Admitting ageing error when fitting growth curves: An example using the von Bertalanffy growth function with random effects

Canadian Journal of Fisheries and Aquatic Sciences

Volumn 64, Issue 2, 2007, Pages 205-218

  Cope, Jason M ^a   Punt, André E ^a  

^a UNIVERSITY OF WASHINGTON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

AGING POPULATION; COMPARATIVE STUDY; ESTIMATION METHOD; GAMMA RAY RADIATION; GROWTH CURVE; GROWTH MODELING; LIFE HISTORY; RECRUITMENT; SENSITIVITY ANALYSIS;

EID: 34248136856     PISSN: 0706652X     EISSN: None     Source Type: Journal    
DOI: 10.1139/F06-179     Document Type: Article

References (66)

1. Appledoorn, R.S. 1982. Variation in the growth rate of Mya arenaria and its relationship to the environment as analyzed through principle component analysis and the omega parameter of the von Bertalanffy equation. Fish. Bull. 81: 75-84.
2. Beamish, R.J., and Fournier, D.A. 1981. A method for comparing the precision of a set of age determinations. Can. J. Fish. Aquat. Sci. 38: 982-983.
3. Beverton, R.J.H. 1992. Patterns of reproductive strategy parameters in some marine teleost fishes. J. Fish Biol. 41(Suppl. B): 137-160.
4. Beverton, R.J.H., and Holt, S.J. 1957. On the dynamics of exploited fish populations. Chapman and Hall, London, UK.
5. Beverton, R.J.H., and Holt, S.J. 1959. A review of the life-spans and mortality rates of fish in nature, and their relationship on growth and other physiological characteristics. In Ciba Foundation Colloquia on Ageing. Vol. 5. The lifespan of animals. J. & A. Churchill Ltd., London, UK.
6. Bowker, D.W. 1995. Modeling the patterns of dispersion of length at age in teleost fishes. J. Fish Biol. 46(3): 469-484.
7. Bradford, M.J. 1991. Effects of ageing errors on recruitment time series estimated from sequential population analysis. Can. J. Fish. Aquat. Sci. 48: 555-558.
8. Cailliet, G.M., and Goldman, K.J. 2004. Age determination and validation in chondrichthyan fishes. In Biology of sharks and their relatives. Edited by J. Carrier, J.A. Musick, and M.R. Heithaus. CRC Press LLC, Boca Raton, Fla. pp. 399-447.
9. Cailliet, G.M., Yudin, K.G., Tanaka, S., and Taniuchi, T. 1990. Growth characteristics of two populations of Mustelus manazo from Japan based upon cross-readings of vertebral bands. NOAA Tech. Rep. No. 90.
10. Campana, S.E. 2001. Accuracy, precision and quality control in age determination, including a review of the use and abuse of age validation methods. J. Fish Biol. 59(2): 197-242.
11. Campana, S.E., Annand, M.C., and McMillan, J.I. 1995. Graphical and statistical methods for determining the consistency of age determination. Trans. Am. Fish. Soc. 124: 131-138.
12. Casella, G., and Berger, R.L. 2002. Statistical inference. Duxbury, Pacific Grove, Calif.
13. Chang, W.Y.B. 1982. A statistical method for evaluating the reproducibility of age determination. Can. J. Fish. Aquat. Sci. 39: 1208-1210.
14. Charnov, E.L. 1993. Life history invariants: some explorations of symmetry in evolutionary ecology. Oxford University Press, Oxford, UK.
15. Chen, Y., Jackson, D.A., and Harvey, H.H. 1992. A comparison of von Bertalanffy and polynomial functions in modeling fish growth data. Can. J. Fish. Aquat. Sci. 49: 1228-1235.
16. Clark, W.G. 1991. Groundfish exploitation rates based on life history parameters. Can. J. Fish. Aquat. Sci. 48: 734-750.
17. Cloern, J.E., and Nichols, F.H. 1978. A von Bertalanffy growth model with a seasonally varying coefficient. J. Fish. Res. Board Can. 35: 1479-1482.
18. Dunn, A., Francis, R.I.C.C., and Doonan, I.J. 2002. Comparison of the Chapman-Robson and regression estimators of Z from catch-curve data when non-sampling stochastic error is present. Fish. Res. 59(1-2): 149-159.
19. Evans, G.T., and Hoenig, J.M. 1998. Testing and viewing symmetry in contingency tables, with application to readers of fish ages. Biometrics, 54: 620-629.
