The sailfish (Istiophorus platypterus) is distributed widely in the tropical and temperate waters of the world’s oceans. According to data from longline catches, sailfish are usually distributed between 30°S and 50°N in the Pacific Ocean, and highest densities are found in the warm Kuroshio Current and its subsidiary currents. This species has a tendency to be found close to the coast and near islands (Nakamura, 1985). During the 1990s the annual landings of sailfish off Taiwan ranged between 600 and 2000 metric tons, of which approximately 54% came from waters off Taitung (eastern Taiwan). Sailfish are seasonally abundant from April to October (peak abundance from May to July) and contribute substan-tially to the economic importance of the eastern coast of Taiwan where this species is taken primarily by drift gill nets, although they are also caught by set nets, harpoons, and as incidental bycatch in inshore longline fisheries.
Age and growth of sailfish caught in recreational fisheries in the Atlan-tic Ocean have been studied by using various methods, including length-frequency analysis (de Sylva, 1957), analysis of release-recapture data (Far-ber1), and inferences from observed marks on hard parts, such as spines (Jolley, 1974, 1977; Hedgepeth and Jolley, 1983) and otoliths (Radtke and Dean, 1981; Radtke, 1983; Prince et al., 1986). In contrast, very few attempts
Age and growth of sailfish (Istiophorus platypterus)
in waters off eastern Taiwan
Wei-Chuan Chiang Chi-Lu Sun
Su-Zan Yeh
Institute of Oceanography National Taiwan University No. 1, Sec. 4, Roosevelt Road Taipei, Taiwan 106
E-mail address (for C. L. Sun, contact author): chilu@ntu.edu.tw
Wei-Cheng Su
Taiwan Fisheries Research Institute No. 199, Ho-Ih Road
Keelung, Taiwan 202
Manuscript approved for publication 22 December 2003 by Scientific Editor. Manuscript received 20 January 2004 at NMFS Scientific Publications Office. Fish. Bull. 102(2): 251–263 (2004).
have been made to age sailfish in the Pacific Ocean. Koto and Kodama (1962) estimated the growth of sailfish caught with longlines from 1952 to 1955 in the East China Sea using length-frequency analysis, and Alvarado-Castillo and Fé-lix-Uraga (1996, 1998) used the fourth spine of the first dorsal fin to estimate age and growth of sailfish caught from 1989 to 1991 in the recreational fishery off Mexico. However, western Pacific sailfish have not been aged with calci-fied structures in any previous study.
The aging of fishes, and consequently the determination of their growth and mortality rates, is an integral compo-nent of modern fisheries science (Paul, 1992). Mortality and growth rates pro-vide quantitative information on fish stocks and are needed for stock assess-ment methods such as yield-per-recruit and cohort analysis (Powers, 1983).
The objectives of this study were to estimate age and growth of sailfish by counting growth rings on cross sections of the fourth spine of the first dorsal fin and to determine which of the Richards function and the standard von Berta-lanffy growth function best represents growth of sailfish in waters off eastern Abstract—Age and growth of sailfish
(Istiophorus platypterus) in waters off eastern Taiwan were examined from counts of growth rings on cross sections of the fourth spine of the first dorsal fin. Length and weight data and the dorsal fin spines were collected monthly at the fishing port of Shinkang (southeast of Taiwan) from July 1998 to August 1999. In total, 1166 dorsal fins were collected, of which 1135 (97%) (699 males and 436 females) were aged suc-cessfully. Trends in the monthly mean marginal increment ratio indicated that growth rings are formed once a year. Two methods were used to back-calculate the length of presumed ages, and growth was described by using the standard von Bertalanffy growth function and the Richards function. The most reasonable and conserva-tive description of growth assumes that length-at-age follows the Rich-ards function and that the relationship between spine radius and lower jaw fork length (LJFL) follows a power function. Growth differed significantly between the sexes; females grew faster and reached larger sizes than did males. The maximum sizes in our sample were 232 cm LJFL for female and 221 cm LJFL for male.
