye tuna) and Fiji (targeting albacore Thunnus alalunga) (Miao and Huang 2003). Bigeye tuna also is one of main target species in the Chinese tuna fishery, and the annual catch was about 25,000 t in 2006. Effective management of any fishery requires reliable information regarding population parameters such as length-weight, age and growth, mortality and recruitment pattern of exploited stock (Ahmed et al. 2003). Age and growth information of bigeye tuna in some areas of the Pacific Ocean was derived from a variety of sources such as (a) size–frequency data (Iversen 1955; Shomura and Keala 1963; Yukinawa and Yabuta 1963; Kume and Joseph 1966; Suda and Kume 1967), (b) tag-recapture study (Lehodey et al. 1999; Schaefer and Fuller 2006) and (c) direct aging of calcified tissues such as otoliths (Matsumoto 1998; Lehodey et al. 1999; Kato 2001; Farley et al. 2003), scales (Nose et al. 1957; Yukinawa and Yabuta 1963), and dorsal spines (Sun et al. 2001). However, uncompleted information is available on some key biological parameters such as age and growth of bigeye tuna in the eastern and central tropical Pacific Ocean (ECTPO) (Sun et al. 2001; Schaefer and Fuller 2006). Precise measurements of age and growth can be obtained by means of tagging (and direct aging). However they are expensive, labor intensive, and time

Environ Biol Fish (2009) 85:127–137

consuming. In contrast, size-frequency analysis (SFA) is cost effective, easy to apply, and widely used (Stéquert and Conand 2000) and can yield reliable results (Mytilineou and Sardá 1995). SFA processes rely on the assumption that a sampled length frequency consists of a number of age classes. An overall length frequency distribution is therefore the result of a number of (assumed normally distributed) length frequencies for each age class (Pilling et al. 2007). In recent years a number of modern software package are currently available to decompose a time series of size-frequency data into age classes and to estimate von Bertalanffy growth parameters, such as MIX (MacDonald and Green 1990), MULTIFAN (Fournier et al. 1990) and the FiSAT package (Gayanilo et al. 1988). The mean lengths of the cohorts determined by using MIX, which analyzed each of the monthly length-frequency distributions independently, were similar to those yielded by MULTIFAN, which constrains the means of each of the sequential and corresponding cohorts to a von Bertalanffy growth curve. Another widely used, and simpler, method than MULTIFAN is ELEFAN (Pauly 1987). ELEFAN uses the number and positions of peaks in a single or series of length frequencies to estimate growth. Growth curves, derived through a specified growth model and using growth parameter sets selected from a specified range, are fitted. The coincidence between observed and expected modes in length frequency distribution(s) is used to indicate the suitability of that growth parameter set (Pauly 1987). In this study, a size-frequency analysis is conducted using the FiSAT program (Gayanilo et al. 1994) to analyze growth and mortality of bigeye tuna in the ECTPO. The FiSAT program uses an automatic search option of the ELEFAN routine (Gayanilo et al. 1994). The objective of the study is to provide information on the age and growth of bigeye tuna in the ECTPO. Such information can give a reference for the tuna fisheries management in the Pacific Ocean.

Materials and methods Study area and data sampling A total of 1187 bigeye tuna were randomly sampled on board the Chinese longline vessels operating in the ECTPO (Fig. 1) on a daily basis from February to

Environ Biol Fish (2009) 85:127–137

129

155˚W 150˚W 145˚W 140˚W 135˚W 130˚W 5˚N

0˚S

5˚S

10˚S 0

250

500km

Fig. 1 Map of the sampling area and sampling sites for bigeye tuna in the eastern and central tropical Pacific Ocean from February to November 2006

