Von Bertalanffy References

Summary of selected papers on growth. (Canadian authors are well represented!) Slide in abbreviated form was shown at 1995 AES meeting in Edmonton.

Please send comments, corrections, and updates to henry@elasmollet.org

Bertalanffy, L. von 1938. A quantitative theory of organic growth (Inquiries on growth laws. II). Human Biol. 10: 181-213. Von Bertalanffy introduced growth function (VBGF). Form used was L(t) = Loo - (Loo - Lo) exp (-kt).
Gulland, J. A. & Holt S. J. 1959. Estimation of growth parameters for data at unequal time intervals. J. du Conseil International pour l'Explorations de la Mer 25: 47-49.
Richards, F. J. 1959. A flexible growth function for empirical use. J. Exp. Botany 10: 290-300.
Bertalanffy, L. von 1960. Principles and theory of growth. In Fundamental aspects of normal and malignant growth. Pp 137-259. W. W. Nowinski ed. Elsevier, Amsterdam.
Aasen, O. 1963. Length and growth of the porbeagle (Lamna nasus, Bonnaterre) in the North West Atlantic. Rep. Norw. Fishery Mar. Invest. 13: 20-37.
Fabens, A. J. 1965.. Properties and fitting of the von Bertalanffy growth curve. Growth 29: 265-289.
Allen, K. R. 1966. A method of fitting growth curves of the von Bertalanffy type to observed data. J. Fish. Res. Bd. Canada 23: 163-169.
Knight, W. 1968. Asymptotic growth: an example of nonsense disguised as mathematics. J. Fish, Res. Bd. Canada 25: 1303-1307.
Knight, W. 1969. Re-formulation of the von Bertalanffy growth curve when the growth rate is roughly constant. J. Fish. Red. Bd. Canada 26: 3069-3072. Linear re-formulation of VBGF.
Hile, R. 1970. Body-scale relation and calculation of growth. Transactions of the American Fisheries Society 3: 468-474. (suggested by Patrícia Tiago)
Weatherly, A. H. 1972. Growth and ecology of fish populations. Academic Press London.
Chapter 2: Growth in animals: Central concepts.
Ricker, W. E. 1973. Linear regressions in fishery research. J. Fish. Res. Bd. Canada 30: 409-434.
Ketchen, K. S. 1975. Age and growth of dogfish Squalus acanthias in British Columbia waters. J. Fish. Res. Board Can. 32: 43-59.
Kingsley C.S. 1979. Fitting the von Bertalanffy growth equation to polar bear age-weight data. Canadian Journal of Zoology 57: 1020-1025.
Galucci V. F. & Quinn T. J. 1979. Reparameterization, fitting, and testing a simple growth model. Trans. Amer. Fish. Soc. 108: 14-25. Re-parameterization of VBGF.
Pauly, D. 1979. Gill size and temperature as governing factors in fish growth: a generalization of von Bertlanffy's growth formula. Berichte aus dem Instiute fuer Meereskunde 63: ?. Kiel University, Kiel, Germany. Generalized VBGF, 4th parameter D = 3(m-d) = D(W); k is stress factor rather than catabolic constant.
Ricker, W. E. 1979. Growth rates and models. In Fish physiology Vol. VIII. Pp. 677-743. Academic Press.
Sainsbury, K. J. 1980. Effect of individual variability on the von Bertalanffy growth equation. Can. J. Fish. Aquat. Sci. 37: 241-247.
Kingsley 1980. Incomplete reference.
Reparameterization of VBGF does not solve the problem .
Roff, D. A. 1980. A motion for the retirement of the von Bertalanffy function. Can. J. Fish. Aquat. Sci 37: 127-129.
Kimura, D. K. 1980. Likelihood estimates for the von Bertalanffy growth curve. Fishery Bulletin 77: 765-776.
Schnute, J. & D. Fournier 1980. A new approach to length-frequency analysis: growth structure. Can. J. Fish. Aquat. Sci. 37: 1337-1351.
Schnute, J. 1981. A versatile growth model with statistically stable parameters. Can. J. Fish. Aquat. Sci. 38: 1128-1140. VBGF, Richards, Gomperts, Logistic, and Linear Growth as special cases of new comprehensive model.
Francis, M. P. 1981. Von Bertalanffy growth rates in species of Mustelus (Elasmobranchii: Triakidae). Copeia 1981: 189-192.
Vaughan, D. S. & P. Kanciruk 1982. An empirical comparison of estimation procedures for the von Bertalanffy growth equation. J. cons. int. Explor. Mer. 40: 211-219.
Kirkwood, G. P. 1983. Estimation of von Bertalanffy growth curve parameters using both length increment and age-length data. Can. J. Fish. Aquat. Sci. 40: 1405-1411.
Kirkwood, G. P. and I. F. Somers 1984. Growth of two species of tiger prawns, Penaeus esculentus and P. semisulcatus, in the western Gulf of Carpentaria. Aust. J. Mar. Freshwater. Res. 35: 703-12.
Joint confidences regions for VBGF parameters.
Sundberg, P. 1984. A Monte Carlo study of three methods for estimating the parameters in the von Bertalanffy equation. J. cons. int. Explor. Mer 41: 248-258.
Chien, Y. H. and R. E. Condrey 1987. Bias in estimating growth parameters using Fabens' mark-recapture procedure. Asian Fisheries Science 1: 65-74. Asian Fisheries Society, Manila, Philippines.
