ASSESSING COMPONENTS OF UNCERTAINTY IN VPA ABUNDANCE AND MORTALITY ESTIMATES USING AN ALTERNATIVE EXPLOITATION RATE-BASED ALGORITHM
Using an exploitation rate (not fishing mortality) based virtual population analysis (VPA) algorithm, which is itself a generalization of the Pope approximation to the original VPA equations, I show how to derive variance estimates for the key VPA outputs (recruitment, SSB, exploitation rates) given...
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| Published in | Natural resource modeling Vol. 25; no. 4; pp. 574 - 598 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Malden, USA
Blackwell Publishing Inc
01.11.2012
John Wiley & Sons, Inc |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0890-8575 1939-7445 |
| DOI | 10.1111/j.1939-7445.2011.00113.x |
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| Abstract | Using an exploitation rate (not fishing mortality) based virtual population analysis (VPA) algorithm, which is itself a generalization of the Pope approximation to the original VPA equations, I show how to derive variance estimates for the key VPA outputs (recruitment, SSB, exploitation rates) given variance information on the key inputs (catch‐at‐age/terminal exploitation rates). Given the alternative VPA algorithm permits closed‐form solutions for the outputs in terms of the inputs, the delta method is employed to obtain the variance estimates, removing the need for complex simulation techniques. Using North Sea herring data as an example, the method’s utility is demonstrated by exploring the impact of aging error in the catch data and tuning error on the precision of estimates of SSB, recruitment and exploitation rates, and the parameters of the stock‐recruit relationship. |
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| AbstractList | Abstract Using an exploitation rate (not fishing mortality) based virtual population analysis (VPA) algorithm, which is itself a generalization of the Pope approximation to the original VPA equations, I show how to derive variance estimates for the key VPA outputs (recruitment, SSB, exploitation rates) given variance information on the key inputs (catch-at-age/terminal exploitation rates). Given the alternative VPA algorithm permits closed-form solutions for the outputs in terms of the inputs, the delta method is employed to obtain the variance estimates, removing the need for complex simulation techniques. Using North Sea herring data as an example, the method's utility is demonstrated by exploring the impact of aging error in the catch data and tuning error on the precision of estimates of SSB, recruitment and exploitation rates, and the parameters of the stock-recruit relationship. [PUBLICATION ABSTRACT] Using an exploitation rate (not fishing mortality) based virtual population analysis (VPA) algorithm, which is itself a generalization of the Pope approximation to the original VPA equations, I show how to derive variance estimates for the key VPA outputs (recruitment, SSB, exploitation rates) given variance information on the key inputs (catch‐at‐age/terminal exploitation rates). Given the alternative VPA algorithm permits closed‐form solutions for the outputs in terms of the inputs, the delta method is employed to obtain the variance estimates, removing the need for complex simulation techniques. Using North Sea herring data as an example, the method’s utility is demonstrated by exploring the impact of aging error in the catch data and tuning error on the precision of estimates of SSB, recruitment and exploitation rates, and the parameters of the stock‐recruit relationship. Abstract Using an exploitation rate (not fishing mortality) based virtual population analysis (VPA) algorithm, which is itself a generalization of the Pope approximation to the original VPA equations, I show how to derive variance estimates for the key VPA outputs (recruitment, SSB, exploitation rates) given variance information on the key inputs (catch‐at‐age/terminal exploitation rates). Given the alternative VPA algorithm permits closed‐form solutions for the outputs in terms of the inputs, the delta method is employed to obtain the variance estimates, removing the need for complex simulation techniques. Using North Sea herring data as an example, the method’s utility is demonstrated by exploring the impact of aging error in the catch data and tuning error on the precision of estimates of SSB, recruitment and exploitation rates, and the parameters of the stock‐recruit relationship. |
