Analysis of sex-specific spawning biomass per recruit of the sailfish (Istiophorus platypterus) in the waters off eastern Taiwan.
Sailfish (Istiophorus platypterus) is a circumtropically distributed species (Hoolihan, 2005). Sailfish is a member of the billfish family, Istiophoridae, which also includes marlins and spearfishes, and is considered a bycatch species in commercial fisheries. Off the eastern coast of Taiwan, sailfish are economically important and seasonally abundant from April to October (abundance peaks from May to July). Sailfish are mainly caught by drift gill nets, although some are also caught by set nets, harpoons, and as incidental bycatch in inshore long-line fisheries (Chiang, 2004). There are virtually no discards of sailfish in Taiwan. For the past decade, the annual landings of sailfish off Taiwan waters have fluctuated between 500 and 1000 metric tons, of which over 50% have come from waters off Taitung (eastern Taiwan).
Globally, large predatory fish species, including billfish, are declining at alarming rates because of excessive exploitation (Myers and Worm, 2003). Recent increases in the exploitation of billfish stocks by both commercial and recreational fisheries clearly point to the need for accurate assessments, if the goal is to develop sustainable billfish fisheries (Uozumi, 2003). However, because few fisheries target sailfish, assessments have not been conducted, resulting in few or no effective management measures. For sailfish in the Pacific Ocean and Indian Ocean, no assessments have been conducted, and stock status remains unknown. Historical sailfish catch data from the Pacific Ocean are scant, as are data on the length and age composition of the catch. This lack of data precludes the use of most stock assessment tools such as production models and age-structured models (Punt, 1997; Prager and Goodyear, 2001; Liu et al., 2006). However, recent biological studies on sailfish in the waters off eastern Taiwan (Chiang et al., 2004, 2006) have provided an opportunity to apply yield per recruit (Y/R) and spawning biomass per recruit (SSB/R) models (Govender, 1995; Griffiths, 1997) to estimate biological reference points including the fishing mortality rate corresponding to the point where the slope of the yield-per-recruit curve equals 10% of the slope at the origin ([F.sub.0.1]; Gulland and Boerema, 1973) and the fishing mortality rate corresponding to a specific percentage (x%) of the spawning biomass per recruit at the unfished level ([F.sub.SSBx]) for the eastern Taiwan sailfish stock. The status of the fishery for this stock could be examined by comparing the fishing mortality at the current level ([F.sub.CUR]) with the biological reference points.
A per-recruit analysis requires information on growth, mortalities, and selectivity of fishing gear. Ca analysis (Ricker, 1975) is the most common method employed for estimating total mortality when data on the age composition of catch are available. For a specified natural mortality, [F.sub.CUR] could be computed simply by subtracting the natural mortality from the total mortality. However, in most cases large uncertainty is associated with the estimation of natural mortality and other life history parameters, which can lead to large uncertainty in the estimation of [F.sub.CUR] and biological reference points.
The objective of this study was to evaluate the current status of the sailfish fishery in waters off eastern Taiwan by comparing the current fishing mortality rate (estimated from analyzing length composition data collected from the fishery) with the biological reference points derived from the per-recruit analyses (Butter-worth et al., 1989; Sun et al., 2002, 2005). In addition, a Monte Carlo simulation study was conducted for evaluating the influence of uncertainty associated with mortalities and the age at first catch ([t.sub.c]) on the estimation of biological reference points. This study provides an approach that can be used to assess the status of fisheries for which limited information does not allow us to conduct a full stock assessment.
Materials and methods
Length and age composition of the catch
Length composition data were obtained by measuring sailfish landed at the Shinkang fish market in eastern Taiwan (Fig. 1) during the period from July 1998 to July 2005. Specimens were randomly selected from the landings and measured for their lengths and weights. The sex of each specimen was identified from the appearance of its gonads. Samples of the first dorsal fin were taken from 1166 of the sampled individuals for which lengths were measured and used to age the sailfish (Chiang et al. 2004). These subsampled fish were used to construct sex-specific age-length keys, which in turn were used to convert the length-frequency data into age-composition data.
Estimating mortality rates
For each sex, the dynamics of a simulated year class can be projected forward from one year to another by using the exponential survival equation (Ricker, 1975):
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)
where [N.sub.t] = the number of fish at the beginning of age t;
M = the instantaneous natural mortality rate;
F = t the fishing mortality of fully-recruited fish; and
[S.sub.t] = the fishing gear selectivity of fish at age t.