November 2006. For each sampled fish, fork length (FL) was measured to the nearest 0.1 cm and grouped into 5 cm fork length classes. Round weight (RW) and dressed weight (DW, gilled and gutted weight) were measured with electronic platform balances to the nearest 0.1 kg. The body cavity was cut open with a knife, and the gonads removed. The specimens were sexed by inspecting gonad morphology. Capture locations and dates were recorded for each of the specimens sampled. All the samplings were conducted by trained scientific observers onboard the fishing vessels. Daily sea surface temperature (SST) was recorded using Conductivity Temperature and Depth (CTD) sensors (Conductivity Temperature and Depth sensors, Sea-Bird 37, Sea-Bird Electronics, Inc.). With internal battery pack and large memory, the CTD sensor is suitable for both self recording operations down to 350 m depth, and real time use with a choice of data output protocols. Monthly sea surface temperature was obtained by averaging daily sea surface temperature. Length-weight relationship The length–weight relationship was fitted by an exponential regression equation W ¼ aLb e" , ε~ N (0, σ2), where W is the dressed weight (kg), L the fork length (FL) (cm), b the growth exponent or length-weight factor, and a is a constant. The parameters (a and b), the coefficient of determination (r2) and the standard errors of b value (S.E.b) were estimated over

the entire period by least squares regression using the log transformed weights and sizes. Regression analysis was done separately for males and females and the difference of slopes between females and males was tested with analysis of covariance (ANCOVA). The hypothesis of isometric growth (Ricker 1975) was tested using the t-test (Sokal and Rohlf 1987). In order to identify the effect of season on the length–weight relationship of bigeye tuna, the sampling time period (February to November) was divided into 4 quarters (quarter 1: February to March; quarter 2: April to June; quarter 3: July to September; quarter 4: October to November). The differences of length–weight relationship between the four quarters were examined using a t-test. The difference of FL distribution between sexes was tested by two-sample Kolmogorov-Smirnov test (K-S test). The 95% confidence intervals of mean monthly SST and mean FL were estimated from running 1000 bootstrap runs (Efron and Tibshirani 1986). Efron (1979) propose a “bootstrap” method of approximating the distribution of a function of the observations and population. This method can be used to set confidence intervals and to estimate the bias and variance of an estimate. The bootstrap prediction process for computing the confidence intervals comprises three steps: resampling for generating bootstrap samples, calculation for generating bootstrap percentiles and computation of confidence intervals from generated bootstrap percentiles (Efron and Tibshirani 1986). Growth The ELEFAN method (Gayanilo et al. 1988; Gayanilo et al. 1994) was used to fit the size frequency data for estimating the von Bertalanffy growth model, written as Lt ¼ L1 ð1  eðkðtt0 Þ Þ

ð1Þ

where Lt= Length at age t; L∞= asymptotic fork length; k = growth coefficient t0 = age at length 0. The seasonality part was neglected because of the highly migratory nature of bigeye tuna in the oceanic waters with small seasonal temperature fluctuations. t0 can be calculated by Pauly’s empirical equation (Pauly 1980): log10 ðt0 Þ ¼ 0:3922  0:2752 log10 L1 0  1:038 log10 k

ð2Þ

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Environ Biol Fish (2009) 85:127–137

0

f ¼ logk10 þ2  logL101

ð3Þ

140 Dressed weight (kg)

Where L∞′ = asymptotic total length. The estimated growth parameters were compared with values from other studies using the growth performance index phi-prime f′ (Pauly and Munro 1984) expressed as:

Slope = 0.9206 S.E. = 0.0020 Intercept = -2.2550 S.E. = 0.1042

120

2

r = 0.9983 n = 347

100 80 60 40 20 0

0

50

Mortality The instantaneous total mortality (Z) was estimated by using FiSAT program based on the lengthconverted catch curve method (Pauly 1983; Munro 1984; Gayanilo et al. 1994) and the estimated growth parameter. The natural logarithm of the ratio between the number of fish in each length class and the time needed for the fish to grow through the length class (ln Ni/dti) was plotted against their corresponding relative age (t); total mortality was estimated from the descending slope b. The natural mortality M was calculated by Pauly’s empirical equation (Pauly 1980): 0

log M ¼ 0:1228  0:1912 log L1 þ 0:7485 log k

þ 0:2391 log T

(5)

Fig. 3 Linear relationship between dressed weight and round weight for bigeye tuna in the eastern and central tropical Pacific Ocean from February to November 2006

Fishing mortality (F) and exploitation rate (E) were calculated according to the following equations (Ricker 1975; Cadima 2003): F¼ZM

E¼

ð5Þ

F ð1  ez Þ Z

ð6Þ

Results Sea surface temperature The average monthly SST was estimated from the 113 samples of sea surface temperatures measured (Fig. 2). The average SST was 26.38±1.69°C (mean ± S.E.).