Moreau, J. 1987. Mathematical and biological expression of growth in fishes: recent trends and further developments, pp. 81-113. In The age and growth of fish. R.C. Summerfelt & G. E. Hall eds. ISU Press, Ames IA. Review of growth models including Pauly 1979.
Weisberg, S. & R. V. Frie 1987. Linear models for the growth of fish, pp. 127-143. In The age and growth of fish. R.C. Summerfelt & G. E. Hall eds. ISU Press, Ames IA.
McDonald, P. D. M. 1987. Analysis of length-frequency distributions, pp. 371-384. In The age and growth of fish. R.C. Summerfelt & G. E. Hall eds. ISU Press, Ames IA.
Francis, R. I. C. C. 1988. Maximum likelihood estimates of growth and growth variability from tagging data. New Zealand Journal of Marine and Freshwater Research 22: 42-51.
Francis, R. I. C. C. 1988. Are growth parameters estimated from tagging and age-length data comparable? Can. J. Fish. Aquat. Sci. 45: 936-942.
Maller, R. A. & E. S. deBoer 1988. An analysis of two methods of fitting the von Bertalanffy curve to capture-recapture data. Aust. J. Freshwater Res. 39: 459-66.
Stamatopoulus, C. & J. F. Caddy 1989. Estimation of von Bertalanffy growth parameters: A versatile linear regression approach. J. Cons. int. Explor. Mer 45: 200-208.
Cerrato, R. M. 1990. Interpretable statistical tests for growth comparisons using parameters in the von Bertalanffy equation. Can. J. Fish. Aquat. Sci. 47: 1416-1426.
Schnute, J. T. & L. J. Richards 1990.. A unified approach to the analysis of fish growth, maturity, and survivorship data. Can. J. Fish. Aquat. Sci. 47: 24-40.
Francis, R. I. C. C. 1990. . Back-calculation of fish length: a critical review. J. Fish Biol. 36 883-902.
Casselman, J.M. 1990. Growth and relative size of calcified structures of fish. Transactions of the American Fisheries Society 119: 673-688. (suggested by Patrícia Tiago)
Weatherley, A.H. 1990. Approaches to understand fish growth. Transactions of the American Fisheries Society 119: 662-672. (suggested by Patrícia Tiago)
James, I. R. 1991.. Estimation of von Bertalanffy growth curve parameters from recapture data. Biometrics 47, 1519-1530.
Hampton, J. 1991. Estimation of southern bluefin tuna Thunnus maccoyii growth parameters from tagging data, using von Bertalanffy models incorporating individual variation. Fishery Bulletin U.S. 89: 577-590.
Essington, T. E., Kitchell J. F., and Walters C. J. (2001). The von Bertalanffy growth function, bioenergetics, and the consumption rates of fish. Can. J. Fish. Aquat. Sci. 58, 2129-2138.
Cailliet, G. M., H. F. Mollet, G. G. Pittenger, D. Bedford, & L. J. Natanson 1992. Growth and demography of the pacific angel shark (Squatina californica), based upon tag returns off California. Aust. J. Mar. Freshwater Res. 43: 1313-30. Resurrection of Gulland-Holt method.
Pauly, D., M. Soriano-Bartz, J. Moreau & A. Jarre-Teichmann1992.. A new model accounting for seasonal cessation of growth in fishes. Aust. J. Mar. Freshwater Res. 43: 1151-6.
Moulton et al. 1992. Age and Growth Studies of Gummy Shark and School Shark. Incomplete reference.
Anderson et al. 1992. Age and Growth of Murray Cod. Incomplete reference.
Rowling and Reid 1992. Effect of Temporal Changes in Size Composition on Estimates of VBGF Parameters for Gemfish. Incomplete reference.
Francis R. et al. 1992. Aging of adult Snapper from Otoliths Annual Ring Counts. Incomplete reference.
Francis, M. P. & Francis, R. I. C. C. 1993. Growth rate estimates of New Zealand rig, Mustelus lenticulatis. Incomplete reference., see VBGF papers.
Kimura, D. K., A. M. Shimada, S. A. Lowe 1993. . Estimating von Bertalanffy growth parameters of sablefish Anoplopoma fimbria and Pacific cod Gadus macrocepahlus using tag-recapture data. Fishery Bulletin U.S. 91: 271-280.
Saunders, M. W., & G. A. McFarlane 1993.. Age and length at maturity of the female spiny dogfish (Squalus acanthias) in the Strait of Georgia, British Columbia, Canada. In The reproduction and development of sharks, skates, rays and ratfishes. Eds. L. S. Demski & J. P. Wourms. Reprinted from Environmental Biology of Fishes 38: 49-57.
Bjorndal, K. A., A. B. Bolten, A. L. Coan Jr., & P. Kleiber 1995. Estimation of green turtle (Chleonia mydas) growth rates from length-frequency analysis. Copeia 1995: 71-77.
2006. Updated technical summary based on presentation at the June 1995 AES meeting in Edmonton, Canada. Items from this page were later published in Caillet et al. (2006, download pdf, p.219 "L0 vs. t0 and other aspects of the von Bertalanffy growth function (VBGF)" ) and in Natanson et al. (2006, download pdf, p.373 "Longevity")
Created February 1998; updated March 2006.

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