Ohnishi et al The von Bertalanffy growth function concerning the allocation of surplus energy to reproduction 
229 
be used to model age and size at maturity. Am. Nat. 
149:381-393. 
Eveson, J. P., G. M. Laslett, and T. Polacheck. 
2004. An integrated model for growth incorporating 
tag-recapture, length-frequency, and direct aging 
data. Can. J. Fish. Aquat. Sci. 61:292-306. 
Jensen, A. L. 
1996. Beverton and Holt life history invariants result from 
optimal trade-off of reproduction and survival. Can. 
J. Fish. Aquat. Sci. 53:820-822. 
Jorgensen, C., and 0. Fiksen. 
2006. State-dependent energy allocation in cod ( Gadus 
morhua). Can. J. Fish. Aquat. Sci. 63:186-199. 
Kozlowski, J. 
1992. Optimal allocation of resources to growth and 
reproduction: Implications for age and size at matu- 
rity. Trends Ecol. Evol. 7:15-19. 
1996. Optimal allocation of resources explains inter- 
specific life-history patterns in animals with inde- 
terminate growth. Proc. R. Soc. Lond. B 263:559 
-566. 
Kozlowski, J., and A. T. Teriokhin. 
1999. Allocation of energy between growth and reproduc- 
tion: The Pontryagin Maximum Principle solution for 
the case of age- and season-dependent mortality. Evol. 
Ecol. Res. 1:423-441. 
Lester, N. P., B. J. Shuter, and P. A. Abrams. 
2004. Interpreting the von Bertalanffy model of somatic 
growth in fishes: the cost of reproduction. Proc. R. 
Soc. Lond. B 271:1625-1631. 
Lincoln, R. J., G. A. Boxshall, and P. F. Clark. 
1998. A dictionary of ecology, evolution and systematics, 
361 p. Cambridge Univ. Press, New York. 
Martin, I., and R. M. Cook. 
1990. Combined analysis of length and age-at-length 
data. J. Cons. Int. Explor. Mer 46:178-186. 
Ohnishi, S., and T. Akamine. 
2006. Extension of von Bertalanffy growth model incor- 
porating growth patterns of soft and hard tissues in 
bivalve molluscs. Fish. Sci. 72:787-795. 
Pecquerie, L., P. Petitgas, and S. A. L. M. Kooijman. 
2009. Modeling fish growth and reproduction in the con- 
text of the Dynamic Energy Budget theory to predict 
environmental impact on anchovy spawning duration. J. 
Sea Res. 62:93-105. 
Porch, C. E., C. A. Wilson, and D. L. Nieland. 
2002. A new growth model for red drum ( Sciaenops ocella- 
tus) that accommodates seasonal and ontogenic changes 
in growth rates. Fish. Bull. 100:149-152. 
Quince, C., P. A. Abrams, B. J. Shuter, and N. P. Lester. 
2008a. Biphasic growth in fish 1: theoretical founda- 
tions. J. Theor. Biol. 254:197-206. 
Quince, C., B. J. Shuter, P. A. Abrams, and N. P. Lester. 
2008b. Biphasic growth in fish II: empirical assess- 
ment. J. Theor. Biol. 254:207-214. 
Quinn, T. J., II, and R. B. Deriso. 
1999. Quantitative fish dynamics, 542 p. Oxford Univ. 
Press, New York. 
R Development Core Team. 
2011. R: A language and environment for statistical 
computing. R Foundation for Statistical Computing, 
Vienna, Austria. [Available from: URL http://www.R- 
proiect.org] 
Roff, D. A. 
1983. An allocation model of growth and reproduction in 
fish. Can. J. Fish. Aquat. Sci. 40:1395-1404. 
1984. The evolution of life history parameters in teleosts. 
Can. J. Fish. Aquat. Sci. 41:989-1000. 
Schnute, J. T., and 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. 
Soriano, M., J. Moreau, J. M. Hoenig, and D. Pauly. 
1992. New functions for the analysis of two-phase growth 
of juvenile and adult fishes, with application to Nile 
perch. Trans. Am. Fish. Soc. 121:486-493. 
Tribuzio, C. A., G. H. Kruse, and J. T. Fujioka. 
2010. Age and growth of spiny dogfish ( Squalus acanthias) 
in the Gulf of Alaska: analysis of alternative growth 
models. Fish. Bull. 108:119-135. 
