Bigeye tuna (Thunnus obesus Lowe, 1839) are a commercially important species of tuna inhabiting the warm waters of the Atlantic, Indian, and Pacifi c oceans. They are found across the entire Pacifi c between northern Japan and North Island of New Zea-land in the west and from 40°N to 30°S in the east (Calkins, 1980; Mat-sumoto, 1998). Adult bigeye tuna are caught mainly by longlines, but sub-stantial numbers of juveniles are taken by purse seines.
Taiwanese distant water tuna long-line fl eets have operated throughout these three oceans since the late 1960s targeting albacore. In the early 1980s, the Taiwanese began equipping their longliners with very cold (below –55°C) freezers and deep longlines in the Indi-an Indi-and AtlIndi-antic oceIndi-ans, which allowed them to target bigeye tuna for the lu-crative sashimi market in Japan. In the western Pacifi c, the Taiwanese off-shore longline fl eets, based in domestic (Tungkang mainly) and foreign fi shing ports, have landed more bigeye tuna than in the past.
Growth studies of Pacifi c bigeye tu-na conducted in the 1950s and 1960s were based either on increments be-tween modal points in size-composition data (Iversen, 1955; Shomura and Ke-ala, 1963; Yukinawa and Yabuta, 1963; Kume and Joseph, 1966; Suda and Kume, 1967) or on the number of an-nual markings (annuli) on scales (Nose et al., 1957; Yukinawa and Yabuta, 1963). Recently, Hampton and Leroy1 and Matsumoto (1998) presented pre-liminary results from growth studies based on otolith increment counts. No previous study had aged Pacifi c and In-dian bigeye tuna from dorsal spines,
al-Age and growth of the bigeye tuna,
Thunnus obesus, in the western Pacifi c Ocean
Chi-Lu Sun
Chien-Lung Huang
Su-Zan Yeh
Institute of Oceanography National Taiwan University Taipei, Taiwan
E-mail address (for C.L. Sun): chilu@ccms.ntu.edu.tw
Manuscript accepted 12 December 2000. Fish. Bull. 99:502–509 (2001).
though a few age determination studies existed for Atlantic bigeye tuna (Gaikov et al., 1980; Draganik and Pelczarski, 1984; Delgado de Molina and Santana, 1986; Alves et al., 1998). Accurate age structure of stocks is essential for stock assessment and fi shery management. Our study provides estimates of the age and growth rate of bigeye tuna in the western Pacifi c from growth rings on sections of the fi rst dorsal spine.
Materials and methods
Fork length (in cm), weight (in kg), and sex were determined for bigeye tuna caught by Taiwanese offshore longlin-ers in the fi shing area from 23°N to 0°N and 110°E to 140°E (Fig. 12) and sold at the Tungkang fi sh market between February 1997 and January 1998. In addition, a total of 1149 fi rst dorsal spines were collected. Three cross sec-tions were taken along the length of each spine above the condyle base (Fig. 2A) with a low-speed “ISOMET” saw
Abstract–Bigeye tuna (Thunnus
obe-sus) age and growth studies were last
conducted in the western Pacifi c in 1967 and no study has ever attempted to age bigeye tuna from this area by using dorsal spines. The objective of our study was to estimate bigeye tuna age and growth rate in the western Pacifi c based on counts of growth rings on sections of the fi rst dorsal spine. Length and weight data, and the fi rst dorsal spine from bigeye tuna in the Tungkang (southwest of Taiwan) fi sh market were collected monthly from February 1997 to January 1998. In total, 1149 specimens were collected. The fork lengths of individuals ranged from 45.6 to 189.2 cm. Cross sections from dorsal spines were taken and examined under a dissecting microscope equipped with an image analysis system. The monthly percentage of speci mens having a terminal translucent zone indicated that growth rings formed once a year; therefore, the age of each fi sh was determined from the number of visible growth rings. Von Bertalanffy growth parameters were estimated for males, females, and both sexes combined. There was no signifi cant difference between males and females. The parameter estimates for the combined sexes were asymptotic length (L∞) = 208.7 cm, growth coef fi cient (K) = 0.201/yr, and age at zero length (t0) = –0.9906 yr.