[FIGURE 1 OMITTED]
Selectivity is the relative vulnerability of different age or size classes to the fishing gear. In this study, we assumed that the selectivity follows a dome-shaped distribution because our length-frequency data were mostly collected from gill nets. This dome-shaped selectivity can be quantified with the following normal distribution density function:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)
where [mu] = the age at the mode of the dome-shaped selectivity; and
[sigma] = the standard deviation of the dome-shaped selectivity.
The expected catch ([[??].sub.t]) offish at age t can be estimated based on the catch equation (Ricker, 1975):
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (3)
The parameters of [N.sub.0], F, [mu], and [sigma] can be estimated simultaneously by minimizing the following composite objective function:
[summation over t] [([C.sub.t] - [[??].sub.t]).sup.2] + [(max([S.sub.t]) - 1).sup.2], (4)
where [C.sub.t] = the observed numbers of catch at age t.
The F estimated above was considered as the current fishing mortality ([F.sub.CUR]) in this study. The approach outlined above for the catch-curve analysis is similar to the one described in Rudershausen et al. (2008).
A total of 1000 independent bootstrap samples of F were derived from 1000 sets of length-frequency data drawn randomly with replacement from the individuals of original length-frequency data.
Pauly's (1980) empirical equation was used to estimate M for each sex, and the mean sea surface temperature around eastern Taiwan waters fitted to the equation was about 26[degrees]C.
Yield per recruit (Y/R) of sailfish in the waters off eastern Taiwan was estimated from the following model:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (5)
where [bar.W.sub.t] = the mean weight of fish at age t; and [t.sub.c] = the age at first capture.
Mean weight at age was computed as a power function of midyear lower jaw fork length ([L.sub.t]):
[W.sub.t] = a x [L.sup.b.sub.t], (6)
and midyear lower jaw fork length was estimated from the von Bertalanffy growth function
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (7)
where K = the growth parameter;
[L.sub.[infinity] = the average asymptotic length; and
[t.sub.[infinity]] = hypothetic age at length of 0 (Ricker, 1975; see Table 1).
The maximum lifespan ([t.sub.max]) of sailfish in the waters off eastern Taiwan was unknown but was estimated by using the empirical relationship of Taylor (1958):
[t.sub.max] = [t.sub.0] + [2.996/K], (8)
The equation for spawning stock biomass per recruit (SSB/R) is
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (9)
where [W.sub.t] = the mean weight at age t that was calculated from the von Bertalanffy function and length-weight relationship for female sailfish; and
fr = the fraction of female sailfish that are mature.
In this case fr is represented by a logistic equation fitted to maturity data collected from sailfish caught in the eastern waters off Taiwan (Chiang et al., 2004, 2006). The logistic equation can be written as
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (10)
where [r.sub.m] = the slope of the logistic curve; and [t.sub.m] = age at which 50% of fish are mature.
Biological reference points
The following biological reference points were estimated in order to determine the current status of the sailfish fishery: [F.sub.0.1], [F.sub.SSB25], and [F.sub.SSB40] x [F.sub.SSB25], and [F.sub.SSB40] are fishing mortality rates corresponding to the 25% and 40% of the spawning biomass per recruit at unfished level. The choice of 25% or 40% was relatively arbitrary for the fishery, but these values have been used as different levels of reference points for other relatively long-lived marine fishes (e.g., Griffiths, 1997; Kirchner, 2001; Sun et al., 2002, 2005). The spawning potential ratio (SPR) is the SSB/R at a given fishing mortality divided by the SSB/R without fishing (Gabriel et al., 1989; Goodyear, 1993; Katsukawa et al., 1999; Watanabe et al., 2000; Sun et al., 2002, 2005) and can be calculated as
SPR = [SSB/R/[SSB/R|.sub.F=0]]. (11)
Several authors have advocated designating [F.sub.0.1] or [F.sub.SSB40] as target reference points and [F.sub.SSB25] as a threshold reference point in order to obtain near optimal yields while minimizing the likelihood of stock collapse (Gulland and Boerema, 1973; Deriso, 1987; Hilden, 1993; Sun et al., 2002, 2005). We adopted these target and threshold reference points in this study.