1 Farber, M. I. 1981. Analysis of Atlantic billfish tagging data: 1954−1980 Unpubl. manuscr. ICCAT workshop on billfish, June 1981. Southeast Fisheries Center Miami Laboratory, National Marine Fish-eries Service, NOAA, 75 Virginia Beach Drive, Miami, FL 33149.
Figure 1
Fishing grounds of the gillnet (cross lines) and longline (oblique lines) fish-ing boats based at Shinkang fishfish-ing port.
Taiwan. This information could be used to determine the age composition of the catch and to assess the status of sailfish in these waters by using yield-per-recruit or se-quential population analysis techniques.
Materials and methods
Materials
Data on total length (TL), eye fork length (EFL), lower jaw fork length (LJFL) (in cm), round weight (RW) (in kg) and the first dorsal fins of male and female sailfish were collected monthly at the fishing port of Shinkang (Fig. 1) from July 1998 to August 1999. In total, 304 TLs, 1166 LJFLs, 1166 RWs, and 1166 dorsal fins were collected. The dorsal fins were kept in cold storage before being boiled to remove surrounding tissue and to separate the fourth spines. Three cross sections (thickness 0.75 mm) were taken successively along the length of each spine with a low-speed “ISOMET” saw (model no. 11-1280) and diamond wafering blades, at a location equivalent to 1/2 of the maximum width of the condyle base measured above the line of maximum condyle width (Fig. 2A) (Ehrhardt et al., 1996; Sun et al., 2001, 2002). The sections were
immersed in 95% ethanol for several minutes for cleaning, placed on disposable paper to air dry, and then stored in a labeled plastic case for later reading. Spine sections were examined with a binocular dissecting microscope (model: Leica-MZ6) under transmitted light at zoom magnifica-tions of 10−20× depending on the sizes of the secmagnifica-tions. The most visible one of these three sections was read twice, approximately one month apart. If the two ring counts differed, the section was read again, and if the third ring count differed from the previous two ring counts, the spine was considered unreadable and discarded. The precision of reading was evaluated by using average percent error (APE) (Beamish and Fournier, 1981; Campana, 2001) and coefficient of variation (CV) (Campana, 2001) statistics.
Images of the cross sections were captured by using the Image-Pro Image analysis software package (Media Cy-bernetics, Silver Spring MD, 1997) in combination with a dissecting microscope equipped with a charged coupled de-vice (CCD) camera (model: Toshiba IK-630) and a Pentium II computer equipped with a 640 × 480 pixel frame grab card and a high-resolution (800 × 600 pixel) monitor.
The distance from the center of the spine section to the outer edge of each growth ring was measured in microns with the Image-Pro software package after calibration against an optical micrometer. The center of the spine
Figure 2
Schematic diagram of the fourth dorsal spine of sailfish (I. platypterus) and the location of the cross section (A), and a cross section showing the measurements taken for age determination of sailfish (B). W = maximum width of condyle base, R = radius of spine, ri = radius of ring i, d = diameter of spine, di = diameter of ring i.
The vascularized core and growth rings (1, 2, 3, 4, 5) are also shown.
section was estimated according to the methods of Cayré and Diouf (1983) (Fig. 2B). The distances (di) were then converted into radii (ri) by using the equation (Megalofo-nou, 2000; Sun et al., 2001):
ri = di – (d/2), where ri = radius of the ring i;
di = distance from the outside edge of ring i to the opposite edge of the cross section; and d = diameter of the spine.
False growth rings were defined according to criteria of Berkeley and Houde (1983), Tserpes and Tsimenides (1995), and Ehrhardt et al. (1996).
Accounting for missing early rings
The first several growth rings of the larger specimens may be obscured because of the large size of the vascularized
core of the spine. The number of early but missing growth rings was therefore estimated by the replacement method applied to Pacific blue marlin (Makaira nigricans) by Hill et al. (1989). This method involved first compiling ring radii statistics from younger specimens that had at least the first or second ring visible. Radii of the first four visible rings from samples that had missing early rings were then com-pared with the radii for these younger specimens. When the radii of at least two successive rings of the first four visible rings each fitted well within one standard deviation from the mean radii of each of two or more rings from the data compiled from the younger specimens, the number of missing rings was computed as the difference between the ring counts for the matched radii compiled from younger specimens and those for the specimen of interest.