20. Fabens, A.J. 1965. Properties and fitting of the von Bertalanffy growth curve. Growth, 29: 265-289.
21. Gay, D. 1996. More AD of nonlinear AMPL models: computing Hessian information and exploiting partial separability. In Computational differentiation: techniques, applications, and tools. Edited by M. Berz, C. Bischof, G. Corliss, and A. Griewank. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, Pa. pp. 173-184.
22. Grebel, J.M. 2003. Age, growth, and maturity of cabezon, Scorpaenichthys marmoratus, in California. M.S. thesis, Moss Landing Marine Laboratories, San Jose State University, Calif.
23. Gulland, J.A. 1983. Fish stock assessment: a manual of basic methods. John Wiley & Sons, Chichester, UK.
24. Haddon, M. 2001. Modelling and quantitative methods in fisheries. Chapman and Hall, London, UK.
25. Jensen, A.L. 1998. Simulation of relations among fish life history parameters with a bioenergetics-based population model. Can. J. Fish. Aquat. Sci. 55(2): 353-357.
26. Kimura, D.K. 1980. Likelihood estimates for the von Bertalanffy growth curve. Fish. Bull. 77: 765-776.
27. Kimura, D.K. 2000. Using nonlinear functional relationship regression to fit fisheries models. Can. J. Fish. Aquat. Sci. 57(1): 160-170.
28. Kimura, D.K., and Anderl, D.M. 2005. Quality control of age data at the Alaska Fisheries Science Center. Mar. Freshw. Res. 56(5): 783-789.
29. Kimura, D.K., and Lyons, J.J. 1991. Between-reader bias and variability in the age-determination process. Fish. Bull. 89(1): 53-60.
30. Lai, H.L., and Gunderson, D. 1987. Effects of ageing error on estimates of growth, mortality and yield per recruit for walleye pollock (Theragra chalcogramma). Fish. Res. 5: 287-302.
31. Marquardt, D.W. 1963. An algorithm for least-squares estimation of nonlinear parameters. J. Soc. Indust. Appl. Math. 11(2): 431-441.
32. Nummi, T. 2000. Analysis of growth curves under measurement errors. J. Appl. Stat. 27(2): 235-243.
33. Otter Research Ltd. 2005a. An introduction to AD Model Builder. Version 7.0.1. For use in non-linear modeling and statistics. Otter Research Ltd., Sydney, B.C.
34. Otter Research Ltd. 2005b. Random effects in AD Model Builder: ADMB-RE user guide. Otter Research Ltd., Sydney, B.C.
35. Palmer, M.J., Phillips, B.F., and Smith, G.T. 1991. Application of nonlinear models with random coefficients to growth data. Biometrics, 47: 623-635.
36. Parma, A.M., and Deriso, R.B. 1990. Dynamics of age and size composition in a population subject to size-selectivity mortality: effects of phenotypic variability in growth. Can. J. Fish. Aquat. Sci. 47: 274-289.
37. Pilling, G.M., Kirkwood, G.P., and Walker, S.G. 2002. An improved method for estimating individual growth variability in fish, and the correlation between von Bertalanffy growth parameters. Can. J. Fish. Aquat. Sci. 59(3): 424-432.
38. Piner, K.R., Hamel, O.S., Menkel, J.L., Wallace, J.R., and Hutchinson, C.E. 2005. Age validation of canary rockfish (Sebastes pinniger) from off the Oregon coast (USA) using the bomb radiocarbon method. Can. J. Fish. Aquat. Sci. 62(5): 1060-1066.
39. Piner, K.R., Wallace, J.R., Hamel, O.S., and Mikus, R. 2006. Evaluation of ageing accuracy of bocaccio (Sebastes paucispinis) rockfish using bomb radiocarbon. Fish. Res. 77(2): 200-206.
40. Pitcher, T.J., and MacDonald, P.D.M. 1973. Two models for seasonal growth in fishes. J. Appl. Ecol. 10(2): 599-606.
41. Prajneshu, and Venugopalan, R. 1999. von Bertalanffy growth model in a random environment. Can. J. Fish. Aquat. Sci. 56: 1026-1030.
42. Quinn, T.J., and Deriso, R.B. 1999. Quantitative fish dynamics. Oxford University Press, New York.
43. Rafail, S.Z. 1973. A simple and precise method for fitting a von Bertalanffy growth curve. Mar. Biol. 19: 354-358.
44. Reeves, S.A. 2003. A simulation study of the implications of age-reading errors for stock assessment and management advice. ICES J. Mar. Sci. 60(2): 314-328.
