Nonequilibrium Production Model of Yellowfin Tuna in the Central and Western Pacific

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1 ACTA OCEANOGRAPHICA T AIWANICA VOL.34, NO.4 PP31-41, 2TABS, 7FIGS., DECEMBER 1995 Nonequilibrium Production Model of Yellowfin Tuna in the Central and Western Pacific Chi-Lu Sun l and Su-Zan Yeh l (received 1995/11123, revised 1995/12/26, accepted 1995/12/30) ABSTRACT Yellowfin tuna catch and effort data from 1970 to 1992 in the western Pacific area by country (Taiwan, Japan, U.S., and others) and by gear (longline, purse seine, and pole and line) were collected and compiled separately. The effort data were standardized by the general linear model (GLM). A nonequilibrium stock production model --- ASPIC and a bootstrap procedure with 1000 trials were then applied to assess the current status ofthe yellowfin tuna stock The results showed that fishing mortality rate in 1992 was 0.261, the F msy of the stock is 0.745, and the maximum sustainable yield (MSY) of the stock is 670,000 MT. These results are similar to those obtained by Hampton and Lewis (1993) by using the tag-attrition model. Based on these results, the current status ofthe yellowfin tuna stock is optimistic. However, in view of the recent rapid increase in catch, it is pointed out that the stock condition and developments in the fishery still need to be monitored. (Key words: Stock Assessment, Yellowfin Tuna, Nonequilibrium Production Model) INTRODUCTION Western Pacific yellowfin tuna were caught by purse seine, longline, and pole and line fleets of distant-water fishing nations and Pacific Island Countries. The yellowfin tuna were also caught by ringnet, purse seine and handline in the Philippines, and by pole and line in eastern Indonesia (South Pacific Commission, SPC, 1990). The total catch (Figure 1) increased from 90,916 MT in 1970 to 394,704 MT in 1992 (Western Pacific Yellowfin Tuna Research Group, WPYRG, 1994) Hampton and Lewis (1993) noted that the yellowfin tuna catch has almost doubled in the last ten years, with most of the increase occurring since This rapid increase in catch has caused concern about the status ofthe stock The most recent appraisal ofthe yellowfin tuna stock using an equilibrium production model was performed by Suzuki et al. (1989) Hampton (1992) and Hampton and Lewis (1993) assessed the current yellowfin tuna status by using tag-attrition models. The purpose ofthis paper is to assess the yellowfin tuna stock status by using a nonequilibrium stock-production model, ASPIC (A Surplus-Production model Incorporating Covariates) (Prager, 1991, 1992, 1993, 1994) I Institute of Oceanography. National Taiwan University. Taipei. Taiwan. Republic of China. 31

2 32 Nonequilihrium Production Model ofyellowfin Tuna in the Central and Western Pacific i=' ::!E J: o f0- e:( o YEAR Figure 1. Total Catch by gear ofyellowfin tuna from the western Pacific Ocean, DATA SOURCES AND ANALYSIS METHOD The total catches by country and by year for the period were obtained from WPYRG (1994). The data used for standardized effort are shown in Table 1. Table I. Data sources and contents used in the ASPIC production model analysis for the western Pacific yellowfin tuna. All data are in the form of year, month and SOxSo unit area. Country Japan Taiwan us Gear Type Period Type ofeffort Type ofcatch Data Source" Longline hooks number offish SPc+ & NRIFSF Purse seine days weight (MT) SPC' & NRIFSF Pole and line days weight (MT) SPC & NRIFSF Longline hooks number of fish NTU Purse seine days weight (MT) SPC &NTU Purse seine days weight (MT) SWFSC *SPc+ : Released by South Pacific Commission under the authorization of Dr. Suzuki (NRIFSF). NRIFSF: National Research Institute of Far Seas Fisheries NTU : National Taiwan University. SPC : South Pacific Commission. SWFSC : Southwest Fisheries Science Center. Because the effort must be standardized before being input into the ASPIC production model, each ofthe six effort data sets were standardized individually by the general linear model (GLM), which was similarly used by Sun and Yeh (1993a, 1993b, 1994) The main effect variables were