Validation
The marginal increment ratio (MIR), which was used to validate the rings as annuli, was estimated for each
specimen by using the following equation (Hayashi, 1976, Prince et al., 1988; Sun et al., 2002):
MIR = (R – rn)/(rn – rn–1), where R = spine radius; and
rn and rn–1 = radius of rings n and n−1.
The mean MIR and its standard error were computed for each month by sex for all ages combined, and also for the ages 1−5 and 6−11 for males and 1−5 and 6−12 for females.
Growth estimation
Growth for males and females was estimated by back-cal-culation of lengths at presumed ages. Two methods were used. Method 1 was based on the assumption that the rela-tionship between spine radius (R) and LJFL (L) is linear, i.e., L=a1+b1R (Berkeley and Houde, 1983; Sun et al., 2002), whereas method 2 was based on the assumption that this relationship is a power function, i.e., L=a2Rb2 (Ehrhardt,
1992; Sun et al., 2002). The parameters of the relationships were estimated by maximum likelihood, assuming log-nor-mally distributed errors. Akaike’s information criterion (AIC, Akaike, 1969) was used to select which of the linear and power functions best represented the data:
AIC = –2lnL + 2p,
where lnL = logarithm of likelihood function evaluated at the maximum likelihood estimates for the model parameters, and
p = number of model parameters.
The equations used to back-calculate the lengths at presumed ages were
L a r R L a r R L n n n b = + − 1 1 2 ( ) , linear relationship power relationship
where Ln = LJFL when ring n was formed; L = LJFL at time of capture; and rn = radius of ring n.
The standard von Bertalanffy growth function (stan-dard VB) (von Bertalanffy, 1938) and the Richards func-tion (Richards, 1959) were then fitted to the mean back-calculated male and female lengths-at-age from methods 1 and 2, assuming additive error.
Standard VB: Lt=L∞
(
1−e−k t t(−0))
, Richards function: Lt L e K m t t m = ∞(
1− − 1− −0)
− 1 1 ( )( )( ) ,where Lt = the mean LJFL at age t; L∞ = the asymptotic length;
t0 = the hypothetical age at length zero; k and K = the growth coefficients; and
m = the fourth growth-equation parameter. An analysis of residual sum of squares (ARSS) was used to test whether the growth curves for the two sexes were dif-ferent (Chen et al., 1992; Tserpes and Tsimenides, 1995; Sun et al., 2001), and the log-likelihood ratio test was used to determine whether the Richards function provided a statistically superior fit to the data than the length-at-age standard VB growth function.
Results
Of the 1166 dorsal spines sampled, 1135 (97%) (699 males and 436 females) were read successfully. The average per-cent error (APE) was 6.31% (5.91% for males and 6.93% for females) and the coefficient of variation (CV) was 8.93% (8.36% for males and 9.81% for females). Of the 31 spines that could not be read, 22 were considered unreadable because the existence of multiple rings made the identifi-cation of annuli difficult or resulted in aging discrepancies between readings, and the remaining nine spines were unreadable because of abnormal growth.
The length-frequency and weight-frequency distribu-tions for the 1166 individuals are shown in Figure 3. These individuals ranged from 78 to 221 cm LJFL (mean=177.62, SD =16.13, n=720) or 1 to 49 kg RW (mean=22.13, SD=5.68) for the males and from 80 to 232 cm LJFL (mean=179.96, SD=17.90, n=446) or 2 to 58 kg RW (mean=23.65, SD=7.34) for the females. The females were significantly larger than the males (t-test, P<0.05). Table 1 summarizes the relationships between EFL and LJFL and TL, and that between LJFL and weight. The latter relationship differed significantly between males and females (analysis of covariance; P<0.05).
At least the first or second ring in 417 (60%) of male spines and 300 (69%) of female spines was visible. The ring radii statistics by sex is summarized in Figure 4. All other specimens were assigned inner rings and final age estimates based upon these data. The mean ring radii by age group, for males and females, after correction for miss-ing early rmiss-ings, are listed in Table 2. The maximum age of the sampled sailfish, after correction for missing early rings, was 11 years for males and 12 years for females. The maximum ages before correction were 8 years for both sexes.