| Author | HILLARY, R. M. |
| Author_xml | – sequence: 1 givenname: R. M. surname: HILLARY fullname: HILLARY, R. M. email: CSIRO Marine and Atmospheric Research, Wealth from Oceans National Research Flagship, Castray Esplanade, Hobart, TAS 7001, Australia rich.hillary@csiro.au, rich.hillary@csiro.au organization: CSIRO Marine and Atmospheric Research, Wealth from Oceans National Research Flagship, Castray Esplanade, Hobart, TAS 7001, Australia E-mail: rich.hillary@csiro.au |
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| References | M. Maunder, and R.B. Deriso 2003], Estimation of recruitment in catch-at-age models , Can. J. Fish. Aquat. Sci. 60, 1204-1216. G. Wang 2007], On the latent state estimation of nonlinear population dynamics using Bayesian and non-Bayesian state-space models , Ecological Modelling, 200(3-4), 521-528. J. Horwood 1982], The variance of population and yield from an age-structured stock, with application to the North Sea herring (Clupea harengus) , ICES J. Mar. Sci. 40, 237-244. R.B. Miller, and R. Meyer 2000], Bayesian state-space modeling of age-structured data: fitting a model is just the beginning , Can. J. Fish. Aquat. Sci. 57, 43-50. G.W. Oehlert 1992], A Note on the Delta Method. The American Statistician , 46(1), 27-29. D.A. Fournier, J. Hampton, and J.R. Sibert 1998], MULTIFAN-CL: a length-based, age-structured model for fisheries stock assessment, with application to South Pacific albacore, Thunnus alalunga , Can. J. Fish. Aquat. Sci. 55, 2105-2116. ICES-HAWG [2008], Report of the Herring Assessment Working Group South of 62N (HAWG) . ICES CM 2008/ACOM:02, Copenhagen , Denmark . M.K. McAllister, and J.N. Ianelli 1997], Bayesian stock assessment using catch-age data and the sampling-importance resampling algorithm , Can. J. Fish. Aquat. Sci. 54, 284-300. T.J. Quinn II, and R.B. Deriso 1999], Quantitative Fish Dynamics , Oxford University Press, New York . A.D. MacCall 1986], Virtual population analysis (VPA) equations for nonhomogeneous populations, and a family of approximations including improvements on Pope's cohort analysis , Can. J. Fish. Aquat. Sci. 43, 2406-2409. Ø. Ulltang 1977], Sources of errors in and limiations of virtual population analysis (cohort analysis) , J. Cons. Int. Explor. Mer. 37, 249-260. L.T. Kell, I. Mosqueira, P. Grosjean, J.-M. Fromentin, D. Garcia, R.M. Hillary, E. Jardim, S. Mardle, M.A. Pastoors, J.-J. Poos, F. Scott, and R.D. Scott 2007], FLR: an open source framework for the evaluation and development of management strategies , ICES J. Mar. Sci. 64, 640-646. S.E. Sims 1982], Algorithms for solving the catch equation forward and backward in time , Can. J. Fish. Aquat. Sci. 39, 197-202. B. Bull, R.I.C.C. Francis, A. Dunn, A. McKenzie, D.J. Gilbert and M.H. Smith 2005], CASAL User Manual v2.07-2005/07/06 , NIWA Technical Report, 126. J.G. Shepherd 1999], Extended Survivors Analysis: an improved method for the analysis of catch-at-age data and abundance indices , ICES J. Mar. Sci. 56, 584-591. ICES-WGMG [2009], Report of the Working Group on Methods of Fish Stock Assessment (WGMG) , ICES CM 2009/RMC:12, Copenhagen , Denmark . A.E. Punt, and R. Hilborn 1997], Fisheries stock assessment and decision analysis: the Bayesian approach , Rev. Fish. Bio. Fish. 7, 35-63. M.J. Bradford 1991], Effects of ageing errors on recruitment time series estimated from sequential population analysis , Can. J. Fish. Aquat. Sci. 48, 555-558. J.G. Pope 1972], An investigation of the accuracy of virtual population analysis using cohort analysis , Int. Comm. Northwest Atl. Fish. Res. Bull. 9, 65-74. D.B. Sampson 1987], Variance estimators for Virtual Population Analysis , J. Cons. Int. Explor. Mer 43, 149-158. T.A. Branch 2009], Differences in predicted catch composition between two widely used catch equation formulations , Can. J. Fish. Aquat. Sci. 66, 126-132. S. Gavaris 1988], An adaptive framework for the estimation of population size , Canadian Atlantic Fisheries Science Advisory Committee (CAFSAC), Dartmouth , N.S. Res. Doc. 88/29. R.D. Methot 1989], Synthetic estimates of historical abundance and mortality for northern anchovy , Am. Fish. Soc. Symp. 6, 66-82. K.R. Patterson 1999], Evaluating uncertainty in harvest control law catches using Bayesian Markov chain Monte Carlo virtual population analysis with adaptive rejection sampling and including structural uncertainty , Can. J. Fish. Aquat. Sci. 56, 208-221. S.A. Reeves 2003], A simulation study of the implication of age-reading errors for stock assessment and management advice , ICES J. Mar. Sci. 60, 314-328. M. Aksland 1994], A general cohort analysis method , Biometrics. 