3 Chi-Lu Sun and Su-Zan Yeh 33 year, month, area, and set-type (the last variable for purse seine fishery only). terms of seven sub-areas as shown in Figure 2. Area was defined in BO W '=~..ll:.-~-f'rh-f--~-~ - ~-~ WPVF-6-- -WPVF-7- ~_o ~ I 60 - ~ _-0 ~ _- --_-- _ S Figure 2. WPYRG statistical areas for compiling fisheries data. (Reproduced from WPYRG, 1994) ~.L..-L-..L-L-'---L-l-JL...-L-L-J Because ASPIC allows multiple data-series with different units to be incorporated during fitting, a total of nine data-series were constructed. Each data series represented one of the following categories offishery: Japanese longline, Taiwanese longline, all other longline, Japanese purse seine, Taiwanese purse seine, US purse seine, all other purse seine, Japanese pole and line, and all other pole and line. The category "all other longline fisheries" included those countries for which the effort data was unavailable. Countries represented by this category included Korea, Philippines, Indonesia, et cetera. The combined countries' effective effort was determined by use ofthe formula k L Y ij j = 1 Ii = CPU E, where Yij is the yearly catch of each fishery j ofthe k country and CPUE i is the standardized catch per unit effort (CPUE) oftaiwanese longline fishery for year i, This estimate was coupled with IY f and was used in the construction ofthis separate data-series.

4 34 Nonequilibrium Production Model of Yellowfin Tuna in the Central and Western Pacific The category "all other purse seine fisheries" included Korea, Philippines, Russia, et cetera. The combined countries' effective effort was calculated by means ofthe same model as mentioned above, but the CPUE, used was the standardized CPUE ofthe Japanese purse seine fishery. The category "all other pole and line fisheries" included Indonesia, Papua New Guinea, et cetera. The combined countries' effective effort was also calculated using the above formula, but the CPUE, used was that ofthe Japanese pole and line fishery. These nine data-series were compiled separately, and each consisted of the total catch and effective effort of its respective category. The complete data-series were input into ASPIC simultaneously. ASPIC then estimated several parameters -- population carrying capacity (K), intrinsic rate of increase (r), and the fishery-specific catchability coefficients (qj). These parameters were used to generate annual estimates of absolute biomass B, fishing mortality F, and the following management benchmarks (Prager, 1991, 1992, 1993, 1994): MSY B msy F msy FO.1 Y O I B-ratio F-ratio maximum sustainable yield (= Kr/4), stock biomass at MSY (= K/2), fishing mortality at MSY (= r/2), management benchmark (= 0.45r), equilibrium yield at F O. l (= Kr), ratio ofb, to B msy, and ratio off I to F msy. Also, a bootstrapping procedure of 1000 trials was used independently to assess the variability of the estimated parameters, adjust for estimation bias, and compute approximate bias-corrected confidence intervals according to the method ofefron and Gong (1983). RESULTS AND DISCUSSION The model and management parameter estimates (Table 2) from ASPIC were: r = 1.49/year, K = 1,800,000 MT, MSY = 670,700 MT, B msy = 900,000 MT, F msy = 0.745, F O. l = 0.671, and = 664,000 MT. Y O l The computed ordinary and bias-corrected point estimates ofmsy were 670,700 MT and 675,100 MT, respectively, with an 80% confidence interval of481, ,000 MT. The total mortality rate (Figure 3) increased slowly and steadily from in 1972 (the annual values ofthe first two years, 1970 and 1971, were omitted due to extreme imprecision) to in 1992 This figure is still far below the model's F msy of0.745.

5 Chi-Lu Sun and Su-Zan Yeh Table 2. Estimated management parameters and benchmarks for the ASPIC production model fitted to nine fisheries for yellowfin tuna in the Central and Western Pacific Ocean. MODEL PARAMETER ESTIMATES Parameter r q( I) q( 2) q( 3) q( 4) q( 5) q( 6) q( 7) q( 8) q( 9) Biomass ratio in 1970 Maximum stock biomass Estimate 3.587E-OI 1.800E+06 Intrinsic rate ofincrease 1.490E+00 Catchability coefficients by fishery: Taiwan longline 4.887E-08 Japan longline 4.91IE-08 Other longline 4.265E-08 Taiwan purse seine 1059E-06 Japan purse seine 5.053E-07 US purse seine 2.547E-06 Other purse seine 7.540E-07 Japan pole and line 9.698E-08 Other pole and line 9.587E-08 MANAGEMENT PARAMETER ESTIMATES Parameter Estimate MSY Maximum sustainable yield 6.707E+05 Bmsy Stock biomass at MSY 9.000E+05 Fmsy Fishing mortality at MSY 7.452E-O I Fco I) Management benchmark 6.707E-OI Y CO I ) Equilibrium yield at Fco I) 6.640E+05 B-ratio Ratio of B(1993) to Bmsy 1665E+00 F-ratio Ratio of F CI992 ) to Fmsy 3.503E-OI Fishing effort at MSY in units of each fishery fmsy{ I) Taiwan longline 1525E+07 fmsy( 2) Japan longline 1.518E+07 fmsy( 3) Other longline I 747E+07 frnsv< 4) Taiwan purse seine 7036E+05 fmsy( 5) Japan purse seine 1.475E+06 fmsy{ 6) US purse seine 2.925E+05 fmsy( 7) Other purse seine 9.883E+05 fmsy( 8) Japan pole and line 7.684E+06 fmsy( 9) Other pole and line 7.773E+06 frol) = I.372E+07 fcol) = 1.366E+07 fcol) = 1.573E+07 fco I) = 6.332E+05 fro 1)= 1.327E+06 fcol) = 2.633E+05 fcol) = 8.895E+05 fcol) = 6.916E+06 fro I) = 6.996E+06