The monthly means of the marginal increment ratio (MIR) for males of all ages during May−August were high (~0.72) but declined markedly thereafter and reached a minimum of 0.46 in November (Fig. 5). Similarly, the MIR for females dropped from 0.71 in September to a minimum of 0.47 in November (Fig. 6). The monthly means of MIR did not differ significantly from each other over the period December−March (ANOVA, P0=0.86, PR=0.96). However, the monthly means of MIR from April through August for males and from April through September for females were
Figure 3
The size-frequency distributions by 5-cm intervals (upper figure) and by 2-kg intervals (lower figure) for male and female sailfish (I. platypterus) collected from the waters off eastern Taiwan.
0 20 40 60 80 100 75 85 95 105 115 125 135 145 155 165 175 185 195 205 215 225 235 0 30 60 90 120 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 Male Female Frequency
Lower jaw fork length (cm)
Round weight (kg) (n =720)
(n =446)
significantly higher than those from September through November for males (t-test, P<0.001) and from October through November for females (t-test, P<0.001). Also, the mean MIR in November was significantly lower than that in December (t-tests, P0<0.05, PR<0.05). The trends in the monthly means of MIR when the data were split into ages 1−5 and 6+ were similar to those for all ages combined. The results in Figures 5 and 6 indicate that one growth ring is formed each year, most likely from September to November for males and from October to November for females.
Figure 7 shows the sex-specific relationships between LJFL and spine radius based on method 1 (linear regres-sion) and method 2 (power function). The relationships for males and females are significantly different (method 1:
F698, 435=56.07, P<0.01; method 2: F698, 435=59.93, P<0.01).
According to AIC, the power function provides a better fit to the data (ΔAIC=38.57 and 30.96 for males and females,
respectively). Therefore, the most parsimonious repre-sentation of the data is the power function with separate parameters for males and females.
The mean back-calculated lengths-at-age obtained from methods 1 and 2 are listed in Table 3. After the first year of life, the growth rates of both sexes slow appreciably. However, females still grow faster and consequently reach larger sizes than males. The standard VB and the Rich-ards function for males and females are shown in Figure 8 and the corresponding parameter estimates are listed in Table 4. The growth curves for males differ significantly from those for females (F=99.86 P<0.05 and F=107.38 P<0.05 for the standard VB curve [methods 1 and 2], and F=144.01 P<0.05 and F=48.43 P<0.05 for the Richards function [methods 1 and 2]). The Richards function pro-vides a statistically superior fit to the data (log-likelihood ratio test; P<0.001) when method 2 is used to back-calcu-late length-at-age but not when method 1 is used.
Table 1
Linear relationships (Y=a+bX) among total length (TL, cm), lower jaw fork length (LJFL, cm) and eye fork length (EFL, cm), and the log-linear length-weight (round weight, RW, kg) relationships for sailfish in the waters off eastern Taiwan. Values in parentheses are standard errors.
Y X a b n LJFL range (cm) RW range (kg) r2 Male TL LJFL 19.660 1.205 184 78–211 0.854 (6.334) (0.037) TL EFL 24.782 1.364 184 78–211 0.854 (6.176) (0.042) EFL LJFL –5.196 0.893 720 78–221 0.983 (0.772) (0.004) log10RW log10LJFL –5.381 2.985 720 78–221 1–46 0.906 (0.080) (0.036) Female TL LJFL 6.728 1.286 120 109–210 0.824 (9.351) (0.055) TL EFL 6.754 1.489 120 109–210 0.820 (9.505) (0.064) EFL LJFL –2.209 0.876 446 80–232 0.989 (0.802) (0.004 log10RW log10LJFL –5.338 2.970 446 80–232 2–58 0.905 (0.103) (0.046)
Discussion
Age estimate determined from dorsal-fin spines
Dorsal-fin spines appear to be useful for aging sailfish. They are easily sampled without reducing the economic value of the fish and can also be read easily (the growth rings stand out clearly). In contrast, scales cannot be used to age sailfish because scale deposition patterns change as sailfish age (Nakumura, 1985), and otoliths are extremely small and fragile and are often difficult to locate (Radtke, 1983). Reading otoliths is more time consuming and expensive than reading spines and spines can also be easily stored for future re-examination (Compeán-Jimenez and Bard, 1983; Sun et al., 2001, 2002).
