VPAの概要と国内資源評価での適用例

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4 () VPA TAC ABC VPA VPA VPA VPA % ( ) 40% VPA 30% 20% 10% 0% ( 2004) ig. 1 VPA (Megre 1989) VPA Pope(1972) Gulland s virtual population analsis (Gulland 1965) is an extremel useful technique when assessing a fisher, because it enables estimates of population at age and fishing mortalit to be made independentl of the measurement of effort Cohort analsis is a new form of virtual population analsis developed b the author to overcome these problems

5 Gulland VPAPope VPA Pope VPA Pope VPA VPA Pope VPA VPA VPA VPA VPA Derzhavin (1922)Megre (1989) virtual population( ) r(1949)r virtual population virtual population VPA Jones (1964) 1964 Murph (1965) VPA Gulland (1965) VPA Gulland VPA ( + M ) C a, = ( 1 e ) a, (1) + M a C a, M a C M a, 2

6 =L a+ 1, + 1 = a, e ( + M ) (2) Pope (1972) (2) M 2 M 2 ( e C ) e = (3) a+ 1, + 1 a, a, Pope Pope (1972) 7 1 Allen and Hearn (1989) 6 1 Pope Evans (1989)Hiramatsu (1995) Doubleda(1976) Pope and Shepherd (1982) VPA (SVPA) a a, S = S a, a (4) a (separable) ADAPT VPA VPA CPUE ADAPT (Gavaris 1988) Powers and Restrepo(1992) Butterworth and Punt(1992)ICCAT 3

7 Jones (1981) von Bertalanff Lai and Gallucci (1988) Sullivan et al.(1990) (1996, 1997) (Quinn and Deriso 1999, Ueda and Matsuishi 2004, Ueda and Matsuishi in press, Ueda et al. 2001, Zheng et al. 1995, Zheng et al. 1996, et al. in press, et al. 2000) (Ueda and Matsuishi 2004, Ueda and Matsuishi 2005, Ueda et al. 2001) r VPA CPUE VPA VPA VPA Age-Length Ke(ALK) ALK Quinn and Deriso (1999) a SE ( a ) 4

8 SE 2 2M a 2 M a ( ) SE ( ) e + SE ( C ) e 2 ( a a = + (5) a 1 a SE C ) a M a a VPA ig. 2 VPA VPA Pope(1972) ( ) (2001) VPA 5

9 M C e (6) M a, = a 1, + 1e a, a, a, = ln M (7) a+ 1, + 1 ( )( A ) A CA, M 2 A, = e (8) A, 1 e (8) A+, + M A, = CA+, (9) A+, A, 1 A+, + M = ( M ) = ( M ) C A+, A +, + A+ + 1 e 1 e A+,, (9) A (10) A A 1, 1 A+, (10) (9) (10) (9) ( A +, 1+ M ) ( A +, 2 + M ) A, + A, 1e + A, 2e +... ( M ) ( M ) A+, + 2 A+, + A, = A, ( 1+ e + e +...) = ( A+, + M ) 1 e ( ) (9)(10) (1)(2) Pope (3) 2 6

10 A ( A+, + M ) 1 e M 2 = C A, e A+ + 1 e (11) CA+, M 2 = e A+ 1 e (12),, A+,, (11),(12) Pope (3)(2) Pope (9),(10) (8) (9) (11) (5) (6) A, A 1, 1 A, A 1, 1 C A 1, 1 A, A 1, = (13) A 1, 1 (6) = A, 1 A 1, 1 A, 1 A, 1 A 1, 2 A 1, 2 (13) A, 2 = A 1, 2 1 A, 2 A 1, 1 A 1, 2 A 1, 3 1 A 1, = ( A 1, 1 + A 1, 2 + A 1, 3) (14) 3 1 (7) CA 1, M 2 A 1, = e (15) A 1, 1 e (5) A 2, 1 7

11 1 A 2, = ( A 2, 1 + A 2, 2 + A 2, 3) (16) 3 A 2,, 1(13) A (14) (13) A, = A 1, A 1, A, A, A 1, = A, A 1, A, = A, VPA Tabel 1 16 ( 2004) TAC VPA CPUE CPUE 2 8

12 ig. 3 ( 2004) ADAPT VPA 1 I 1, 7 CPUE X a, SSQ = ln I ln q 7 + ln X ln b 5 (17) ( ( ) ( ) ( ( a, ) ( a, ) 14 1, 1, q,b ig (retrospective) VPA 9

13 ig. 5 ig ig. 5 VPA 0 VPA ig VPA VPA

14 VPA CPUE M =0.3, M=0.2 M=0.4 VPA 2 M M 2.5 ( 1960) Hoenig(1983) (Paul 1980) (Gunderson 1980)() VPA (Beer et al. 1999, Lorenzen 2000) (Hightower 1998, Vetter 1988) VPA VPA VPA VPA 11