6 36 Nonequilibrium Production Model ofyellowfin Tuna in the Central and Western Pacific Level of Fmsy ~ 0.6 ::i ~ 0.5 D:: o :::IE 0.4 C) ~ 0.3 J: ~ L O+--r-~-r--""T"""--r--,-,---r-'-T'--''--''T''""-r-~-r--"''T"""--r--,''--,---r-~-r--' YEAR Figure 3. Estimated annual total fishing mortality from the fitted ASPIC model. Figure 4 shows the trajectory of the point estimates of relative biomass (BtlB msy ) which decreased slowly and steadily in the past two decades. (The first five years were omitted due to extreme imprecision). In Figure 5, the trajectory of the point estimates of relative fishing mortality (FtlF msy ) indicates the trend is a stable and slow increase. (The first two years are once again omitted due to extreme imprecision.) The bias-corrected point estimates ofrelative biomass and fishing mortality, along with the nonparametric 80% confidence intervals from the bootstrapping procedure of 1000 trials are shown in Figures 6 and 7. Based on the above analyses, the conclusions are optimistic. The current status of the yellowfin tuna stock in the western Pacific appears to be in a state of moderate exploitation. These results are reasonably consistent with those of the tagging analysis conducted by Hampton (1992) and Hampton and Lewis (1993) in which they estimated MSY at above 600,000 MT and fishing mortalilty of 1992 at per year as compared to 670,000 MT and per year in this study Suzuki et al. (1989) used an equilibrium production model to fit longline catch and effort data for the western Pacific yellowfin tuna and obtained the estimates of MSY around 70, ,000 MT. The total surplus production was apparently underestimated, as the total catch, and even the catch of"longline-size" yellowfin, has now far outstripped the MSY estimates with no signs ofthe stock collapse that would have been predicted by equilibrium production models (SPC, 1995). Equilibrium production models have generally proven unreliable in estimating MSY and other management parameters for many fish stocks (Hilborn and Walters, 1992; Polacheck et al., 1993).

7 Chi-Lu Sun and,\'u-zan Yeh ,--,.----, , ,-, ,---,------,---,------,----, ,r--, ,--,-----, YEAR Figure 4. Annual relative biomass from the fitted ASPIC model Annual values for the first five years are omitted due to extreme imprecision >- J 0.6 u: O+----, ,-----,--, ,---,------,---,------, ,----,----,r--, ,--,------, , YEAR Figure 5. Annual relative fishing mortality from the fitted ASPIC model Annual values for the first two years are omitted due to extreme imprecision.

8 38 Nonequilibrium Production Model of Yellowfin Tuna in the Central and Western Pacific '" 1.8 ~ E CO 1.75 as' ,--r--,----,--, ,----,--, ,----,--,, ,--,,-._--,--,-,,--, YEAR Figure 6. Bootstrapped annual relative biomass from the fitted ASPIC model. Confidence intervals are based on 1000 trials. Annual values for the first five years are omitted due to extreme imprecision ~ '" E U. 0.3 Ii"' o +-,--r--,--.,.--~---,-_. r-...,--r-,-._---.--,---,,- r--,--.--~,--r--,---, YEAR Figure 7. Bootstrapped annual relative fishing mortality from the fitted ASPIC model. Confidence limits are based on 1000 trials. Annual values for the first two years are omitted due to extreme imprecision

