age 0 age 1 age 2 age 3
age 4 age 5 age 6 age 7
age 8 age 9 age 10 plus
Figure 8. The recruits in number estimated from the present analysis for bluefin tuna in the North Pacific Ocean.
1 2 3 4 5 6 7 8 9 10
1960 1962 1964 1966 1968 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004
Year
Recruitment (millions of fish)
Figure 9. The stock recruit relationship of bluefin tuna in the North Pacific Ocean, Spawner and recruits were estimated from the virtual population analysis.
1 2 3 4 5 6 7 8 9 10
10000 20000 30000 40000 50000
Recruitment (millions of fish)
SSB (mt)
Figure 10. Time series catch per unit effort of Japanese far-seas longline fishery (upper panel) with the expected (red curve), the fitting residual was shown as the lower panel.
Figure 11. Time series catch per unit effort of Japanese purse seine fishery (upper panel) with the expected (red curve), the fitting residual was shown as the lower panel.
Figure 12. Time series catch per unit effort of Japanese troll fishery (upper panel) with the expected (red curve), the fitting residual was shown as the lower panel.
Figure 13. Time series catch per unit effort of Taiwanese small scale longline fishery (upper panel) with the expected (red curve), the fitting residual was shown as the lower panel.
Figure 14. Time series catch per unit effort of purse seine fishery (upper panel) with the expected (red curve) in the eastern Pacific Ocean; the fitting residual was shown as the lower panel.
Appendix I. Abundance indices used in the present study, in which Index 1:
Japanese far-sea fishery; Index 2: Japanese coastal longline fishery; Index 3:
Taiwanese small scale longline fishery; Index 4: Eastern Pacific Ocean purse seine fishery and Index 5: Japanese troll fishery.
year Index 1 Index 2 Index 3 Index 4 Index 5 Index 6
1960 3.11 0.25
1981 0.0012 -2.12 1.89 0.238
1982 0.248 -0.913 0.194
1983 -0.743 -2.12 1.3 -0.896
1984 -1.9 -2.52 -0.576 1.27
1985 -2.3 -0.124 0.0972 0.137
1986 -2.42 1.14 0.426 -0.455
1987 -1.31 -0.576 -0.149 -0.511
1988 -1.78 -1.27 -1.56 0.581
1989 -3.92 -0.171 0.319 -0.47
1990 -2.07 -0.382 -0.624 0.429
1991 -1.27 -1.14 -0.0328 -0.488
1992 -0.899 0.281 -0.189 -0.784
1993 0.869 -0.817 0.987 -0.709
1994 0.315 -1.27 0.49 1.53
1995 0.183 -1.61 -0.0814 0.0257
1996 0.223 0.974 1.19 0.864
1997 0.322 0.219 -0.0539 -0.559
Appendix II -1. Estimated catch at age (0 – 10+) in number of bluefin tuna in the North Pacific Ocean by overall fisheries combined. (Data were adopted from Yamada et al. 2006)
Appendix II-2. Estimated catch at age in number for age 0 – age 10+ of bluefin tuna in the North Pacific Ocean by Japanese purse seine fishery. (Data were adopted from Yamada et al. 2006)
Appendix II-3. Estimated catch at age in number for age 0 – age 10+ of bluefin tuna in the Sea of Japan in summer by Japanese purse seine fishery. (Data were adopted from Yamada et al. 2006)
Appendix II-4. Estimated catch at age in number for age 0 – age 10+ of bluefin tuna in the Sea of Japan in winter by Japanese purse seine fishery. (Data were adopted from Yamada et al. 2006)
Appendix II-5. Estimated catch at age in number for age 0 – age 10+ of bluefin tuna in the North Pacific Ocean by Japanese longline fishery. (Data were adopted from Yamada et al. 2006)
Appendix II-6. Estimated catch at age in number for age 0 – age 10+ of bluefin tuna in the North Pacific Ocean by Japanese pole and line fishery. (Data were adopted from Yamada et al. 2006)
Appendix II-7. Estimated catch at age in number for age 0 – age 10+ of bluefin tuna in the North Pacific Ocean by Japanese troll fishery. (Data were adopted from Yamada et al. 2006)
Appendix II-8. Estimated catch at age in number for age 0 – age 10+ of bluefin tuna in the North Pacific Ocean by Japanese set net fishery. (Data were adopted from Yamada et al. 2006)
Appendix II-9. Estimated catch at age in number for age 0 – age 10+ of bluefin tuna in the North Pacific Ocean by Japanese drift net fishery. (Data were adopted from Yamada et al. 2006)
Appendix II-10. Estimated catch at age in number for age 0 – age 10+ of bluefin tuna in the Tsugaru Strait by Japanese handline fishery. (Data were adopted from Yamada et al. 2006)
Appendix II-11. Estimated catch at age in number for age 0 – age 10+ of bluefin tuna in the Eastern North Pacific Ocean by purse seine fishery. (Data were adopted from Yamada et al. 2006)
Appendix II-12. Estimated catch at age in number for age 0 – age 10+ of bluefin tuna in the North Pacific Ocean by Taiwanese longline fishery. (Data were adopted from Yamada et al. 2006)
Appendix II-13. Estimated catch at age in number for age 0 – age 10+ of bluefin tuna in the North Pacific Ocean by Korean purse seine fishery. (Data were adopted from Yamada et al. 2006)
5. Reproductive potential analysis of bluefin tuna in the North Pacific Ocean Title: Reproductive potential analysis of bluefin tuna, Thunnus orientalis, in the North Pacific Ocean
Chien-Chung Hsu
Institute of Oceanography, National Taiwan University, 1, Section 4, Roosevelt Road, Taipei, Taiwan 106