The Monte Carlo simulation approach was applied to evaluate the sensitivity of estimating biological reference points with respect to parameters F, M, and [t.sub.c]. To quantify the uncertainty of F, F was assumed to follow a normal distribution with a mean and standard deviation ([[sigma].sub.F])--the latter estimated from the bootstrapped estimation of F. However, there was no information on the distribution of M and [t.sub.c]. We assumed a uniform distribution for M and [t.sub.c] by referring to the estimation of Pauly's empirical equation and the age at full recruitment from the age composition of sailfish in the waters off eastern Taiwan. The values of M and [t.sub.c] were sampled randomly from the corresponding uniform distributions defined in Table 2. Ten scenarios were designed to examine the effects of different combinations of the uncertain in parameters F, M, and [t.sub.c] on the estimation of biological reference points (Table 2). Scenarios A-D were used to evaluate the effects of changes in a single parameter, scenarios E-H were used to evaluate the results of changes in combinations of two parameters, and scenarios I and J were used to evaluate the results when three parameters were subject to uncertainty. For each scenario, 100 replicates of biological reference points were estimated by using the parameters of F, M, or [t.sub.c] randomly drawn from their assumed distributions. The median and the interquartile range were used to quantify the central tendency and variation for the distributions of estimated biological reference points.
Length data were obtained for 12,323 sailfish (3532 females and 8791 males), and age data for 1166 of these fish (446 females and 720 males). The range of lower jaw fork length was 80-239 cm for females and 78-227 cm for males (Fig. 2). Age compositions of samples collected during the entire study period indicated that most sailfish caught off eastern Taiwan are larger than the age at 50% maturity, and peak in length at 5 years (Fig. 3). Accordingly, the estimates of age at full recruitment ([t.sub.c]) and the sample size during studying periods are shown in Table 3. The estimates of [t.sub.c] varied from 5 to 7 years for different time periods. Few sampled fishes were older than 11 years for both sexes and hence age 12 and higher were combined into the 12+ group (Fig. 3). The empirical estimates of maximum lifespan ([t.sub.max]) were 13 years for males and 21 years for females.
[FIGURE 2 OMITTED]
[FIGURE 3 OMITTED]
The estimates of F were 0.24/yr for females and 0.43/yr for males based on the samples collected during the entire study period. Based on bootstrap analysis, the standard deviation of F was 0.046/yr and 0.045/yr for females and males, respectively. In addition, 79% of bootstrap replicates of [t.sub.c]. were 5 years old and few were 6 or 7 years old. The values of M estimated from the Pauly's empirical equation were 0.26/yr for females and 0.27/yr for males. In this study, therefore, F of 0.24/yr for females and 0.43/yr for males, [t.sub.c] of 5 years and M of 0.26/yr for females and 0.27/yr for males were set as the base case values for the subsequent analyses. Sensitivity analyses were also conducted for examining the results of Y/R and SPR analyses by assuming values of 0.20, 0.30, and 0.35 for M.
Y/R and SPR models and biological reference points
In this study, selectivities for females and males were assumed to be dome-shaped, and the estimated selectivity curves are shown in Figure 4. The estimates of [F.sub.CUR], [F.sub.0.1], and Y/R under various values of M are summarized in Table 4. For the base case, [F.sub.CUR] (0.24/yr for females and 0.43/yr for males) were substantially lower than the corresponding biological reference points [F.sub.0.1] (0.62/yr for females and 0.79/yr for males). The estimates of Y/[R.sub.CUR] were 3.37 kg for females and 3.72 kg for males and the estimates of Y/[R.sub.0.1] were 5.11 kg for females and 4.68 kg for males (Fig. 5). Even in the most conservative case, when M was assumed to be 0.2, [F.sub.CUR] was still lower than [F.sub.0.1] for both females and males.
The effect of varying [t.sub.c] on Y/R is shown in Figures 6 and 7. At low levels of F, Y/R generally increased rapidly over the range of [t.sub.c] values tested. The values of [t.sub.c] that maximized the yield per recruit decreased with the magnitude of M and increased with the level of F but typically ranged between 2 and 5 years for females and males.