1 Hampton, J., and B. Leroy. 1998. Note
on preliminary estimates of bigeye growth from presumed daily increments on oto-liths and tagging data. Working paper 18, eleventh meeting of the standing com-mittee on tuna and billfi sh, Honolulu, Hawaii, USA, 30 May–6 June 1998, 3 p. Oceanic Fisheries Programme, Secretar-iate of the Pacifi c Community, B.P.D5, 98848 Noumea, New Caledonia.
2 Yang, R. T., R. F. Chung, and C. L. Chang.
1982. Taiwanese offshore tuna longline fi shery. Part I: fi shing ground, fi shing season, and fi shing condition. Spec. Rep. 36, 6 p. [In Chinese with English abstract.] Insitute of Oceanography, National Taiwan University, no. 1, sec 4, Roosevelt Rd, Taipei, 106 Taiwan.
Figure 1
Fishing areas of the Taiwanese offshore tuna longline fi shery in the western Pacifi c Ocean (Yang et al.2).
Figure 2
First dorsal spine and the site of cross section (A) and the cross section showing annual rings and measurements taken (B) for age determination of the western Pacifi c bigeye tuna (c =width of condyle base; L1DS=length of the fi rst dorsal spine; R=radius of spine; RI=radius of ring i; d=diameter of spine; dI=diameter of ring i).
(model no. 11-1280) and diamond wafering blades. Sections ranging from 0.8 to 1.0 mm thick (Fig. 2B) were examined with a dis-secting microscope (model: Olympus SZH-ILLD) with transmitted light. Images of the dorsal spine sections were captured by using an image analysis software package, a CCD (charged coupled device) camera, and a high-resolution computer monitor. Translucent rings on the section images were counted by two readers independently. When ring counts disagreed, images were read again by both readers simultaneously, and any ques-tionable spines were discarded.
Spine sections as the structure to estimate age have the advantage of requiring easy sampling and easy reading (the growth rings stand out clearly), and samples are easily stored for future reexamination (Compeán-Jimenez and Bard, 1983). However, early growth rings may be lost in larger specimens because of increased size of the vascularized core in the spine. Accordingly, we estimated the number of lost (obscured) rings from ob-servations of their position and number in spines from young specimens as has been done for little tunny (Euthynnus alletteratus) (Cayré and Di-ouf, 1983), eastern Atlantic bluefi n tuna (Thunnus thynnus) (Compeán-Jimenez and Bard, 1983), and Pacifi c blue marlin (Makaira nigricans) (Hill et al., 1989).
Age was determined from the translucent rings, assuming that two rings are formed each year—a translucent (light colored) ring formed during the slower growth period and an opaque (dark colored) ring formed during the fast growth period. This as-sumption was validated by observing a translucent or opaque edge on the dorsal-spine sections and a monthly variation in the number of translucent edg-es (Antoine et al., 1983).
Distance between the center of the dorsal spine and the outer edge of each annual ring was mea-sured in microns with the software package after calibration against an optical micrometer. The cen-ter of the spine was estimated by following Cayré and Diouf (1983) (Fig. 2B). Distances (di) were then converted into radii (Ri) by following González-Gar-cés and Fariña-Perez (1983).
The relationship between fork length (FL) and dorsal spine radius (R) was modeled by a linear equation (Zar, 1999). Fork length was then back-cal-culated for each ring with the formula (Lee, 1920)
FL a FL a R
R
i
i
= +( − ) ,
where FLi = predicted fork length of the fi sh corre-sponding to age or ring i in cm; a = ordinate in the origin of the equation
Table 1
Sample sizes, ranges of fork lengths (FL, cm), and sampling months and areas of bigeye tuna from the western Pacifi c Ocean. A, B, C, D, and E denote areas in Figure 1.
Sampling Sample Minimum Maximum
Month area size FL FL
Feb 1997 A 80 70.0 174.5 Mar 1997 A 104 64.0 169.5 Apr 1997 B 70 101.3 171 May 1997 B 54 83.8 157.4 Jun 1997 B 71 75.5 162.8 Jul 1997 B, D 131 72.2 165.6 Aug 1997 E 94 78.5 187.7 Sep 1997 E 98 45.6 189.2 Oct 1997 A, C 115 86.5 176.6 Nov 1997 A, C 116 89.6 161.1 Dec 1997 C 123 104.6 162.1 Jan 1998 A 93 88.7 159.1 Total 1149 45.6 189.2 Figure 3
Length-frequency distribution for the western Pacifi c bigeye tuna sampled at Tungkang fi sh market from February 1997 to January 1998.