Tel: +886 2 33661393; Fax: +886 2 23661198; E-mail: [email protected] Running title: reproductive potential of Pacific bluefin tuna
Keyword: Reproductive value, Leslie model, intrinsic rate of population growth;
population reproductive potential
Introduction
The spawning stock biomass (SSB) is generally used to decide whether a fish stock has sufficient productivity. Although a large number of studies have examined the sustainable level of SSB (Mace 1993; Zheng and Quinn II 1993;
Myers et al. 1994; Machal and Horwood 1995). For a fish stock sustainable use in a long term fishery, using stock abundance to represent a long-term stock productivity is needed. Katsukawa (5) developed the unit stock abundance called population reproductive potential (PRP), which is defined as the expected total reproductive value of the standing stock, to evaluate stock productivity by considering both immediate and future spawning. However, the effectiveness of PRP for stock assessment and fisheries management has not yet been presented.
Also it is doubtful whether SSB is an appropriate index of stock sustainability.
For example, SSB ignores the value of immature fish, which are indispensible for long-term sustainability. Under the circumstance, decision-making that depends on SSB to be shortsighted. Therefore, in order to evaluate the sustainability of a fish stock, we should consider both immediate and future spawning of the standing stock.
Materials and Methods
The estimated abundance in number by ages and fishing mortality by ages from the results of the virtual population analysis were adopted here in the present study. Also the maturity oogive was used.
In biology, Fishers’ reproductive value is widely used as an index of the reproductive contribution of an individual. The value is defined as:
R e · m · l
λ
where R is Fishers’ reproductive value (6) for an age i individual, r is the instantaneous growth rate of the population, in which conservatively, the r was set to 0; m is the average number of offspring which an individual at age x contributed, l is the survival rate of an individual until the spawning season at age x, and t is the maximum age of an individual with capability of spawning.
Where the first term on the right-hand side, e represents the discount rate
annual age abundance in number estimated from virtual population analysis. For the case, R is equivalent to the total spawning in the rest of the individual’s lifetime. If the reproductive value can be estimated from equation (1), the total reproductive value for the entire stock can be summed up the reproductive value for all the ages, that is
R R N
where N is the number of individuals at age i for the study stock.
The stock reproductive value is to evaluate the stock productivity, unlike the spawning stock biomass it can be not only due to immediate spawning, but due to future spawning. The value of immature cohort is also evaluated for future reproduction, in which the part was almost ignored in estimating spawning stock biomass (Katsukawa et al. 2002).
Table 1 shows the life history parameters of PBF (Anon. 2007). The fecundity m was approximated as the product of the maturation schedule f and body weight w for the age x at June, which is since the spawning season of PBF is from May to August each year (Chen et al. 2006). Then, the reproductive value at the beginning of the year can be expressed by the fishing mortality at age i as F
.
and the natural mortality at age i as M.
. The natural mortality used in previous report (Yamada et al. 2007) for age 1, 2, 3, 4 and 5 over are 1.6, 0.8, 0.4, 0.25 and 0.25, respectively.R m · l f · w · e
. F . M ∑ F M
For reproductive value of the plus group, i.e., R , is affected by the average age of 10+ (a ) and is empirically approximated by a extrapolation of the relationship between age and fishing mortality in Table 1.
Thus, using data shown in Table 1, the reproductive Value at age was calculated and shown in last two columns of Table 1.
contribution of young individuals, and spawning stock biomass ignores individuals with a high reproductive value per body weight.
Table 2 shows the trend in PBF abundance expressed by spawning stock biomass, biomass and total number of age 0-10+ fish (N) of PBF. And the annual SSB, abundance in number were also shown in Fig. 1. Spawning stock biomass fluctuated increasingly; the spawning stock biomass reached its historical highest in 1994, while recent N peaked in 1995. This inconsistency is also found then after, and there are simultaneously in the recent peak in 2001, but the spawning stock biomass was the lowest in the same time. This is may be due to the newly introduced fishery made by Taiwan small scale longliners to take the giant spawner from 1993, the trend can be found as the Taiwan fishery employed, the spawning stock biomass showed declined tendency. Fishing pressure on giant spawning cohorts declined drastically after 1999, and this change in the fishing pattern caused the spawning stock biomass increasing again (Fig. 1).