The rapid growth and relatively late [t.sub.c] (5 years) of sailfish in the waters off eastern Taiwan produced low Y/R and high SPR at current fishing mortalities compared with reference points (Figs. 4 and 7). The estimates of [F.sub.SSB25], [F.sub.SSB40], SPR and Y/R under the various values of M are summarized in Table 5 and Figure 8. The base-case estimate of [F.sub.CUR] for females (0.24/ yr) was lower than the corresponding reference points [F.sub.SSB40] (0.46/yr) and [F.sub.SSB25] (0.94/yr); the current SPR was estimated to be about 57.20% of its unfished level. Under the low value of M (0.2/yr), the estimate of [F.sub.CUR] for females (0.26/yr) was lower than [F.sub.SSB40] (0.36/yr) and substantially lower than [F.sub.SSB25] (0.67/yr). Increasing [t.sub.c] to older than six years of age would ensure that the SPR was maintained at a value higher than the threshold level (i.e., 25% of its unfished level) at almost any level of fishing mortality (Fig. 9) with relatively little effect on Y/R.
[FIGURE 4 OMITTED]
The box plots of the estimates of [F.sub.0.1] and [F.sub.CUR]/[F.sub.0.1] are shown in Figure 10 for scenarios A-J with the assumption of uncertainty in F, M, and [t.sub.c] defined in Table 2. Although the medians of these two quantities were close to those of the base case for most scenarios, the variations of these quantities were diverse depending on the assumptions of uncertainty of the parameters. For scenarios A-D with only one parameter subject to uncertainty, the estimates of [F.sub.0.1] were independent of the changes in F but were very sensitive to the uncertainty in M. Adding the uncertainty in [t.sub.c]. resulted in slightly higher estimates of [F.sub.0.1] than that for the base case. Higher estimates of [F.sub.0.1] could have resulted from [t.sub.c] with values larger than 5 years (base case) selected in this scenario. In the case of this study, higher [t.sub.c] produced higher estimates of [F.sub.0.1] for sailfish in the water of eastern Taiwan. For scenarios E-J that incorporated the combinations of uncertainties in F, M, and [t.sub.c], large variations were observed for estimates of [F.sub.0.1] when a higher level of uncertainty was assumed for M (scenarios F, H, and J). Even though combinations of parameters with higher uncertainties were considered, the upper bounds (the third quartile) of [F.sub.CUR]/[F.sub.0.1] were lower than 1 for all scenarios. This result implied that it was highly unlike that [F.sub.CUR] could exceed [F.sub.0.1]. In contrast, the effects of adding uncertainties in F and [t.sub.c] were relatively minor.
[FIGURE 5 OMITTED]
[FIGURE 6 OMITTED]
Figure 11 shows the box plots of the estimates of [F.sub.SSB40], [F.sub.SSB25], [F.sub.CUR]/[F.sub.1SSB40], and [F.sub.CUR]/[F.sub.0.1SSB25] for scenarios A-J (with uncertainty). Similarly, higher levels of uncertainties in M resulted in higher variations for the estimates of [F.sub.SSB40] and [F.sub.SSB25] (scenarios C, F, H, and J). Moreover, the estimates of [F.sub.SSB40] and [F.sub.SSB25] were obviously higher than those of the base case when the uncertainty in [t.sub.c] was considered (scenarios D, G, H, I, and J), which might result from female fish younger than [t.sub.c], being less vulnerable to fishing gear. Therefore, higher values of SSB/R would be obtained when larger values of [t.sub.c] were selected and higher estimates of [F.sub.SSB40] and [F.sub.SSB25] were revealed for these scenarios. For all scenarios, the medians of [F.sub.CUR]/[F.sub.SSB40] and [F.sub.CUR]/[F.sub.SSB25] were 0.71 and 0.37, respectively, which were similar to those of the base case (Table 5). The upper boundaries of [F.sub.CUR]/[F.sub.SSB40] and [F.sub.CUR]/[F.sub.SSB25] were substantially lower than 1 for all the scenarios and no simulation runs were observed to have the values higher than 1.
The Y/R curve is so flat-topped that maximum Y/R cannot be well defined and may not be attained under any practical fishing mortality rate (Fig. 5). Reference points such as [F.sub.0.1], [F.sub.SSB25], and [F.sub.SSB40] have often been used to develop fishery management strategies. Previous studies have indicated that Y/R and SPR are sensitive to values of M (Griffiths, 1997; Kirchner, 2001; Sun et al., 2005). In this study, however, the estimates of [F.sub.CUR] were much lower than the target levels of [F.sub.0.1] or [F.sub.SSB40], except for the scenario when M was assumed at the lower bound of 0.2. Moreover, the estimates of [F.sub.CUR] were never larger than the threshold level of [F.sub.SSB25] even when M was assumed to be 0.2. This result would indicate that the stock of sailfish in the waters off eastern Taiwan appears to be moderately exploited and has relative low risk of being overfishing.