FL = observed fork length of the fi sh in cm; Ri = radius of the ring calculated as the
aver-age value observed in ring i (Fig. 2B); and R = dorsal spine radius.
Back-calculated fork lengths were used in Ford-Walford (Gulland, 1983) and nonlinear (Ratkowsky, 1983) meth-ods to fi t the von Bertalanffy growth function (VBGF) and to obtain vital parameters by sex. Analysis of the residual sum of squares (ARSS) was employed to com-pare the VBGF between sexes (Ratkowsky, 1983; Chen et al., 1992).
Weight was related to fork length by using the power function, and analysis of covariance (ANCOVA) (Steel, 1980; Zar, 1999) was conducted to examine differences between sexes.
Results
Spines from 1149 specimens ranging in size from 45.6 to 189.2 cm FL were examined (Table 1, Fig. 3). There was 90% agreement between the readers’ counts of growth rings and second readings improved this agreement to 95.6%, which resulted in discarding 51 specimens from analysis.
The relationship between FL (cm) and weight (kg) is shown in Figure 4. The ANCOVA indicated no signifi cant difference between males and females (P>0.05); thus the FL-W relationship with sexes combined was expressed as
W = 3 × 10–5 FL2.9278 (r2=0.97, n=856). The relationship of fi rst dorsal spine lengths (L1DS) and FL was (Fig. 5)
FL = 6.9367 L1DS + 6.6667 (r=0.94, n=567). The trend of the monthly percentages of terminal trans-lucent edges (Fig. 6) suggested that the period from Febru-ary to September was the long period of inhibited growth (translucent edge). From October to November, growth ap-peared to resume (opaque edge) and later, from December to January, a new translucent edge appeared; indicating the formation of one growth ring per year.
Given the signifi cant linear relationship between the dorsal spine radius and fork length (FL=26.455R + 19.916, r=0.94, n=1098), we used spine measurements to
back-calculate the fork lengths of previous ages. The mean back-calculated fork lengths for the fi rst 10 years of life for the western Pacifi c bigeye tuna are given in Table 2.
Parameters of the VBGF estimated by the Ford-Wal-ford method for males, females, and sexes combined are shown in Table 3. Growth was not signifi cantly different between sexes (ARSS, F=1.98; df=3, 452; P>0.05); the pooled growth curve is shown in Figure 7. VBGF param-eters computed by nonlinear regression are also shown in Table 3 and Figure 7. Length-at-age of bigeye tuna esti-mated by nonlinear regression is larger (up to age 6 years) than that estimated by the Ford-Walford method.
Discussion
Available genetic information supports the hypothesis of a single bigeye stock in the Pacifi c Ocean (Hampton et al.,
Figure 6
Monthly variation in percentage of the western Pacifi c big-eye tuna with a terminal translucent zone in dorsal spine sections, February 1997 to January 1998.
Figure 7
Comparison of the growth curve obtained by the Ford-Walford plot with the growth curve obtained by nonlinear regression method for the western Pacifi c bigeye tuna.
1998; Grewe and Hampton3). Although the fi shing area of the Taiwan fl eet and thus the sampling area of bigeye tuna used in our study was limited to a small area of the western Pacifi c, our results may be representative of bigeye tuna throughout the Pacifi c Ocean.
Monthly variation in percent terminal translucent edges in our study suggested the formation of growth rings once a year. Ehrhardt et al. (1996) attributed the narrow,
trans-3 Grewe, P. M., and J. Hampton. 1998. An assessment of
bigeye (Thunnus obesus) population structure in the Pacifi c Ocean, based on mitochondrial DNA and DNA microsatellite analysis. University of Hawaii, Joint Institute for Marine and Atmosphere Research Contribution 98-320, 29 p. Pelagic Fish-eries Research Program, University of Hawaii at Manoa, 1000 Pope Road, Honolulu, HI 96822.
Figure 4
Relationships between weight and fork length of the west-ern Pacifi c bigeye tuna sampled at Tungkang fi sh market.