50(4), 917-932. F.I. Baranov 1918], On the question of the biological basis of fisheries , Nauch. Issledov. Iktiol. Inst. Izv. I (1), Moscow , pp. 81-128. G. Mertz, and R.A. Myers 1996], An extended cohort analysis: incorportating the effect of seasonal catches , Can. J. Fish. Aquat. Sci. 53, 159-163. K. Patterson, and G. Melvin 1996], Integrated catch-at-age analysis version 1.2 , Stochttish Fisheries Research Report, 56. FRS Marine Laboratory, Aberdeen , UK . J. Horwood 1983], A General Linear Theory for the Variance of the Yield from Fish Stocks , Mathematical Biosciences. 64, 203-225. 2009; 66 2007; 200 1972; 9 1982; 39 1989; 6 2009 2008 1996 2005 2002 1918 1996; 53 1997; 7 1999 1987; 43 1991; 48 1977; 37 1997; 54 1986; 43 1982; 40 2000; 57 1983; 64 1999; 56 1992; 46 2007; 64 2003; 60 1994; 50 1998; 55 1988 e_1_2_6_10_1 ICES‐HAWG (e_1_2_6_11_1) 2008 e_1_2_6_31_1 e_1_2_6_30_1 Quinn T.J. (e_1_2_6_26_1) 1999 Bradford M.J. (e_1_2_6_5_1) 1991; 48 e_1_2_6_13_1 Wang G. (e_1_2_6_32_1) 2007 e_1_2_6_14_1 Patterson K.R. (e_1_2_6_22_1) 1999; 56 Miller R.B. (e_1_2_6_19_1) 2000; 57 e_1_2_6_17_1 e_1_2_6_15_1 e_1_2_6_16_1 Gavaris S. (e_1_2_6_8_1) 1988 e_1_2_6_20_1 ICES‐WGMG (e_1_2_6_12_1) 2009 e_1_2_6_9_1 Methot R.D. (e_1_2_6_18_1) 1989; 6 Pope J.G. (e_1_2_6_23_1) 1972; 9 e_1_2_6_4_1 e_1_2_6_7_1 Baranov F.I. (e_1_2_6_3_1) 1918 e_1_2_6_25_1 e_1_2_6_24_1 Bull B. (e_1_2_6_6_1) 2005 e_1_2_6_2_1 Patterson K. (e_1_2_6_21_1) 1996 e_1_2_6_29_1 e_1_2_6_28_1 e_1_2_6_27_1 |
| References_xml | – reference: K.R. Patterson 1999], Evaluating uncertainty in harvest control law catches using Bayesian Markov chain Monte Carlo virtual population analysis with adaptive rejection sampling and including structural uncertainty , Can. J. Fish. Aquat. Sci. 56, 208-221. – reference: S.A. Reeves 2003], A simulation study of the implication of age-reading errors for stock assessment and management advice , ICES J. Mar. Sci. 60, 314-328. – reference: J. Horwood 1982], The variance of population and yield from an age-structured stock, with application to the North Sea herring (Clupea harengus) , ICES J. Mar. Sci. 40, 237-244. – reference: G.W. Oehlert 1992], A Note on the Delta Method. The American Statistician , 46(1), 27-29. – reference: ICES-WGMG [2009], Report of the Working Group on Methods of Fish Stock Assessment (WGMG) , ICES CM 2009/RMC:12, Copenhagen , Denmark . – reference: R.D. Methot 1989], Synthetic estimates of historical abundance and mortality for northern anchovy , Am. Fish. Soc. Symp. 6, 66-82. – reference: L.T. Kell, I. Mosqueira, P. Grosjean, J.-M. Fromentin, D. Garcia, R.M. Hillary, E. Jardim, S. Mardle, M.A. Pastoors, J.-J. Poos, F. Scott, and R.D. Scott 2007], FLR: an open source framework for the evaluation and development of management strategies , ICES J. Mar. Sci. 64, 640-646. – reference: A.E. Punt, and R. Hilborn 1997], Fisheries stock assessment and decision analysis: the Bayesian approach , Rev. Fish. Bio. Fish. 7, 35-63. – reference: F.I. Baranov 1918], On the question of the biological basis of fisheries , Nauch. Issledov. Iktiol. Inst. Izv. I (1), Moscow , pp. 81-128. – reference: G. Mertz, and R.A. Myers 1996], An extended cohort analysis: incorportating the effect of seasonal catches , Can. J. Fish. Aquat. Sci. 53, 159-163. – reference: J. Horwood 1983], A General Linear Theory for the Variance of the Yield from Fish Stocks , Mathematical Biosciences. 