[FIGURE 7 OMITTED]
Sex-specific per-recruit analyses and sensitivity analyses
Most assessment methods require historic information on catch, effort, and catch-at-age (or catch-at-length). The lack of long-term fishery statistics usually makes it difficult to evaluate the status of populations exploited by small-scale fisheries or taken incidentally (e.g., Govender, 1995; Barbieri et al., 1997; Griffiths, 1997; Jones and Wells, 2001; Sun et al., 2002, 2005). Per-recruit analyses, which require only parameters related to life span and mortality, combined with an analysis of catch curves, can become an alternative method for evaluating the status of a fishery. Because per-recruit analyses can provide the estimates of biological reference points and the catch curve analysis can yield the estimate of current fishing mortality rate, the status of a fishery can be readily determined by comparing current fishing mortality with the biological reference points. Nevertheless, few results of previous studies have been discussed as to how the biological reference points based on per-recruit analyses were influenced by the uncertainties of biological parameters.
[FIGURE 8 OMITTED]
[FIGURE 9 OMITTED]
In this study, the effects of F, M, and [t.sub.c] on the estimates of [F.sub.0.1], [F.sub.SSB40], and [F.sub.SSB25] were evaluated by using the Monte Carlo simulation method. Although other parameters (e.g., growth) are essential inputs for per-recruit analyses, we focused on the effects of F, M, and [t.sub.c] which are generally more difficult to estimate owing to a lack of enough auxiliary information (Chen et al., 2007). In addition, the assumption of selectivity of fishing gear could influence the results of per-recruit analyses. Generally, longline selectivity is assumed to be asymptotic and gillnet selectivity is assumed to be dome shaped. In this study, a dome-shaped selectivity was assumed for incorporating into the per-recruit analyses. Sailfish in the waters off eastern Taiwan were exploited by various fishing gears although large proportion of the catch was made by gillnet. However, insufficient length-frequency data recorded by fishing gear lead to difficulty in estimating the selectivity for different fishing gear. Therefore, collecting the information from fishing gear for length-frequency data is necessary to evaluate the influence of different selectivity assumptions on the results of assessment.
Implications of sex-specific assessment and management of the species
Uozumi (2003) indicated that the problems in the stock assessment of sailfish are the inability to obtain reliable biological parameters, standardization of catch per unit of effort, and a mechanism to develop reliable abundance indices. Sailfish are known to be sexually dimorphic (females grow faster and to a larger size than males (Chiang et al., 2004; Hoolihan, 2007), females become mature later than males, and sex ratio varies with length (Chiang, 2004). These attributes indicate that sex-specific assessments should be done to evaluate the status of sailfish. The sex-specific per-recruit analyses with the consideration of parameter uncertainty used in this study provide a method for evaluating management strategies.
[FIGURE 10 OMITTED]
There is a possibility that the low F estimates may be an artifact of an influx of fish from outside the study area. Such a bias could occur if the probability that a fish will move from distant waters to within range of the eastern Taiwanese fleet is substantial and increases with the age of the fish (Sun et al., 2005). In principle, estimates for M could be obtained from research (such as tagging studies to determine M; Hampton, 2000). However, in the short to medium term, the values for M will have to be obtained from the results of studies for other stocks of sailfish. They have been similar to those obtained by Pauly's (1980) method. This difference should be evaluated in relation to environmental factors. Although recent analyses of molecular markers do not support recognition of separate Atlantic and Indo-Pacific species of sailfish (Graves and McDowell, 2003), there is no evidence to indicate that sailfish become increasingly likely to migrate to Taiwan with increasing age. Although Prince et al. (2006) examined the tagging results in the eastern Pacific Ocean, they considered this species a single stock. It is unclear whether the sailfish population in the Pacific Ocean comprises a single or multiple stocks, and their regional or global abundance is unknown (Ehrhardt and Fitchett, 2006). A tagging program in which electronic and conventional tags are used to examine the spatial movement patterns and stock structure of sailfish in this geographical region would prove beneficial for the sustainable management of the species.