Combined sexes (n=856) W=0.00003 FL2.9278 r2=0.97
Figure 5
Relationship between fork length and length of the fi rst dorsal spine (L1DS) of the western Pacifi c bigeye tuna sam-pled at Tungkang fi sh market.
FL=6.9367L1DS + 6.6667 r =0.94
n=567
Table 2
Observed and back-calculated mean fork length (FL, cm) at age for the western Pacifi c bigeye tuna, Thunnus obesus. (“—” means there were no data owing to vascularization at core area). Numbers in normal print represent the mean back-calculated fork lengths; numbers in parentheses represent the number of specimens for which the specifi ed ring was readable.
Observed Annulus number
Age mean FL
(yr) n (cm) I II III IV V VI VII VIII IX X
1 8 67.9 57.0 (8) 2 79 93.7 50.0 80.8 (29) (79) 3 329 115.3 52.4 85.8 102.9 (69) (265) (329) 4 413 131.7 51.9 82.7 107.1 121.2 (19) (162) (384) (413) 5 188 145.9 — 80.9 112.1 122.8 135.8 (14) (77) (184) (188) 6 59 158.4 — — 115.5 126.6 138.2 149.5 (3) (36) (58) (59) 7 11 169.3 — 119.5 130.1 142.6 152.1 161.8 (1) (5) (9) (11) (11) 8 6 174.7 — — — 123.8 139.6 150.8 161.0 172.1 (1) (5) (6) (6) (6) 9 3 178.5 — — — 121.0 129.2 142.0 154.2 169.2 174.2 (1) (2) (2) (3) (3) (3) 10 2 188.5 — — — — 138.2 148.4 162.5 174.1 180.6 186.2 (1) (2) (2) (2) (2) (2) Total 1098 (125) (520) (794) (640) (263) (80) (22) (11) (5) (2) Weighted back-calculated mean FL (cm) 52.1 83.9 105.9 122.0 136.6 149.8 160.6 171.7 177.4 186.2 Growth increment (cm) — 31.9 21.9 16.2 14.6 13.1 10.9 11.1 5.7 8.7 Table 3
Growth parameters obtained by the Ford-Walford plot method and the nonlinear regression method for the bigeye tuna from the western Pacifi c Ocean.
Ford-Walford plot Nonlinear regression
Parameter Male Female Pooled Total1 Total1
n 278 180 458 1098 1098
K 0.1789 0.191 0.1842 0.185 0.2011
L∞ 220.6 211.4 216.1 226.4 208.7
t0 –0.5566 –0.4592 –0.5266 –0.4465 –0.9906
1 Male, female, and sex-unknown combined.
4 Sun, C. L., S. L. Chu, and S. Z. Yeh. 1999. Note on
reproduc-tion biology of bigeye tuna in the western Pacifi c. SCTB12/WP/ BET-4, 6 p. Twelfth meeting of the standing committee on tuna and billfi sh; Tahiti, French Polynesia, June 14–23, 1999. Oce-anic Fisheries Programme, Secretariate of the Pacifi c Commu-nity, B.P.D5, 98848 Noumea, New Caledonia.
lucent rings to slower growth periods, whereas the wide, opaque rings were attributed to periods of fast growth. The spawning season of bigeye tuna in the western Pacifi c is between February and September and peaks from March to June (Sun, et al.4), the period that we found to coincide
50
7
T
hunnus obesus
Comparisons of estimates of parameters of von Bertalanffy growth function for the Pacifi c bigeye tuna by various authors. Partly reproduced from Table 10 of Shomura (1966).