The problems associated with the fin-spine aging meth-od used in this study were the possible existence of false rings and the presence of the vascularized core which can obscure early growth rings in larger fish. These problems were also noted by Berkeley and Houde (1983), Hedge-peth and Jolley (1983), Tserpes and Tsimenides (1995), Megalofonou (2000), and Sun et al. (2001, 2002). However, Tserpes and Tsimenides (1995) and Megalofonou (2000) noted that experienced readers can overcome the problem of multiple rings by determining whether the rings are continuous around the circumference of the entire spine section and by judging their distance from the preceding and following rings. We observed false rings in spines for all age classes larger than age two, which we read with-out problem by using these guidelines. The missing early
growth rings in larger specimens were accounted for by compiling ring radii statistics for younger specimens for which at least the first or second ring was visible and by comparing the radii of the first several visible rings of the specimens that had missing early rings to the mean radii and standard deviations of the compiled data. Similar ap-proaches for solving the problem of missing rings have also been used for Pacific blue marlin (Hill et al., 1989).
Marginal increment ratio (MIR) analysis is the most commonly applied method for age validation (Campana, 2001). The MIR analysis conducted for sailfish suggested that one growth ring is formed each year from September to November for males and from October to November for females. Spawning for sailfish in the waters east of Taiwan lasts from April through September (Chiang and Sun2). This is exactly the period when growth is low, as indicated by the narrow and translucent rings. Similar findings have been reported for skipjack tuna (Antoine et al., 1983), swordfish (Ehrhardt, 1992; Tserpes and Tsimenides, 1995), and bigeye tuna (Sun et al., 2001). Although the timing of annulus formation coincides with spawning sea-son for sailfish in the eastern Taiwan, annulus deposition
2 Chiang, W. C., and C. L. Sun. 2000. Sexual maturity and sex ratio of sailfish (Istiophorus platypterus) in the eastern Taiwan waters. Abstracts of contributions presented at the 2000 annual meeting of the Fisheries Society of Taiwan, Keelung, Taiwan, 16−17 December 2000, 15 p. The Fisheries Society of Taiwan, 199 Hou-Ih Road, Keelung, 202 Taiwan.
Figure 4
Mean (±1 SD) ring radius for male and female sailfish (I. platypterus) collected from the waters off eastern Taiwan that had at least the first or second ring present. The numbers above the vertical bars are the sample sizes.
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4. 5.0 1 2 3 4 5 6 7 8 9 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 1 2 3 4 5 6 7 8 9 175 417 413 395 327 175 42 93 300 299 282 245 113 39 5 2 R in g ra di us ( m m ) Ring number Male Female
may also be related to sailfish migration and environmen-tal factors, as suggested by Sun et al. (2002) for swordfish. The MIR analysis provides only a partial age validation; complete validation requires either mark-recapture data or the study of known-age fish (Beamish and McFarlane, 1983; Prince et al., 1995; Tserpes and Tsimenides, 1995; Sun et al., 2001, 2002).
Selection of a growth curve
Female sailfish are typically larger for similar ages in males and grow faster than males, and the length-weight relationship differs significantly between the sexes. Similar results have been reported for east Pacific Ocean
sailfish (Hernández-Herrera and Ramírez-Rodríguez, 1998), Indian Ocean sailfish (Williams, 1970) and Atlantic Ocean sailfish (Beardsley et al., 1975; Jolley, 1974, 1977; Hedgepeth and Jolley, 1983).
The Richards function appears to fit the data better than the standard VB curve (Fig. 8) and provides a more realistic description of growth for animals of age 0. The standard VB curve is commonly used to describe asymp-totic growth in fish but did not fit the back-calculated lengths for fish younger than three (Table 4, Fig. 8).