12

(14) (15) (10) (15) (9)

n = 1187

10

(23) (19)

26 (18)

24 22

Frequency

Sea surface temperature ( C )

28

150

ð4Þ

where T (in°C)= the mean annual temperature, which is assumed to reflect the sea surface temperature 0 (Pauly personal communication). The L1 value was estimated from a linear regression model between dressed weight and round weight and the length– weight relationship.

30

100

Round weight (kg)

8 6 4 2

20 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Month

0 55

70

85

100

115

130

145

160

175

190

Fork length (cm)

Fig. 2 Mean sea surface temperature (°C) in the eastern and central tropical Pacific Ocean during February to November 2006 (Vertical bars signify standardized deviations, Number of fish sampled is in parentheses)

Fig. 4 Size frequency distribution of bigeye tuna in the eastern and central tropical Pacific Ocean from February to November 2006

Dressed weight (kg)

180 160 140 120 100 80 60 40 20 0

180 160 140 120 100 80 60 40 20 0

Dressed weight (kg)

Dressed weight (kg)

Environ Biol Fish (2009) 85:127–137

180 160 140 120 100 80 60 40 20 0

131

0.9983 (n = 347, P<0.001), suggesting a high and significant linear relationship between the two weight measurements (Fig. 3).

DW= 0.00001052FL3.0909 r 2 = 0.9748 n=423 =423 (Female)

Length–weight relationship

DW= 0.00001219FL3.0637 r 2 = 0.9786 n =649 (Male)

DW= 0.00001073FL3.0881 r 2 = 0.9768 n =1072 (Combined)

0

50

100

150

200

250

Fork length (cm)

Fig. 5 Relationships between dressed weight and fork length of bigeye tuna in the eastern and central tropical Pacific Ocean from February to November 2006

Dressed weight–round weight relationship

Fig. 6 The von Bertalanffy growth curves of bigeye tuna in the eastern and central tropical Pacific Ocean as superimposed on the length–frequency histograms

Fork length (cm)

The coefficient of determination for the relationship between dressed weight and round weight r2 is

Overall, 1187 specimens were collected and used for the growth analysis. The length of sampled bigeye tuna ranged between 50 and 198 cm FL and mean FL was 124.9 cm (123.3 – 126.4 cm for the bootstrapped 95% confidence interval) (Fig. 4). The mean FLs of females and males were 127.3 cm (125.2 -130.0 cm) and 128.0 cm (126.0 -129.8 cm), respectively. The size frequency distribution wasn’t significantly different between sexes (K-S test: Z=0.806, P= 0.534>0.05). The size range of males (75 - 198 cm FL) was wider than that of females (85 - 192 cm FL). The length-weight relationship was DW = 0.00001219FL 3.0637 (r 2 =0.9786, n=649, S.E. b = 0.0178) for males and DW = 0.00001052FL3.0909 (r2=0.9748, n=423, S.E.b=0.0242) for females. The slope was significantly different between sexes (ANCOVA, P<0.001), and significantly higher than the theoretical value of 3 for males (t-test: t=3.448, P<0.001) and females (t-test: t=3.752, P<0.001), the result indicating positive allometric growth for both sexes. The ANCOVA indicated the length-weight relationship had no significant difference between males and females (P=0.8227>0.05); thus the length-weight relationship was pooled by sexes and estimated as DW = 0.00001073FL3.0881 (r2= 0.9768, n=1130, S.E.b=0.0142) (Fig. 5). The slope was also significantly higher than 3 (t-test: t=6.198, P<0.001).