Parameters
Area Investigator(s) Method of analysis L∞(cm) K t0 Size range of fi sh (cm) Comments
Pacifi c-wide, north of 10°S
Western North Pacifi c (north of 2°N and west of 180°) Pacifi c (north of 10°S) Pacifi c (north of 10°S) Central Pacifi c (Hawaiian Islands) Central Pacifi c (Hawaiian Islands) Eastern Pacifi c (east of 130°W and between 10°N and 25°S) Pacifi c area Western Pacifi c Eastern Pacifi c Western Pacifi c Nose et al. (1957)
Yukinawa and Yabuta (1963)
Yukinawa and Yabuta (1963)
Yukinawa and Yabuta (1963)
Shomura and Keala (1963)
Shomura and Keala (1963)
Kume and Joseph (1966)
Suda and Kume (1967) Hampton and Leroy (1998) Matsumoto (1998) This study Scales Size frequency Scales
Scales (same basic data as above) Size frequency (males) Size frequency (females) Size frequency Size frequency Otolith and tagging Otolith Spine 195.2 0.106 –1.128 257.5 0.156 –0.107 215 0.10412 0.0010995 213.1 0.212 0.017 196.7 0.267 –0.929 183.0 0.316 0.718 186.95 0.095 2.11 214.8 0.2066 0.0249 165.3 0.3732 0.3420 — — — 208.7 0.2011 –0.9906 Mean observed length for 58–109 Modal sizes estimated to be 65–150 Estimate 51–160 39–209 25–175 33.4–57.9 45.6–189.2
Parameters based on mean observed length by age provided by authors Parameters computed from data provided by authors
Authors’ values; time (t) in half-year units
Parameters computed by graphic method from data provided by authors Authors’ values
Authors’ values
Authors’ values; time (t) in quarter-year units
Preliminary
Author estimated only the lengths of 40 and 55 cm at ages of 0.5 and one year, respectively; preliminary.
with the slow-growth period indicated by the narrow and translucent rings. Similar fi ndings have been reported for skipjack tuna (Antoine et al., 1983), bigeye tuna (Gaikov et al., 1980), and swordfi sh (Ehrhardt, 1992; Tserpes and Tsimenides, 1995). Our efforts only partially validate fi sh age; complete validation requires either mark-recapture data or the study of known-age fi sh in the population (Beamish and McFarlane, 1983; Prince et al., 1995; Tser-pes and Tsimenides, 1995).
We estimated the parameters of the VBGF by using the Ford-Walford and nonlinear methods and found that the nonlinear method had a better fi t (r2=0.95) than the Ford-Walford method (r2=0.91). Comparisons of our VBGF pa-rameters with previous studies (Fig. 8, Table 4) showed similar results to those of Yukinawa and Yabuta (1963) who used scales and to those of Suda and Kume (1967) who also used Pacifi c samples of bigeye tuna. The values of t0 differed because different aging techniques were used. Following the suggestion of Gallucci and Quinn (1979), Vaughan and Kanciruk (1982), and Hanumara and Hoe-nig (1987) that Ford-Walford and other linear methods be replaced by nonlinear fi tting techniques; we propose using parameters of VBGF estimated by the nonlinear method (Table 3) for description of age and growth for the western Pacifi c bigeye tuna.
Acknowledgments
We thank Pei-Ching Chiang who assisted in the fi eld sam-pling at the fi sh market. We thank Sheng-Ping Wang who assisted in preparing some fi gures and tables. We
also thank Clay E. Porch, Southeast Fisheries Sci-ence Center, National Marine Fisheries Service, and Chu-Fa Tsai, visiting professor at the Taiwan Endemic Species Research Institute, who reviewed the manu-script. We are indebted to three anonymous referees for their valuable comments and to John V. Merriner (scientifi c editor) and Sarah Shoffl er (editorial assis-tant) for their editorial suggestions in revising the manuscript.
Literature cited
Alves, A., P. de Barros, and M. R. Pinho.
1998. Age and growth of bigeye tuna Thunnus obesus captured in the Madeira Archipelago. Int. Comm. Conserv. Atl. Tunas, Coll. Vol. Sci. Pap., vol. 48(2): 277–283.
Antoine, L. M., J. Mendoza, and P. M. Cayré.
1983. Progress of age and growth assessment of Atlan-tic skipjack tuna, Euthynnus pelamis, from dorsal fi n spines. In Proceedings of the international workshop on age determination of oceanic pelagic fi shes: tunas, billfi shes, and sharks (E. D. Prince, and L. M. Pulos, eds.), p. 91–97. U.S. Dep. Commer., NOAA Tech. Rep. NMFS 8.
Beamish, R. J., and G. S. McFarlane.
1983. The forgotten requirement for age validation in fi sheries biology. Trans. Am. Fish. Soc. 112:735– 743.
Calkins, T. P.