There are no management measures for sailfish in the waters off eastern Taiwan at present. In the waters off eastern Taiwan, sailfish are targeted by the gillnet fishery and caught incidentally in the longline, harpoon, and set net fisheries. This makes it difficult to effectively control the fishing effort of these fisheries for sailfish. In this case, the isopleths of SPR indicate that increasing [t.sub.c] to an age between six and seven years old would likely result in modest gains in terms of SPR (on the order of 40%) and also hedge against recruitment overfishing. For example, the target level of 40% SPR could be achieved at even double values of [F.sub.CUR] if [t.sub.c] for female sailfish was larger than five years (the age at sexual maturity). Of course the efficacy of increasing [t.sub.c] would be mitigated by any substantial release mortality. At present little is known about the mortality rates of fish released from gillnet and longline vessels operating off eastern Taiwan, and further study is needed before we can confidently recommend increasing [t.sub.c] as a measure to prevent overfishing.
[FIGURE 11 OMITTED]
In summary, sex-specific per-recruit modeling coupled with Monte Carlo simulation analyses are effective in evaluating the stock status of billfish because of the sexual dimorphism and uncertainty in key life history and fishery parameters of these species. This study reveals that sailfish in the waters off eastern Taiwan appear to be moderately exploited and have relative low risk of being overfished. However, in view of the recent rapid increase in fishing effort, it is evident that the stock status and development of the fishery need to be closely monitored.
We would like to thank two reviewers, Michael H. Prager, NMFS Southeast Fisheries Science Center, and Gerard DiNardo, NMFS Pacific Islands Fisheries Science Center, and one anonymous reviewer for their valuable and constructive comments. We thank Michael Prager for proposing the modified catch-curve method. This study was partially financially supported by the Fisheries Agency, Council of Agriculture, Taiwan, through the grant 93AS-9.1.1-FA-F1(2) to Chi-Lu Sun.
Manuscript submitted 17 July 2008. Manuscript accepted 28 January 2009. Fish. Bull. 107:265-277.
The views and opinions expressed or implied in this article are those of the author and do not necessarily reflect the position of the National Marine Fisheries Service, NOAA.
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Wei-Chuan Chiang (1)
Chi-Lu Sun (contact author) (2)
Sheng-Ping Wang (3)
Su-Zan Yeh (2)
Yong Chen (4)
Wei-Cheng Su (5)
Don-Chung Liu (5)
Wen-Yie Chen (1)
Email address for contact author: firstname.lastname@example.org
(1) Eastern Marine Biology Research Center of Fisheries Research Institute No. 22 Wuchuan Rd. Chenkung, Taitung, Taiwan 961
(2) Institute of Oceanography National Taiwan University No. 1, Sec. 4, Roosevelt Rd. Taipei, Taiwan 106
(3) Department of Environmental Biology and Fisheries Science National Taiwan Ocean University No. 2, Beining Rd. Keelung, Taiwan 202
(4) School of Marine Science University of Maine 218 Libby Hall Orono, Maine 04469
(5) Fisheries Research Institute No. 199, Ho-lh Rd. Keelung, Taiwan 202
Table 1 Biological parameters used in the per-recruit analysis for the sailfish (Istiophorus platypterus) in the waters off eastern Taiwan during the period from July 1998 to July 2005. VBGF is the von Bertalanffy growth function, [L.sub.[infinity]] = the asymptotic length, K =the growth coefficient, [t.sub.0] = the hypothetical age at length zero; Length-weight relationship is W = A x [L.sup.B] , where W = rought weight (in kg) and L = lower jaw fork length (in cm); Maturity fraction parameters [r.sub.m] = the slope of logistic equation fitted to the maturity data collected, and [t.sub.m] = the age at 50% sexual maturity. Parameter Female VBGF [L.sub.