Further discussion of growth curves will likely focus on method 2 (i.e., a power function relationship between spine radius and LJFL) because it provides a better fit to the data than method 1. Ehrhardt (1992), Ehrhardt et al.
Ta bl e 2 M ea n ra di u s of ea ch ri n g fo r m al e an d fe m al e sa il fi sh in th e w at er s of f ea st er n T ai w an . R om an nu m er al s in di ca te th e nu m be r of ri n gs . N u m be rs in pa re nt h es es ar e th e nu m be r o f s pe ci m en s fo r w h ic h t h e s pe ci fi ed r in g w as r ea da bl e. “ — ”m ea n s n o d at a o w in g t o v as cu la ri za ti on a t c or e a re a. M ea n r ad iu s ( m m ) o f e ac h r in g A ge S am pl e cl as s si ze I II II I IV V V I V II V II I IX X X I X II M al e 1 1 1. 54 ( 1) 2 4 1. 53 ( 4) 2. 08 ( 4) 3 18 1. 45 ( 12 ) 2. 02 ( 18 ) 2. 51 ( 18 ) 4 68 1. 49 ( 45 ) 2. 02 ( 68 ) 2. 48 ( 68 ) 2. 91 ( 68 ) 5 17 1 1. 48 ( 62 ) 2. 00 ( 15 2) 2. 40 ( 17 1) 2. 79 ( 17 1) 3. 14 ( 17 1) 6 19 8 1. 46 ( 41 ) 2. 02 ( 13 3) 2. 44 ( 18 8) 2. 83 ( 19 8) 3. 17 ( 19 8) 3. 49 ( 19 8) 7 13 0 1. 42 ( 10 ) 1. 96 ( 38 ) 2. 42 ( 94 ) 2. 80 ( 12 3) 3. 18 ( 12 8) 3. 50 ( 13 0) 3. 82 ( 13 0) 8 74 1. 44 ( 1) 1. 96 ( 4) 2. 44 ( 36 ) 2. 79 ( 62 ) 3. 14 ( 72 ) 3. 48 ( 74 ) 3. 81 ( 74 ) 4. 09 ( 74 ) 9 22 — — — 2. 69 (1 1) 3. 02 ( 16 ) 3. 37 ( 22 ) 3. 70 ( 22 ) 4. 02 ( 22 ) 4. 29 ( 22 ) 10 9 — — — — — 3. 09 ( 5) 3. 55 ( 8) 3. 39 ( 8) 4. 23 ( 9) 4. 48 ( 9) 11 3 — — — — — 2. 90 ( 2) 3. 28 ( 2) 3. 74 ( 3) 4. 04 ( 3) 4. 33 ( 3) 4. 50 ( 3) M ea n 1. 47 2. 00 2. 43 2. 81 3. 16 3. 48 3. 79 4. 05 4. 25 4. 45 4. 50 S D 0. 07 0. 14 0. 16 0. 18 0. 20 0. 22 0. 23 0. 23 0. 21 0. 15 0. 15 G ro w th i n cr ea se 0. 53 0. 43 0. 38 0. 34 0. 32 0. 31 0. 26 0. 20 0. 20 0. 05 F em al e 1 1 1. 51 ( 1) 2 1 1. 58 ( 1) 2. 23 ( 1) 3 17 1. 44 ( 15 ) 2. 00 ( 17 ) 2. 47 ( 17 ) 4 38 1. 48 ( 17 ) 2. 00 ( 37 ) 2. 39 ( 38 ) 2. 80 ( 38 ) 5 14 6 1. 49 ( 46 ) 1. 98 ( 13 2) 2. 39 ( 14 6) 2. 80 ( 14 6) 3. 12 ( 14 6) 6 10 7 1. 52 ( 11 ) 2. 05 ( 74 ) 2. 45 ( 10 2) 2. 84 ( 10 7) 3. 17 ( 10 7) 3. 48 ( 10 7) 7 64 1. 52 ( 2) 2. 08 ( 34 ) 2. 55 ( 59 ) 2. 95 ( 64 ) 3. 29 ( 64 ) 3. 60 ( 64 ) 3. 89 ( 64 ) 8 35 1. 53 ( 1) 2. 02 ( 4) 2. 40 ( 10 ) 2. 76 ( 29 ) 3. 17 ( 33 ) 3. 53 ( 34 ) 3. 86 ( 35 ) 4. 16 ( 35 ) 9 17 — 1. 91 ( 1) 2. 36 ( 4) 2. 79 ( 10 ) 3. 07 ( 16 ) 3. 40 ( 17 ) 3. 76 ( 17 ) 4. 07 ( 17 ) 4. 38 ( 17 ) 10 7 — — — — 2. 81 ( 4) 3. 10 ( 7) 3. 46 ( 7) 3. 84 ( 7) 4. 23 ( 7) 4. 55 ( 7) 11 1 — — — — — 3. 31 ( 1) 3. 82 ( 1) 4. 25 ( 1) 4. 44 ( 1) 4. 74 ( 1) 4. 95 ( 1) 12 1 — — — — — — 3. 88 ( 1) 4. 12 ( 1) 4. 49 ( 1) 4. 81 ( 1) 5. 14 ( 1) 5. 32 ( 1) M ea n 1. 49 2. 01 2. 44 2. 83 3. 16 3. 50 3. 84 4. 10 4. 35 4. 60 5. 04 5. 32 S D 0. 06 0. 17 0. 25 0. 23 0. 24 0. 27 0. 27 0. 29 0. 32 0. 41 0. 13 G ro w th i n cr ea se 0. 52 0. 43 0. 39 0. 33 0. 34 0. 34 0. 26 0. 25 0. 25 0. 44 0. 28