Abundance in number and spawning stock biomass also showed opposite reactions to the age-composition fluctuation (Table 3). The trend in total reproductive biomass is intermediate between the trends in N and spawning stock biomass. If age composition is unstable, we must be sensitive to the choice of stock abundance index. The population abundance was projected under various yearly fishing mortalities at age (Table 4). In Table 5, the annual abundance at age in number was shown.
Results and Discussion
Reproductive values and population reproductive potential
Under the assumption that the population is stationary, that is the intrinsic rate of population growth is equal to unit, r 1, the age-specific reproductive values estimated as in Table 2, indicating that the averaged reproductive values at age from 1960 to 2004 increase with age. Then, the reproductive value for all ages from 1960 to 2004 was shown in Fig. 2. The total annual reproductive value is the performance of population reproductive potential (PRP).
The annual total reproductive values of bluefin tuna in the North Pacific Ocean (Fig. 2) indicate that in 1990s the stock has higher relatively reproductive value than others in the study time series, particularly, the reproductive values in 1992
be pursued in the near future. It is rational to assume that the stock with the higher level in the future has the higher long-term productivity as the estimation within the study. The stock level after a long projection, therefore, can represent the long-term productivity of the initial stock.
However, a plus age group may decline the accuracy of stock abundance projection. As the situation, the projection model used for projection, Katuskawa et al. (2002) proposed a plus age group modeling, that was letting N
,
be the number of age i individuals at the beginning of year j. The dynamics can be expressed as, for age i is 1 i 10:N
,
N,
eZ
where Z F M . Individuals older than 10-year-old are grouped as a 10+.
Thus, the number of age 10+ can be expressed as:
N
,
N,
eZ
N,
eZ
The average age of mid-year 15+ fish in year j a is:
a a 1 N
,
eZ
10.5N,
eZ
N
,
eZ
N,
eZ
The weight at age was estimated from the von Bertalanffy growth equation and length-weight relationship (Hsu et al. 2000). This may be different with the current method used herein that the average from age 10 to 12 was used in the present study.
As usual, fish population dynamics can be expressed as a matrix model, e.g.
Leslie matrix model. The estimation of intrinsic growth rate of population was used the Leslie matrix with the consecutive annual abundance at age in number, i.e.,
N AN
where A is the Leslie matrix and it largest real positive eigenvalue, λhas a relationship with the intrinsic growth rate of population,
λ e
Further, the intrinsic growth rate of population can be estimated as:
r ln λ
The annual abundance at age in number was as shown in Table 5. And Leslie matrix A can be constructed as:
s f s f s f s f
population growth as above mentioned. We assumed the intrinsic growth rate as a constant one, this may be not appropriate, as this is so, the estimation of the parameter through Leslie matrix model and its eigenvalue seems necessary for accurate computation of PRP in the present study.
References
Anon. 2007. Report of the Fifth Pacific Bluefin Tuna Workshop. International Scientific Committee for Assessment of Tuna and Tuna-like Species in the North Pacific Ocean. 12-23 April 2007, Shimizu, Shizuoka, Japan.
Chen, K. S., P. Crone and C.C. Hsu. 2006. Reproductive biology of female Pacific bluefin tuna Thunnus orientalis from south-western North Pacific Ocean.
Fish. Sci. 72: 985-994.
Katsukawa, T., H. Matsuda and Y. Matsumiya. 2002. Population reproductive potential: evaluation of long-term stock productivity. Fisheries Science, 68:1106-1112.
Marchal, P. and J. Horwood. 1995. Multi-annual TAGs and minimal biological levels. ICES Journal Marine Science, 52:797-807.
Mace, P. M. Relationship between common biological reference points used as threshold and targets of fisheries management strategies. Canadian Journal of Fisheries and Aquatic Science, 51:110-122.
Myers, R. A., A. A. Rosenberg, P. M. Mace, N. Borrowman and V. R. Restrepo.
1994. In search for thresholds for recruitment overfishing. ICES Journal Marine Science, 51:191-205.
Zheng, J. and T. J. Quinn II. 1993. Comparison and evaluation of threshold estimation methods for exploited fish population. In: Kruse, G., D. M. Eggers, R.
J. Marasco, C. Pautzke, T. J. Quinn II (eds.) Proceedings of the International Symposium on Management Strategies for Exploited Fish Population, 21-24 October 1992. Anchorage, Alaska. Alaska Sea Grant College Program Report no.
93-02. University of Alaska, Fairbanks, AL, 1993.
Table 1 Life history parameters of the Pacific bluefin tuna, abstracted from Yamada et al. (2004; 2006) and the present study in the section of the adaptive virtual population analysis.