64, 203-225. – reference: B. Bull, R.I.C.C. Francis, A. Dunn, A. McKenzie, D.J. Gilbert and M.H. Smith 2005], CASAL User Manual v2.07-2005/07/06 , NIWA Technical Report, 126. – reference: S. Gavaris 1988], An adaptive framework for the estimation of population size , Canadian Atlantic Fisheries Science Advisory Committee (CAFSAC), Dartmouth , N.S. Res. Doc. 88/29. – reference: J.G. Shepherd 1999], Extended Survivors Analysis: an improved method for the analysis of catch-at-age data and abundance indices , ICES J. Mar. Sci. 56, 584-591. – reference: G. Wang 2007], On the latent state estimation of nonlinear population dynamics using Bayesian and non-Bayesian state-space models , Ecological Modelling, 200(3-4), 521-528. – reference: S.E. Sims 1982], Algorithms for solving the catch equation forward and backward in time , Can. J. Fish. Aquat. Sci. 39, 197-202. – reference: Ø. Ulltang 1977], Sources of errors in and limiations of virtual population analysis (cohort analysis) , J. Cons. Int. Explor. Mer. 37, 249-260. – reference: M. Aksland 1994], A general cohort analysis method , Biometrics. 50(4), 917-932. – reference: D.B. Sampson 1987], Variance estimators for Virtual Population Analysis , J. Cons. Int. Explor. Mer 43, 149-158. – reference: M. Maunder, and R.B. Deriso 2003], Estimation of recruitment in catch-at-age models , Can. J. Fish. Aquat. Sci. 60, 1204-1216. – reference: T.J. Quinn II, and R.B. Deriso 1999], Quantitative Fish Dynamics , Oxford University Press, New York . – reference: T.A. Branch 2009], Differences in predicted catch composition between two widely used catch equation formulations , Can. J. Fish. Aquat. Sci. 66, 126-132. – reference: M.J. Bradford 1991], Effects of ageing errors on recruitment time series estimated from sequential population analysis , Can. J. Fish. Aquat. Sci. 48, 555-558. – reference: K. Patterson, and G. Melvin 1996], Integrated catch-at-age analysis version 1.2 , Stochttish Fisheries Research Report, 56. FRS Marine Laboratory, Aberdeen , UK . – reference: J.G. Pope 1972], An investigation of the accuracy of virtual population analysis using cohort analysis , Int. Comm. Northwest Atl. Fish. Res. Bull. 9, 65-74. – reference: R.B. Miller, and R. Meyer 2000], Bayesian state-space modeling of age-structured data: fitting a model is just the beginning , Can. J. Fish. Aquat. Sci. 57, 43-50. – reference: M.K. McAllister, and J.N. Ianelli 1997], Bayesian stock assessment using catch-age data and the sampling-importance resampling algorithm , Can. J. Fish. Aquat. Sci. 54, 284-300. – reference: D.A. Fournier, J. Hampton, and J.R. Sibert 1998], MULTIFAN-CL: a length-based, age-structured model for fisheries stock assessment, with application to South Pacific albacore, Thunnus alalunga , Can. J. Fish. Aquat. Sci. 55, 2105-2116. – reference: A.D. MacCall 1986], Virtual population analysis (VPA) equations for nonhomogeneous populations, and a family of approximations including improvements on Pope's cohort analysis , Can. J. Fish. Aquat. Sci. 43, 2406-2409. – reference: ICES-HAWG [2008], Report of the Herring Assessment Working Group South of 62N (HAWG) . ICES CM 2008/ACOM:02, Copenhagen , Denmark . – year: 2009 – volume: 64 start-page: 640 year: 2007 end-page: 646 publication-title: ICES J. Mar. Sci. – volume: 60 start-page: 314 year: 2003 end-page: 328 publication-title: ICES J. Mar. Sci. – volume: 66 start-page: 126 year: 2009 end-page: 132 publication-title: Can. J. Fish. Aquat. Sci. – volume: 7 start-page: 35 year: 1997 end-page: 63 publication-title: Rev. Fish. Bio. Fish. – volume: 56 start-page: 208 year: 1999 end-page: 221 publication-title: Can. J. Fish. Aquat. Sci. – volume: 60 start-page: 1204 year: 2003 end-page: 1216 publication-title: Can. J. Fish. Aquat. 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| Snippet | Using an exploitation rate (not fishing mortality) based virtual population analysis (VPA) algorithm, which is itself a generalization of the Pope... Abstract Using an exploitation rate (not fishing mortality) based virtual population analysis (VPA) algorithm, which is itself a generalization of the Pope... Abstract Using an exploitation rate (not fishing mortality) based virtual population analysis (VPA) algorithm, which is itself a generalization of the Pope... |
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| SubjectTerms | Algorithms catch-at-age Estimates exploitation rate Marine Studies uncertainty Virtual population analysis |
| Title | ASSESSING COMPONENTS OF UNCERTAINTY IN VPA ABUNDANCE AND MORTALITY ESTIMATES USING AN ALTERNATIVE EXPLOITATION RATE-BASED ALGORITHM |
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