[infinity]] 250.29 cm K 0.138/yr [t.sub.0] -2.99 Length-weight relationship A 2.3234 x [10.sup.-6] B 3.1013 Maturity fraction [r.sub.m] 1.525 [t.sub.m] 5 Parameter Male VBGF [L.sub.[infinity]] 240.539 cm K 0.145/yr [t.sub.0] -2.781 Length-weight relationship A 1.1933 x [10.sup.-5] B 2.7828 Maturity fraction [r.sub.m] [t.sub.m] Table 2 Scenarios designed to examine the effects of uncertainty of F, M, and [t.sub.c] on the estimates of biological reference points of sailfish (Istiophorus platypterus) in the waters off eastern Taiwan. Scenarios A-D were used to evaluate the effects of changes in a single parameter, scenarios E-H were used to evaluate the results of changes in combinations of two parameters, and scenarios I and J were used to evaluate the results when three parameters were subject to uncertainty. [[sigma].sub.F] = standard deviation from the boot-strapped estimation; M = natural mortality per year; [t.sub.c] = age at first catch) Parameters [[sigma].sub.F] M Scenario Female Male Female Male [t.sub.c] Base 0 0 0.26 0.27 5 A 0.046 0.045 0.26 0.27 5 B 0 0 0.2-0.3 0.2-0.3 5 C 0 0 0.15-0.35 0.15-0.35 5 D 0 0 0.26 0.27 5-7 E 0.046 0.045 0.2-0.3 0.2-0.3 5 F 0.046 0.045 0.15-0.35 0.15-0.35 5 G 0 0 0.2-0.3 0.2-0.3 5-7 H 0 0 0.15-0.35 0.15-0.35 5-7 I 0.046 0.045 0.2-0.3 0.2-0.3 5-7 J 0.046 0.045 0.15-0.35 0.15-0.35 5-7 Table 3 Sample sizes and estimates of age at full recruitment for female and male sailfish (Istiophorus platypterus) by year in the waters off eastern Taiwan during the period from July 1998 to July 2005. Sample Age at size full recruitment Female 1998 131 6 1999 702 5 2000 387 7 2001 358 6 2002 349 7 2004 484 5 2005 1121 6 Overall 3532 5 Male 1998 525 6 1999 1943 5 2000 578 7 2001 730 5 2002 576 5 2004 1123 5 2005 3316 5 Overall 8791 5 Table 4 Estimates of current fishing mortality ([F.sub.CUR]), current yield per recruit (Y/[R.sub.CUR]), and the reference points of [F.sub.0.1] and Y/[R.sub.0.l] at different levels of natural mortality (M) for female and male sailfish (Istiophorus platypterus) in the waters off eastern Taiwan during the period from July 1998 to July 2005. [F.sub.0.1] = the fishing mortality rate corresponding to Y/[R.sub.0.1]; Y/[R.sub.0.1] = the point of a yield-per-recruit curve where the slope equals 10%n of the slope at the origin. M [F.sub.CUR] [F.sub.0.1] Y/[R.sub.CUR] Y/[R.sub.0.1] (1/yr) (1/yr) (1/yr) (kg) (kg) Female 0.20 0.26 0.54 5.36 7.08 0.26 0.24 0.62 3.37 5.11 0.30 0.22 0.69 2.45 4.13 0.35 0.20 0.80 1.63 3.19 Male 0.20 0.46 0.70 5.79 6.66 0.27 0.43 0.79 3.72 4.68 0.30 0.41 0.83 3.06 4.04 0.35 0.38 0.91 2.21 3.17 Table 5 Estimates of current fishing mortality ([F.sub.CUR]) and the reference points of SSB/[R.sub.SSBx] and SPR at different levels of natural mortality (M) for female sailfish (Istiophorus platypterus) in the waters off eastern Taiwan during the period from July 1998 to July 2005. [F.sub.SSBx] = the fishing mortality rate corresponding to SSB/[R.sub.SSBx]; SSB/[R.sub.SSBx] = a specific percentage (x%) of the spawning biomass per recruit at the unfished level; SPR (spawning potential ratio) = the SSB/R at a given fishing mortality divided by the SSB/R without fishing. M [F.sub.CUR] [F.sub.SSB40] [F.sub.SSB25] (1/yr) (1/yr) (1/yr) (1/yr) 0.20 0.26 0.36 0.67 0.26 0.24 0.46 0.94 0.30 0.22 0.54 1.22 0.35 0.20 0.70 1.73 M SSB/[R.sub.CUR] SSB/[R.sub.SSB40] (1/yr) (kg) (kg) 0.20 32.50 26.56 0.26 22.22 15.53 0.30 17.42 11.14 0.35 12.97 7.52 M SSB/[R.sub.SSB25] [SPR.sub.CUR] (1/yr) (kg) (%) 0.20 16.60 48.96 0.26 9.71 57.20 0.30 6.96 62.57 0.35 4.70 68.95
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|Author:||Chiang, Wei-Chuan; Sun, Chi-Lu; Wang, Sheng-Ping; Yeh, Su-Zan; Chen, Yong; Su, Wei-Cheng; Liu, Don-C|
|Date:||Jul 1, 2009|
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