1980. Synopsis of biological data on the bigeye tuna,
Thun-nus obesus (Lowe, 1839), in the Pacifi c Ocean. In
Syn-opses of biological data on eight species of scombrids (W. H. Bayliff, ed.), p. 219–259. Inter-Am. Trop. Tuna Comm. Spec. Rep. 2.
Cayré, P. M., and T. Diouf.
1983. Estimating age and growth of little tunny, Euthynnus
alletteratus, off the coast of Senegal, using dorsal fi n spine
sections. In Proceedings of the international workshop on age determination of oceanic pelagic fi shes: tunas, bill-fi shes, and sharks (E. D. Prince, and L. M. Pulos, eds.), p. 105–110. U.S. Dep. Commer., NOAA Tech. Rep. NMFS 8. Chen, Y., D. A. Jackson, and H. H. Harvey.
1992. A comparison of von Bertalanffy and polynomial func-tions in modelling fi sh growth data. Can. J. Fish. Aquat. Sci. 49:1128–1235.
Compeán-Jimenez, G., and F. X. Bard.
1983. Growth increments on dorsal spines of eastern Atlan-tic bluefi n tuna, Thunnus thynnus, and their possible relation to migration patterns. In Proceedings of the international workshop on age determination of oceanic pelagic fi shes: tunas, billfi shes, and sharks (E. D. Prince, and L. M. Pulos, eds.), p. 77–86. U.S. Dep. Commer., NOAA Tech. Rep. NMFS 8.
Delgado de Molina, A., and J. C. Santana.
1986. Estimacion de edad y crescimiento del patudo
(Thun-nus obesus, Lowe 1839) capturado en las Islas Canarias.
Int. Comm. Conserv. Atl. Tunas, Coll. Vol. Sci. Pap., vol. 25:130–137.
Draganik, B., and W. Pelczarski.
1984. Growth and age of bigeye and yellowfi n tuna in the central Atlantic as far data gathered by R/V “Wieczno”. Int. Comm. Conserv. Atl. Tunas, Coll. Vol. Sci. Pap., vol. 20(1):96–103.
Figure 8
Growth curves of Pacifi c bigeye tuna estimated by different authors.
Present study
Suda and Kume (1967), size frequency Yukinawa and Yabuta (1963), scales Yukinawa and Yabuta (1963), size frequency Shomura and Keala (1963), M, size frequency Shomura and Keala (1963), F, size frequency Nose et al. (1957), scales
Ehrhardt, N. M.
1992. Age and growth of swordfi sh, Xiphias gladius, in the northwestern Atlantic. Bull. Mar. Sci. 50:292–301. Ehrhardt, N. M., R. J. Robbins, and F. Arocha.
1996. Age validation and growth of swordfi sh, Xiphias
gla-dius, in the northwest Atlantic. Int. Comm. Conserv. Atl.
Tunas, Coll. Vol. Sci. Pap., vol. 45(2):358–367. Gaikov, V. V., V. N. Chur, V. L. Zharov, and Yu P. Fedoseev.
1980. On age and growth of the Atlantic bigeye tuna. Int. Comm. Conserv. Atl. Tunas, Coll. Vol. Sci. Pap., vol. 9(2):294–302.
Gallucci, V. F., and T. J. Quinn II.
1979. Reparameterizing, fi tting, and testing a simple growth model. Trans. Am. Fish. Soc. 108:14–25.
González-Garcés, A., and A. C. Fariña-Perez.
1983. Determining age of young albacore, Thunnus
ala-lunga, using dorsal spines. In Proceedings of the
interna-tional workshop on age determination of oceanic pelagic fi shes: tunas, billfi shes, and sharks (E. D. Prince, and L. M. Pulos, eds.), p. 117–122. U.S. Dep. Commer., NOAA Tech. Rep. NMFS 8.
Gulland, J. A.
1983. Fish stock assessment: a manual of basic methods. Wiley, Chichester, 223 p.
Hampton, J., K. Bigelow, and M. Labelle.
1998. A summary of current information on the biology, fi sh-eries and stock assessment of bigeye tuna (Thunnus obesus) in the Pacifi c Ocean, with recommendation for data require-ments and future research. Tech. Rep. 36, 46 p. Oceanic Fisheries Programme, Secretariate of the Pacifi c Commu-nity, B.P.D5, 98848 Noumea, New Caledonia.