9 Chi-Lu Sun and Su-Zan Yeh 19 The ASPIC used in this study is a nonequilibrium stock-production model, based on the logistic production model, as developed by Schaefer (1954), but without the equilibrium assumption that has been regarded with increasing disfavor (Hilborn and Walters, 1992) The ASPIC framework provides a flexible format for production modeling (Prager, 1992) Besides its inherent flexibility, the ASPIC approach estimates the parameters minimizing the difference between the observed and predicted catch (or effort) rather than forming a regression between effort and CPUE. This point is important because the CPUE values implicitly contain the reciprocal of effort, therefore the two variables would be correlated even if the catch and effort were not In addition, ASPIC allows for multiple data series with different effort units to be incorporated simultaneously during fitting, the model also handles missing data points from one or more series (Jones and Farber, 1994). Because the ASPIC modeling is realistic and practical, we should continue to use this technique as one ofthe means for monitoring the status of stocks ofthe western Pacific yellowfin tuna. ACKNOWLEDGEMENTS We would like to thank Dr. Gary Sakagawa and Mr. A1 Coan of the SWFSC for releasing the US purse seine data, and Dr. Ziro Suzuki of the NRIFSF for authorizing SPC to release the Japanese data. Thanks are also extended to Dr. Antony Lewis and Mr. Peter Williams of SPC, who helped in distributing the Japanese data. Finally, thanks to the Council of Agriculture, Republic of China, for the financial support ofthis project [contract number: 84 AST FID 01(2)] REFERENCES CITED Jones C D. and M. L Farber (1993) An exploratory stock-production model analysis of sailfish (fstiophorus platypterus) in the western Atlantic Ocean. fccal' Call. Vol. Sci. Pap., 42(2), Efron, B. and G. Gong (1983) A leisurely look at the bootstrap, the jackknife, and crossvalidation. Am. Statistician, 37, Hampton 1 (1992) Assessment of skipjack and yellowfin tuna stocks in the western tropical Pacific, using data from large-scale tagging experiments. Working Document WPYRG2/2, 43 pp. Hampton 1 and A D. Lewis (1993) large-scale tagging experiment Assessment of western Pacific yellowfin on the basis of a Working Document WPYRG3/13, 27 pp. Hilborn, R. and C 1 Walters (1992) Quantitative fisheries stock assessment: Choice, dynamics and uncertainty. Chapman and Hall, New York, NY, 572 pp. Polacheck, T, R. Hilborn and A E. Punt (1993) Fitting surplus production models comparing method and measuring uncertainty. Can. 1. Fish. Aquat. Sci., 50, Prager, M H (1991) User's manual for ASPIC A stock-production model incorporating covariates. Program version 2.8a. Miami Lab. Doc., MIA-91/92-20, 16 pp Prager, M. H (1992) ASPIC -- A surplus-production model incorporating covariates. fcca T Call. Vol. Sci. Pap., 37, (SCRS/91/24, rev.). Prager, M. H (1993) User's manual for ASPIC A stock-production model incorporating Covariates, Program Version Miami Lab. Doc., MIA-92/93-55, 31 pp.

10 Editorial Board Editor-in-Chief: Cho-Teng Liu, Institute of Oceanography, National Taiwan University, Taipei P.O.Box 23-13, Taiwan Associate Editors: Ju-Chin Chen, Institute of Oceanography, National Taiwan University, Taipei, Taiwan Yu-Chia Chung, Institute of Marine Geology, National Sun Yat-sen University, Kaohsiung, Taiwan Thomas N. Lee, Rosenstiel School of Marine and Atmospheric Science, Univ. of Miami, Miami, FL Hin-Kui Mok, Institute of Marine Biology, National Sun Yat-sen University, Kaohsiung, Taiwan Su-Cheng Pai, Institute of Oceanography, National Taiwan University, Taipei, Taiwan Wung-Yang Shieh, Institute of Oceanography, National Taiwan University, Taipei, Taiwan Chengsung Wang, Institute of Applied Geophysics, National Taiwan Ocean Univ., Keelung, Taiwan Information for Contributors 1. Four categories of papers related to the oceanographic research are welcome: Articles, Notes, Letters and Book Reviews. Only original papers will be accepted. 2 Manuscripts are to be submitted in English and should not exceed 10,000 words (including tables and figures). However, manuscripts in Chinese will be considered at the discretion of the editors. 3. Both English and Chinese abstracts are required for articles. The abstracts should not exceed 500 words In conjunction with the abstract, include 3-5 key words. 4 English text should be typewritten and double-spaced. Chinese text should be word-processed rightward (not downward) 5 References in the text should be given by quoting the author's name and year of publication i.e Wang (1970) Full references should be listed at the end of each paper in alphabetical order in the following manner Haxby, W F. and 1 K Weissel (1986) Evidence for small-scale mantle convection from Seasat altimeter data J. Geophys. Res., 91(B3), The author will receive 50 copies of reprint free of charge. Twenty extra free copies per person will be available, if the paper is written by more than one person. Additional copies of reprint could be obtained at the author's expense. 7. The manuscript will be returned if it is not accepted. Acta Oceanographica Taiwanica reserves the right of reviewing and revising the manuscript 8. Manuscripts should be sent to "The Editorial Board, Acta Oceanographica Taiwanica, c/o Institute of Oceanography, National Taiwan University, Taipei, Taiwan, ROC" Acta Oceanographica Taiwanica, AOT, (ISSN ) is co-sponsored by the National Science Council (NSC) and the National Taiwan University (NTU) It is published quarterly by the Institute of Oceanography. NTU. located at # I. Section 4, Roosevelt Road. Taipei. Taiwan. R.O.c. AOT is available for free to Principal Investigators of NSC funded oceanographic research projects. and for exchange of scientific Journals published by the academic institutions or public agencies Publication Charge Policy: Excess fcc of NT$1 000 per page will be charged for papers longer than 20 Journal pages Colored plates may be at author's expense Subscription: please write to Dr J.C Chen, Chairman of ROC-SCaR, Taipei POBox 23-13, Taiwan, ROC

