Von Bertalanffy's growth equation should not be used to model age and size at maturity

American Naturalist

Volumn 149, Issue 2, 1997, Pages 381-393

  Day, Troy ^a   Taylor, Peter D ^a  

^a QUEEN S UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

GROWTH; GROWTH CURVES; MODELLING; MODELS; SEXUAL MATURITY; VON BERTALANFFY; VON BERTALANFFY EQUATION;

EID: 0031004408     PISSN: 00030147     EISSN: None     Source Type: Journal    
DOI: 10.1086/285995     Document Type: Review

References (42)

1. Alford, R. A., and R. N. Harris. 1988. Effects of larval growth history on amphibian metamorphosis. American Naturalist 131:91-106.
2. Alford, R. A., and G. D. Jackson. 1993. Do cephalopods and larvae of other taxa grow asymptomatically? American Naturalist 141:717-728.
3. Bernardo, J. 1993. Determinants of maturation in animals. Trends in Ecology & Evolution 8:166-173.
4. Berrigan, D., and J. C. Koella. 1994. The evolution of reaction norms: simple models for age and size at maturity. Journal of Evolutionary Biology 7:549-566.
5. Blueweiss, L., H. Fox, V. Kudzma, D. Nakashima, R. Peters, and S. Sams. 1978. Relationship between body size and some life history parameters. Oecologia (Berlin) 37:257-272.
6. Brett, J. R. 1979. Environmental factors and growth. Pages 599-675 in W. S. Hoar, D. J. Randall, and J. R. Brett, eds. Fish physiology. Vol. 8. Bioenergetics and growth. Academic Press, New York.
7. Brett, J. R., and J. E. Shelbourne. 1975. Growth rate of young sockeye salmon, Oncorhynchus nerka, in relation to fish size and ration level. Journal of the Fisheries Research Board of Canada 32:2103-2110.
8. Case, T. J. 1978. On the evolution and adaptive significance of postnatal growth rates in the terrestrial vertebrates. Quarterly Review of Biology 53:243-282.
9. Charlesworth, B. 1994. Evolution in age-structured populations. 2d ed. Cambridge University Press, Cambridge.
10. Charnov, E. L. 1989. Natural selection on age of maturity in shrimp. Evolutionary Ecology 3:236-239.
11. _. 1990. On evolution of age of maturity and the adult lifespan. Journal of Evolutionary Biology 3:139-144.
12. _. 1993. Life history invariants. Oxford University Press, Oxford.
13. Comyns, B. H., J. Lyczkowski-Shultz, C. F. Rakocinski, and J. P. Steen. 1989. Age and growth of red drum larvae in the north-central Gulf of Mexico. Transactions of the American Fisheries Society 118:159-167.
14. Deegan, L. A., and B. A. Thompson. 1987. Growth rate and life history events of young-of-the year gulf menhaden as determined from otoliths. Transactions of the American Fisheries Society 116:663-667.
15. Farlow, J. O. 1976. A consideration of the trophic dynamics of a late cretaceous large-dinosaur community (Oldman Formation). Ecology 57:841-857.
16. Hovenkamp, F., and J. J. Witte. 1991. Growth, otolith growth and RNA/DNA ratios of larval plaice Pleuronectes platessa in the North Sea 1987 to 1989. Marine Ecology Progress Series 70:105-116.
17. Jackson, G. D., and J. H. Choat. 1992. Growth in tropical cephalopods: an analysis based on statolith microstructure. Canadian Journal of Fisheries and Aquatic Sciences 49:218-228.
18. Kozłowski, J. 1992. Optimal allocation of resources to growth and reproduction: implications for age and size at maturity. Trends in Ecology & Evolution 7:15-19.
19. _. 1993. Measuring fitness in life-history studies. Trends in Ecology & Evolution 8:84-85.
20. Kozłowski, J., and J. Uchmanski. 1987. Optimal individual growth and reproduction in perennial species with indeterminate growth. Evolutionary Ecology 1:214-230.
21. Kozłowski, J., and R. G. Wiegert. 1986. Optimal allocation of energy to growth and reproduction. Theoretical Population Biology 29:16-37.
22. _. 1987. Optimal age and size at maturity in annuals and perennials with determinate growth. Evolutionary Ecology 1:231-244.
23. _. 1996. Optimal allocation of resources explains interspecific life-history patterns in animals with indeterminate growth. Proceedings of the Royal Society of London B, Biological Sciences 263:559-566.
24. Lavigne, D. M. 1982. Similarity of energy budgets of animal populations. Journal of Animal Ecology 51:195-206.
25. Mylius, S. D., and O. Diekmann. 1995. On evolutionarily stable life histories, optimization and the need to be specific about density dependence. Oikos 74:218-224.
26. Nagai, Y., S. Nagai, and T. Nishikawa. 1971. The nutritional efficiency of cannibalism and an artificial feed for the growth of tadpoles of Japanese toad (Bufo vulgaris sp.). Agricultural and Biological Chemistry 35:697-703.
27. Reiss, M. J. 1989. The allometry of growth and reproduction. Cambridge University Press, Cambridge.
28. Ricker, W. E. 1979. Growth rates and models. Pages 677-743 in W. S. Hoar, D. J. Randall, and J. R. Brett, eds. Fish physiology. Vol. 8. Bioenergetics and growth. Academic Press, New York.
29. Roff, D. A. 1980. A motion for the retirement of the von Bertalanffy function. Canadian Journal of Fisheries and Aquatic Sciences 37:127-129.
30. _. 1983. An allocation model of growth and reproduction in fish. Canadian Journal of Fisheries and Aquatic Science 40:1395-1404.
31. _. 1984. The evolution of life history parameters in teleosts. Canadian Journal of Fisheries and Aquatic Science 41:989-1000.
32. _. 1986. Predicting body size with life history models. BioScience 36:316-323.
33. _. 1992. The evolution of life histories: theory and analysis. Chapman & Hall, New York.
34. Schoener, T. W., and A. Schroener. 1978. Estimating and interpreting body-size growth in some Anolis lizards. Copeia 1978:390-405.
35. Shine, R., and E. L. Charnov. 1992. Patterns of survival, growth, and maturation in snakes and lizards. American Naturalist 139:1257-1269.
36. Sibly, R. M., and P. Calow. 1986. Physiological ecology of animals. Blackwell Scientific, Oxford.
37. Stearns, S. C. 1992. The evolution of life histories. Oxford University Press, Oxford.
38. Stearns, S. C., and J. C. Koella. 1986. The evolution of phenotypic plasticity in life history traits: predictions of reaction norms for age and size at maturity. Evolution 40:893-913.
39. Tzeng, W. N., and S. Y. Yu. 1988. Daily growth increments in the otoliths of milkfish, Chanos chanos (Forsskal), larvae. Journal of Fisheries Biology 32:495-504.
40. Ursin, E. 1967. A mathematical model of some aspects of fish growth, respiration and mortality. Journal of the Fisheries Research Board of Canada 24:2355-2453.
41. von Bertalanffy, L. 1957. Quantitative laws in metabolism and growth. Quarterly Review of Biology 32:217-231.
42. _. 1960. Principles and theory of growth. Pages 137-259 in W. W. Nowinski, ed. Fundamental aspects of normal and malignant growth. Elsevier, Amsterdam.