Hanumara, R. C., and N. A. Hoenig.
1987. An empirical comparison of a fi t of linear and non-linear models for seasonal growth in fi sh. Fish. Res. 5:359–381.
Hill, K. T., G. M. Cailliet, and R. L. Radtke.
1989. A comparative analysis of growth zones in four calci-fi ed structures of Pacicalci-fi c blue marlin, Makaira nigricans. Fish. Bull. 87:829–843.
Iversen, E. S.
1955. Size frequencies and growth of central and western Pacifi c bigeye tuna. Spec. Sci. Rep. U.S. Fish. Wildl. Serv. (Fish.) 162:1–40.
Kume, S., and J. Joseph.
1966. Size composition, growth and sexual maturity of bigeye tuna, Thunnus obesus (Lowe), from the Japanese long-line fi shery in the eastern Pacifi c Ocean. Bull. Inter-Am. Trop. Tuna Comm. 11(2):45–99.
Lee, R. M.
1920. A review of the methods of age and growth determi-nation by means of scales. Fishery Invest., Lond., ser. II, 4(2), 32 p.
Matsumoto, T.
1998. Preliminary analyses of age and growth of bigeye tuna
(Thunnus obesus) in the western Pacifi c Ocean based on otolith increments. In Proceedings of the fi rst world meet-ing on bigeye tuna (R. S. Deriso, W. H. Bayliff, and N. J. Webb, eds.), p. 238–242. Inter-Am. Trop. Tuna Comm. Spec. Rep. 9.
Nose, Y., H. Kawatsu, and Y. Hiyama.
1957. Age and growth of Pacifi c tunas by scale reading. In Collection of works on fi sheries science, Jubilee publication of Professor I. Amemiya, p. 701–716. Univ. Tokyo Press. Prince, E. D., D. W. Lee, J. L. Cort, G. A. McFarlane, and
A. Wild.
1995. Age validation evidence for two tag-recaptured Atlan-tic albacore, Thunnus alalunga, based on dorsal, anal, and pectoral fi nrays, vertebrae, and otoliths. In Recent devel-opments in fi sh otolith research (D. H. Secor, J. M. Dean, and S. E. Campana, eds.), p. 375–398. Univ. South Caro-lina Press, Columbia, SC.
Ratkowsky, D. A.
1983. Nonlinear regression modelling. Marcel Dekker, Inc., New York, NY, 276 p.
Shomura, R. S.
1966. Age and growth studies of four species of tunas in the Pacifi c Ocean. In Proceedings of the government’s confer-ence on central Pacifi c fi shery resources (T. A. Manar, ed.), p. 203–219. Bureau of Commercial Fisheries, Biological Laboratory, Honolulu, Hawaii.
Shomura, R. S., and B. A. Keala.
1963. Growth and sexual dimorphism in growth of bigeye tuna (Thunnus obesus)—a preliminary report. In Pro-ceedings of the world scientifi c meeting on the biology of tunas and related species, La Jolla, California, 2–14 July 1962, p. 1409–1417. FAO Fisheries Report 6.
Steel, R. G. D.
1980. Principles and procedures of statistics: a biometrical approach. McGraw-Hill, Auckland, 633 p.
Suda, A., and S. Kume.
1967. Survival and recruit of bigeye tuna in the Pacifi c Ocean, estimated by the data of tuna longline catch. Rep. Nankai. Reg. Fish. Res. Lab. (25):91–104.
Tserpes, G., and N. Tsimenides.
1995. Determination of age and growth of swordfi sh, Xiphias
gladius L., 1758, in the eastern Mediterranean using
anal-fi n spines. Fish. Bull. 93:594–602. Vaughan, D. S., and P. Kanciruk.
1982. An empirical comparison of estimation procedures for the von Bertalanffy growth equation. J. Cons. Explor. Mer 40:211–219.
Yukinawa, M., and Y. Yabuta.
1963. Age and growth of bigeye tuna, Parathunnus mebachi (Kishinouye). Rep. Nankai Reg. Fish. Res. Lab. 19:103– 118.
Zar, J. H.
1999. Biostatistical analysis. 4th ed., Prentice-Hall, Engle-wood Cliffs, NJ, 929 p.