Figure 5
Monthly means of marginal increment ratio for male sailfish (I. platy-pterus) in the waters off eastern Taiwan for all ages combined and for age classes 1−5 and 6−11, respectively. Vertical bars are ±1 SE; numbers above the vertical bars are sample sizes.
0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.3 0.4 0.5 0.6 0.7 0.8 0.9 J F M A M J J A S O N D 1 4 5 17 28 67 150 85 38 26 10 5 0.3 0.4 0.5 0.6 0.7 0.8 0.9 5 4 7 1 15 50 81 73 10 6 7 3 6 8 12 18 43 117 231 158 48 32 17 8 M ar gi na l i nc re m en t r at io
Male All ages combined
Ages 1– 5
Ages 6 –11
Month
Table 3
Mean back-calculated lower jaw fork lengths at age for sailfish in the waters off eastern Taiwan. Back-calculated length (cm)
Method 1 Method 2 Method 1 Method 2
Age (yr) Male Female Male Female Age (yr) Male Female Male Female
1 108.53 113.41 99.90 103.51 7 181.11 185.36 181.86 186.09 2 125.70 130.79 121.79 126.32 8 188.99 192.82 189.84 193.67 3 138.82 143.90 137.27 141.96 9 194.98 200.60 196.59 201.47 4 150.80 156.02 150.56 155.54 10 200.78 207.85 201.74 208.81 5 161.78 166.22 162.12 166.38 11 208.05 213.29 209.14 214.66 6 171.63 176.60 172.18 177.12 12 217.15 219.05
Figure 6
Monthly means of marginal increment ratio for the female sailfish (I. platypterus) in the waters off eastern Taiwan for all ages combined and for age classes 1−5 and 6−12, respectively. Vertical bars are ±1 SE; num-bers above the vertical bars are sample sizes.
0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 J F M A M J J A S O N D 1 1 1 14 38 37 54 48 15 15 3 4 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1 1 6 14 56 62 40 10 4 7 2 2 2 2 20 52 93 116 88 25 19 10 m
Marginal increment ratio
Month
Female All ages combined
Ages 1–5
Ages 6–12
(1996), and Sun et al. (2002) favored method 2 because they believed it to be more biologically realistic. When the back-calculated lengths-at-age are generated with this method the Richards function provides a statistically superior fit to the length-at-age data. Therefore, the pa-rameter estimates for the Richards function with method 2 listed in Table 4 are recommended as the most appropriate for calculating the age composition of sailfish in the waters to the east of Taiwan. It is perhaps worth noting that the t0 values estimated for the Richards function with method 2 are much closer to zero than those estimated for the Richards function with method 1.