45. Richards, L.J., Schnute, J.T., Kronlund, A.R., and Beamish, R.J. 1992. Statistical models for the analysis of ageing errors. Can. J. Fish. Aquat. Sci. 49(9): 1801-1815.
46. Sainsbury, K.J. 1980. Effect of individual variability on the von Bertalanffy growth equation. Can. J. Fish. Aquat. Sci. 37: 241-247.
47. Schnute, J.T. 1981. A versatile growth model with statistically stable parameters. Can. J. Fish. Aquat. Sci. 38: 1128-1140.
48. Sinclair, A.F., Swain, D.P., and Hanson, J.M. 2002. Disentangling the effects of size-selective mortality, density, and temperature on length-at-age. Can. J. Fish. Aquat. Sci. 59(2): 372-382.
49. Skaug, H., and Fournier, D. 2006. Automatic approximation of the marginal likelihood in non-Gaussian hierarchical models. Computational Statistics & Data Analysis, 51: 699-709.
50. Stamatopoulos, C., and Caddy, J.F. 1989. Estimation of von Bertalanffy growth parameters: a versatile linear regression approach. J. Cons. Int. Explor. Mer, 45: 200-208.
51. Stevens, M.M., Andrews, A.H., Cailliet, G.M., Coale, K.H., and Lundstrom, C.C. 2004. Radiometric validation of age, growth, and longevity for the blackgill rockfish (Sebastes melanostomus). Fish. Bull. 102(4): 711-722.
52. Taylor, N.G., Walters, C.J., and Martell, S.J.D. 2005. A new likelihood for simultaneously estimating von Bertalanffy growth parameters, gear selectivity, and natural and fishing mortality. Can. J. Fish. Aquat. Sci. 62(1): 215-223.
53. Tomlinson, P.K., and Abramson, N.J. 1961. Fitting a von Bertalanffy growth curve by least squares. California Department of Fish and Game, Sacramento, Calif. Fish. Bull. No. 116.
54. Troynikov, V.S. 1999. Use of Bayes theorem to correct size-specific sampling bias in growth data. Bull. Math. Biol. 61: 355-363.
55. Tyler, A.V., Beamish, R.J., and McFarlane, G.A. 1989. Implications of age determination errors to yield estimates. In Effects of ocean variability on recruitment and an evaluation of parameters used in stock assessment models. Edited by R.J. Beamish and G.A. McFarlane. Can. Spec. Publ. Fish. Aquat. Sci. No. 108. pp. 27-35.
56. Vaughan, D.S., and Burton, M.L. 1994. Estimation of von Bertalanffy growth parameters in the presence of size-selected mortality: a simulated example with red grouper. Trans. Am. Fish. Soc. 123(1): 1-8.
57. Venugopalan, R., and Prajneshu. 1997. von Bertalanffy growth model with autocorrelated errors. Indian J. Fish. 44: 63-67.
58. von Bertalanffy, L. 1934. Untersuchungen uber die Gestzlichkeit des Wachstums. 1. Teil. Allgemeine Grundlagen der Theorie; mathematische and physiologische Gesetzlichkeiten des Wachstums bei Wassertieren. Arch. Entwicklungsmech. Org. (Wilhelm Roux), 131: 613-652.
59. von Bertalanffy, L. 1938. A quantitative theory of organic growth. Hum. Biol. 10: 181-213.
60. Walford, L. 1946. A new graphical method of describing the growth of animals. Biol. Bull. 90: 141-147.
61. Wang, Y.-G. 1998. An improved Fabens method for estimation of growth parameters in the von Bertalanffy model with individual asymptotes. Can. J. Fish. Aquat. Sci. 55: 397-400.
62. Wang, Y.-G., and Ellis, N. 1998. Effect of individual variability on estimation of population parameters from length-frequency data. Can. J. Fish. Aquat. Sci. 55: 2393-2401.
63. Wang, Y.-G., and Ellis, N. 2005. Maximum likelihood estimation of mortality and growth with individual variability from multiple length-frequency data. Fish. Bull. 103: 380-391.
64. Wang, Y.-G., and Thomas, M.R. 1995. Accounting for individual variability in the von Bertalanffy growth model. Can. J. Fish. Aquat. Sci. 52: 1368-1375.
65. Weatherley, A.H., and Gill, H.S. 1987. The biology of fish growth. Academic Press, London, UK.
66. Williams, E.H., and Shertzer, K.W. 2003. Implications of life-history invariants for biological reference points used in fishery management. Can. J. Fish. Aquat. Sci. 60(6): 710-720.