Month

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207.4 cm fork length, k = 0.23 year-1, to =-0.43 year, f′ = 4.00 (Fig. 6).

Length converted catch (ln(N/Δt))

Not used Used

Mortality The length-converted catch curve is shown in Fig. 7. The estimated instantaneous total mortality rate for all fish was Z = 0.60 ± 0.04 year-1. The instantaneous natural mortality rate (M) was 0.35 year-1. The value of M/K ratio was 1.52. The fishing mortality was F = 0.25 year-1. The exploitation rate was E = 0.19.

Relative age (year)

Fig. 7 Length-converted catch curve for all bigeye tuna specimens collected from the eastern and central tropical Pacific Ocean from February to November 2006. “Not used” indicate the data refer to length classes not fully recruit to the fishery

Discussion Length-weight relationship The coefficient of the fork length–round weight relationship of bigeye tuna from the catch samples of the ECTPO showed negative allometry growth (b=2.9779), in accordance with the fork length–round

Growth

Dressed weight (kg)

The growth parameters estimated by ELEFAN I routine and the performance index (f′) were: L∞ =

160

(A)

140

DW =0.000008711FL

(B) 3.1252

DW =0.000008091FL

2

r =0.9817 n=90

120 100

3.1446

2

r =0.9776 n=526

80 60 40 20

Dressed weight (kg)

0

160

(C)

140

DW =0.00001579FL

(D) 3.0085

DW =0.00001579FL

2

r =0.9829 n=297

120 100

3.0564

2

r =0.9688 n=216

80 60 40 20 0

0

50

100

150

Fork length (cm)

200

250

0

50

100

150

200

250

Fork length (cm)

Fig. 8 The fork length-dressed weight relationship of bigeye tuna, by quarter, in the eastern and central tropical Pacific Ocean from February to November 2006. a Quarter 1 b Quarter 2 c Quarter 3, d Quarter 4

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133

Table 1 The effect of season on the length-weight relationship of bigeye tuna in the eastern and central tropical Pacific Ocean from February to November 2006 t-test

Qrt 1 and Qrt 2

Qrt 1 and Qrt 3

Qrt 1 and Qrt 4

Qrt 2 and Qrt 3

Qrt 2 and Qrt 4

Qrt 3 and Qrt 4

T

3.968

23.451

12.675

84.357

32.575

16.623

Df

95.448

103.201

141.846

525.000

270.828

331.197

P

<0.0001

<0.0001

<0.0001

<0.0001

<0.0001

<0.0001

“Qrt” signify quarter

weight relationship data given by Sun et al. (2001) (b=2.9278, Western), Nakamura and Uchiyama (1966) (b=2.9018, Central), Iversen (1955) (b= 2.9304, Central) and Kume and Shiohama (1964) (b=2.9180, Central; Gilled and gutted weight is

converted to round weight by a factor of 1.16). On the other hand, Kume and Shiohama (1964) (b=3.1056, Western-north), Kume and Shiohama (1964) (b=3.0475, Western equatorial) and Yang et al. (2005) (b=3.1641, West-central) obtained the

Table 2 Comparison of von Bertalanffy growth parameters of Pacific bigeye tuna reported in various studies ordered by date Area

N

Sampling Von Bertalanffy growth range parameters

f′

Method

Sources

L∞(cm) k (year-a) t0 (year) 58-109a

195.2

0.11

-1.13

3.61 Scales

Nose et al. (1957)

b

215.0

0.21

-0.01

3.98 scales

Yukinawa and Yabuta (1963)

Western North Pacific

65-150b

257.5

0.16

-0.11

4.01 Size frequency

Yukinawa and Yabuta (1963)

Central Pacific (Hawaiian Islands) Central Pacific (Hawaiian Islands) Eastern Pacific

80-155b

196.7

0.27

-0.93

Shomura and Keala (1963)

80-155b

183.0

0.32

0.72

Pacific-wide, north of 10°S Pacific (north of 10°S)