15 VPA CPUE M VPA Allen, K. R., and W. S. Hearn Some procedures for use in Cohort analsis and other population simulations. Can. J. ish. Aquat. Sci. 46: Beer, J., C. Kirchner, and J. Holtzhausen A method to determine size-specific natural mortalit applied to westcoast steenbras (Lithognathus aureti) in amibia. ISHERIES RESEARCH 41: Butterworth, D. S. and A. E. Punt A review of some aspects of the assessment of the western orth Atlantic bluefin tuna. ICCAT Col. Vol. Sci. Pap. 39(3): Doubleda, W. G A least squares approach analzing catch ate age. Int. Comm. orthwest Atl. ish. Res. Bull., 12: Derzhavin, A The stellate sturgeon (Acipenser stellatus Pallas), a biological sketch. Bulleten Bakinskoi Ikhtiologicheskoi Stantsii 1: Evans, G. T Rational approximations to solutions of the VPA equations. Can. J. ish. Aquat. Sci. 46: r,. E. J Statistics of a lake trout fisher. Biometrics 5: Gavaris, S An adaptive framework for the estimation of population size. Departmet of isheries and Oceans Biological Station, St. Andrews. Gulland, J. A Estimation of mortalit rates. Annex to Arctic fisheries Working Group Report. ICES C. M., Hamburg, Januar Gunderson, D. R Using r-k selection theor to predict natural mortalit. Can. J. ish. Aquat. Sci. 37: Hightower, J Estimating natural mortalit. Hiramatsu, K A Theoretical Stud of Equations Used in Virtual Population Analsis. isheries Science 61: VPA(Virtual Population Analsis). Pages in,. 12.,. Hiramatsu, K., and E. Tanaka Reliabilit of stock size estimates from adaptive framework virtual population analsis. isheries Science 70: Hoenig, J. M Empirical use of longevit data to estimate mortalit rates. ish. Bull. 81: Jones, R Estimating population size from commercial statistics when fishing mortalit varies with age. Rapp. p.-v. reun. - Cons. int. explor. mer 155: Jones, R The use of length composition data in fish stock assessments (with notes on VPA and cohort analsis). U.. AO isheries Circ.734, Rome. 12

16 Lai, H. L., and V.. Gallucci Effects of parameter variabilit on length-cohort analsis. J. Cons. int. Explor. Mer 45: Lorenzen, K Allometr of natural mortalit as a basis for assessing optimal release size in fish-stocking programmes. Can. J. ish. Aquat. Sci. 57: , : Megre, B. A Review and comparison of age-structured stock assessment models. Amer. ish. Soc. Smp. 6: 8-48.,,,. in press... Murph, G. I A solution of the catch equation. J. ish. Res. Board Can., 22: Paul, D On the interrelationships between natural mortalit, growth parameters, and mean environmental temperature in 175 fish stockes. J. Cons. int. Explor. Mer 39: Pope, J. G An investigation of accurac of virtual population analsis using cohort analsis. Research Bulletin of the International Commission for the orthwest Atlantic isheries 9: Pope, J. G., and J. G. Shepherd A simple method for the consistent interpretation of catch-at-age data. J. Cons. int. Explor. Mer 40: Powers, J. E., and V. R. Restrepo Additional options for age-sequenced analsis. ICCAT Col. Vol. Sci. Pap. 39(2): Quinn, T. J., II, and R. B. Deriso Quantitative ish Dnamics. Oxford Universit Press, Oxford ,. Sullivan, P. I., H. L. Lai, and V.. Gallucci A Catch-at-Length Analsis that Incorporates a Stochastic Model of Growth. Can. J. ish. Aquat. Sci. 47: : Ueda,., and T. Matsuishi The Weight-based Virtual Population Analsis of Pacific Cod Gadus macrocephalus off the Pacific Coast of Southern Hokkaido, Japan. isheries Science 70: Ueda,., and T. Matsuishi Weight-based ield per recruitment and spawning-biomass per recruitment analses of Pacific cod Gadus macrocephalus off the Pacific coast of southern Hokkaido, Japan. isheries Science 71: Ueda,., and T. Matsuishi. in press. Weight-based ield per recruitment and spawning-biomass per recruitment analses of Pacific cod Gadus macrocephalus off the Pacific coast of southern Hokkaido, Japan. isheries Science. Ueda,., T. Matsuishi, and. Kanno Weight-based population analsis: an estimation method. ISHERIES RESEARCH 50: Vetter, E Estimation of natural mortalit in fish stocks: a review. ish. Bull. 86: ,,, and : Zheng, J., M. C. Murph, and G. H. Kruse A length-based population model adn stock-recruitment relationships for red king grab, Paralithodes camtschaticus, in Bristol Ba, Alaska. Can. J. ish. Aquat. Sci. 52: Zheng, J., M. C. Murph, and G. H. Kruse A catch-length analsis for crab populations. ish. Bull. 94:

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