11 40 Nonequilibrium Production Model of Yellowfin Tuna in the Central and Western Pacific Prager, M. H. (1994) A suite of extensions to a nonequilibrium surplus-production model. Us. Fish. Bull 92, South Pacific Commission (1990) Stock status of yellowfin in the western tropical Pacific. Working Document SCTB3111, 11 pp. South Pacific Commission (1995) Status oftuna stocks in the western and central Pacific Ocean. Working Document SCTB8/3, 32 pp Sun, C L. and S Z Yeh (1993a) Standardized catch rates ofyellowfin tuna (Thunnus albacare) from the Taiwan tuna longline fishery in the central and western Pacific Ocean. Working Document WPYRG311\, 13 pp. Sun, C L. and S. Z Yeh (1993b) Trend ofabundance index ofyellowfin tuna from Taiwan purse seine fishery in the central and western Pacific Ocean. Working Document WPYRG3112, 12 pp. Sun, C L. and S Z Yeh (1994) Standardized CPUEs of central and western Pacific yellowfin tuna from Taiwanese distant-water Fisheries. Working Document WPYRG4111, 12 pp. Suzuki, Z, N. Miyabe, and S Tsuji (1989) Preliminary analysis of fisheries and some inference on stock status for yellowfin tuna in the western Pacific. Working Document SCTB211 0, 19 pp. Western Pacific Yellowfin Tuna Research Group (1994) Report of the third meeting of the western Pacific yellowfin tuna research group. 59 pp.

12 台灣海洋學刊第 34 期第 4 號 頁司 2 表 7 圈 中華民國 84 年 12 月 應用非平衡生產量模式評估西太平洋黃鱗鱗資源 祥 志陸 l 黨素然 } 摘要 本報告整理分析薑灣 日本及美國等自 1970 至 1992 年在西太平洋海域之賄 延繩釣 大型體賄圍網及體竿釣等漁業之黃賭賄漁獲量及漁獲努力量資料 首先 將漁獲努力量以一般線性模式的 LM) 方法, 依國別漁業別分別予以標準 it ; 繼 之, 應用 ASPIC 非平衡生產量模式分析估算出西太平洋海域黃賭賄之年漁獲死 亡率 最大持續生產量 (MSY) 以及在最大持續生產量下之漁獲死亡率 (F msy ) 等重 要資源評估參數, 並以 bootstrap 程序求得各參數估值之信賴區問 : 最後, 根據 這些參數, 對西太平洋黃賭賄進行資源評估 結果得知西太平洋黃賭賄 1992 年漁獲死亡率為 ' 最大持續生產量為 670, 000 公噸, 該資源 F msy 為 0754 ' 資源現況尚屬樂觀, 處於適度開發階段, 無過漁之憂 惟此資源近年開發頗速, 為保此資源之未來持續成長, 其資源狀況及漁業發展仍應予以繼續評估輿監視 ( 關鍵詞 : 資源評估 黃蜻賄 非平衡生產量棋式 ) l 台灣大學加洋研究所, 台北, 台灣, 中華民國 41