463

64752

Eastern Pacific

60-150

82-150

187.0

0.38

0.53

4.01 Size frequency (males) 4.02 Size frequency (females) 4.12 Size frequency

39-209

187.0

0.10

2.11

3.52 Size frequency

Kume and Joseph (1966)

214.8

0.21

-0.02

3.98 Size frequency

Suda and Kume (1967)

Western and Central Pacific Pacific Ocean Western Pacific

192

Shomura and Keala (1963) Kume and Joseph (1966)

165.3

0.37

-0.34

4.01

Kirkwood (1983)

156.8

0.43

0.53

4.02 Tagging data

Hampton et al. (1998)

4.01 Otolith and tagging Hampton and Leroy (1998)

Western Pacific

25-175

165.3

0.37

0.34

French Polynesia

46-185

228.6

0.23

-0.43

46-189

208.7

0.20

-0.99

169.09 0.24

-1.71

Western Pacific

1149

South-west Pacific

1998 39-178

East-central Pacific

36-139

367.7

0.12

4.07 Otolith and tagging Lehodey et al. (1999) data 3.94 Spine Sun et al. (2001) 3.84 Otolith

Farley et al. (2006)

4.21 Tagging data

Schaefer and Fuller (2006)

East-central tropical Pacific

1187

50-198

207.4

0.23

-0.43

4.00 Size frequency

This present study

East-central tropical Pacific

423

85-192

207.4

0.32

-0.44

This present study

East-central tropical Pacific

649

75-198

202.1

0.27

-0.44

3.92 Size frequency (female) 3.77 Size frequency (male)

This present study

Partly reproduced from Table 1 of Shomura et al. (1993), Table 3 of Lehodey et al. (1999) and Table 4 of Sun et al. (2001) a

estimated from mean observed length b estimated from the curve

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Environ Biol Fish (2009) 85:127–137

higher values, respectively, in bigeye tuna from the various waters of Pacific Ocean. Different results can be found to the above studies. Such differences might be attributed to the fact that most of the abovementioned studies did not include seasonal sampling and located in different waters of Pacific Ocean, which is necessary because the condition of fish generally changes as a function of many factors (e.g., season, area, feeding, number of observed individuals, sampling and preservation techniques) (Le Cren 1951). This study shows that the fork length–dressed weight relationships have significant differences between 4 quarters (Fig. 8 and Table 1). The ANCOVA also indicate the length-weight relationship have a significant difference among seasons (F=3.898, P=0.009<0.05) Growth and mortality Bigeye tuna growth in the Pacific Ocean has been studied with various methods (Table 2). Some of results are illustrated and compared in Fig. 9. For the study of growth the length-frequency analysis has been the most frequently used method, even in other oceans, such as the Atlantic Ocean (Champagnat and Pianet 1974; Marcille et al. 1978; Weber 1980; Pereira 1984; Fagundes et al. 2001) and Indian Ocean (Marcille and Stéquert 1976). The size range of the bigeye tuna used in this study was among the widest in bigeye tuna growth studies Fig. 9 Comparison of the growth curve for bigeye tuna estimated in the present study (heavy line) with the growth curves estimated by other authors

published (Fig. 9 and Table 2), and the growth curves estimated from this study are consistent with the growth curves estimated earlier by other authors for bigeye tuna using size-frequency analyses (Suda and Kume 1967) and dorsal spines such as Sun et al. (2001). The values of t0 differed because different aging techniques were used (Sun et al. 2001). Kume and Joseph (1966) concluded that lower L∞ and k value and higher t0 value of bigeye tuna in the eastern Pacific Ocean (east of 130°W and between 10°N and 25°S), and unrealistic higher L∞ value of bigeye tuna in the eastern and central Pacific Ocean can be found in the studies of Schaefer and Fuller (2006). The reliability of these estimates is questionable because of the restricted size range of the samples (in particular the lack of large fish). Differences in growth patterns can also be the result of differences in genetic structure and /or differences in temperature, density of food and diseases (Pauly 1994; Wootton 1998) and other factors (e.g. season, area, number of observed individuals, sampling and preservation techniques) (Le Cren 1951). The reliability of the estimated M was ascertained using the M/K ratio because this ratio has been reported to be within the 1.12 – 2.50 range for most of the fish (Beverton and Holt 1957). The value of M/K ratio was 1.52 in the present study and was fell into the range of 1.12 - 2.50, so the M value can be considered as a reliable value. The natural mortality rate of bigeye tuna was estimated from the analysis of