Comparison with previous studies
Figure 9 compares the age-length relationships of this paper with those for Atlantic (de Sylva, 1957; Hedgepeth
and Jolley, 1983; Farber1) and Pacific sailfish (Koto and Kodama, 1962; Alvarado-Castillo and Félix-Uraga, 1998). De Sylva (1957) and Koto and Kodama (1962) used length-frequency analysis and concluded that sailfish are a very fast growing and short-lived species. However, they likely underestimated age and overestimated growth rate when their results are compared with those of other more recent studies.
The maximum ages found in this study (11 years for males and 12 years for females) are close to the maximum longevity of at least 13 years proposed by Prince et al. (1986) based on tagging data. Farber1 analyzed Atlantic billfish tagging data and suggested that the asymptotic size was essentially reached by age 3 (Hedgepeth and Jol-ley, 1983), whereas the present study found a more gradual increase in length with age, in common with the results of Hedgepeth and Jolley (1983).
Table 4
Parameter estimates and standard errors (in parenthesis) for the standard von Bertalanffy growth function and the Richards function for sailfish in the waters off eastern Taiwan.
Standard von Bertalanffy growth function Richards function
Method 1 Method 2 Method 1 Method 2
Parameter Male Female Male Female Male Female Male Female
L∞ 252.6 261.4 240.4 250.3 271.8 280.4 294.0 343.8 (3.652) (3.397) (3.794) (4.278) (22.713) (19.882) (29.607) (47.921) k 0.115 0.110 0.145 0.138 (0.005) (0.004) (0.008) (0.008) t0 –3.916 –4.207 –2.781 –2.990 –2.473 –2.608 –0.704 –0.468 (0.143) (0.147) (0.154) (0.186) (0.931) (0.896) (0.279) (0.186) K 0.051 0.049 0.023 0.011 (0.034) (0.030) (0.013) (0.007) m –0.551 –0.578 –1.288 –1.639 (0.472) (0.436) (0.308) (0.243) 0 50 100 150 200 250 n = 699 LJFL = 64.825 + 30.471 R r2 = 0.704 LJFL = 79.833 R0.612 r2 = 0.720 0 50 100 150 200 250 0 1 2 3 4 5 n = 436 LJFL = 70.312 + 30.093 R r2 = 0.731 LJFL = 83.461 R0.596 r2 = 0.750 6
Lower jaw fork length
(LJFL , cm) Spine radius (R, mm) Male Female Figure 7
Relationship between lower jaw fork length and spine radius for male and female sailfish (I. platypterus) in the waters off eastern Taiwan.
Even though the aging method used in the present study is the same as that of Hedgepeth and Jolley (1983) and Alvarado-Castillo and Félix-Uraga (1998), there are nev-ertheless differences in the estimated length-at-age. This difference could be due to spatial differences in growth, the range of ages and sizes used in the analysis, or the form of the growth model applied. The size range in the present study is broader than those in previous studies and the growth curve is based on the Richards function rather than the standard VB function. Therefore, we believe that our growth parameter estimates are more appropriate for
Figure 8
Observed and back-calculated length-at-age and standard von Bertalanffy and Richards function model-predicted growth curves for male and female sailfish (I. platypterus) in the waters off eastern Taiwan.
0 50 100 150 200 250 -5 -4 -3 -2 -1 10 11 12 Standard VB - method 1 Standard VB - method 2 Richards function - method 1 Richards function - method 2 0 50 100 150 200 250 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 Standard VB - method 1 Standard VB - method 2 Richards function - method 1 Richards function - method 2
Lo w er ja w fo rk le ng th ( cm ) Male Female Age (year) 0 1 2 3 4 5 6 7 8 9
use in stock assessments of the sailfish popu-lation in the western Pacific Ocean.
Acknowledgments
The authors express sincere gratitude to André Punt, School of Aquatic and Fishery Sciences, University of Washington, for his valuable comments and comprehensive edit-ing of the manuscript. This study was in part supported financially by the “Fisheries Agency, Council of Agriculture, Taiwan,” through grant 91AS-2.5.1-F1(7) to Chi-Lu Sun.
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