200 180 160

Lehodey et al. (1999)

Fork length (cm)

140

Yukinawa and Yabuta (1963) Kume and Joseph (1966)

120

Nose et al. (1957) 100

Yukinawa and Yabuta (1963) Shomura and Keala (1963)-Male

80

Shomura and Keala (1963)-Female 60

Sun et al. (2001) This present study

40

Schaefer and Fuller (2006)-Tagging 20

Schaefer and Fuller (2006)-Otolith

0 0

2

4

6

8

Age (Year)

10

12

14

Environ Biol Fish (2009) 85:127–137

catch-at-age data for the longline fishery to be 0.361 year-1 with the instantaneous annual total mortality rate ranging from 0.6 to 1.4 year-1 (Suda and Kume 1967). Several estimates of natural mortality rate have also been obtained from analyses of Regional Tuna Tagging Project (RTTP) tagging data (Hampton et al. 1998). The present study was also similar to the results of Suda and Kume (1967), but differences were found between the present study and Hampton et al. (1998). The possible reason was that the latter estimates have been obtained for small fish (M = 4.08 – 6.72 year-1 for size range of release within 20 - 40 cm) tagged in the Philippines, for small medium (M = 1.05 – 1.39 year-1, 45 - 65 cm) fish tagged in the western equatorial Pacific Ocean and for medium - large fish (M = 0.52 – 0.59 year-1, 60 110 cm) tagged in the Coral Sea; the size range, the study area and the aging method of Hampton et al. (1998) were different from the present study. The f′ value obtained from the results of sizefrequency method was similar to the values obtained from tagging and otoliths (Table 1). The f′ value of 3.61 (Nose et al. 1957) was lower than others, possibly as a result of the lack of large bigeye tuna in the sample. The f′ value of 4.12 (Kume and Joseph 1966) and 4.21 (Schaefer and Fuller 2006) were higher than the values of other studies, because growth parameters were not estimated over the entire span of life history and the samples did not contain young bigeye tuna (smaller than 80 cm) (Kume and Joseph 1966) or large bigeye tuna in the sample (larger than 140 cm) (Schaefer and Fuller 2006). In general, the value of f′ (4.00) obtained in this study was similar to the values of other studies (3.94 - 4.07) (Table 2). The estimation of growth parameters for bigeye tuna using the size-frequency method in this study was reliable. In conclusion, this study provides the estimates of growth and mortality rate for bigeye tuna in the eastern and central tropical Pacific Ocean, which can be used as biological input parameters in future stock assessment in this region. However, age analysis, additional validation of the size composition and stock structure are needed for future studies. Acknowledgements We thank Liu Wei who assisted in the field sampling in the eastern and central tropical Pacific Ocean. We gratefully acknowledge the captains and crews of the longliners “LONG XIN 602, 603 and 606” for permitting sampling on board their vessels even the vessels were in

135 aboard. Finally, we acknowledge Chen Yong in School of Marine Sciences, University of Maine and the anonymous reviewers for their constructive comments on the manuscript. The present study was sponsored by the Tuna Scientific Observer Program of China, Shanghai (China) Leading Academic Project under Grant No. S30702, Shanghai Scientific Special Funds for Cultivation and Selection of Excellent Young Teaching Staffs of Higher Education under Grant No. B-810108-0022, Innovation Program of Shanghai Municipal Education Commission under Grant No. 09YZ275 and Initial Doctoral Funding of Shanghai Fisheries University under Grant No. B8202-07-0279.

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