Register      Login
Marine and Freshwater Research Marine and Freshwater Research Society
Advances in the aquatic sciences
RESEARCH ARTICLE

Identification of ontogenetic growth models for squid

Alexander I. Arkhipkin A C and Rubén Roa-Ureta A B
+ Author Affiliations
- Author Affiliations

A Falkland Islands Government Fisheries Department, PO Box 598, Stanley, Falkland Islands.

B Departamento de Oceanografía, Universidad de Concepción, PO Box 160-C, Concepción, Chile.

C Corresponding author. Email: aarkhipkin@fisheries.gov.fk

Marine and Freshwater Research 56(4) 371-386 https://doi.org/10.1071/MF04274
Submitted: 20 November 2004  Accepted: 1 April 2005   Published: 27 June 2005

Abstract

Several ontogenetic growth models were fitted to size-at-age data of twelve species of squid from the recent suborders Myopsina and Oegopsina. These squid represent different habitats of the world ocean – from shelf to meso- and bathypelagic waters and from tropical to polar regions. Two main criteria were used in selecting the squid: large sample size (>150 individuals) and wide range of ontogenetic coverage (>2/3 of the whole ontogenesis). The growth models used were the exponential, Gompertz, Schnute and ad hoc two-stage models. They were fitted to size-at-age data using maximum likelihood for estimation and Akaike weights for identification. In all species, the 4-parameter Schnute or the 3-parameter Gompertz models provided the best fit. Size at the inflection point of the growth curve for most squid was smaller than size at 50% maturity, suggesting that maturation is not a major cause of the change in growth rate for these species. Mathematical and statistical procedures to calculate standard measures of growth, such as the instantaneous relative rate of growth, G, which are valid for all continuous growth models, are also presented.


Acknowledgments

We would like to thank our colleagues in the Fisheries Department of the Falkland Islands Government (Stanley, Falkland Islands) for their help in collecting morphometric data and statoliths, to Janna Shcherbich for statolith ageing analysis and to Dr Lianos Triantafillos for comments that improved the paper. We are also grateful to two anonymous reviewers who pointed out deficiencies in an earlier version of the manuscript.


References

Akaike H. (1973). Information theory and an extension of the maximum likelihood principle. In ‘Proceedings of the 2nd International Symposium on Information Theory’. (Eds B. N. Petrov and B. F. Csaki.) pp. 267–281. (Academiai Kiado: Budapest.)

Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control 19, 716–723.
Crossref | GoogleScholarGoogle Scholar | Burnham K. P., and Anderson D. (2002). ‘Model Selection and Multi-Model Inference.’ (Springer-Verlag: New York.)

Caddy J. F. (1991). Daily rings on squid statoliths: an opportunity to test standard population models? In ‘Squid Age Determination Using Statoliths. Proceedings of the International Workshop, Mazara del Vallo, Italy, 9–14. October 1989’. (Eds P. Jereb, S. Ragonese and S. von Boletzky.) pp. 53–66. Note Tecniche e Reprints dell’Instituto di Tecnologia della Pesca e del Pescato Special publications, No.1. Instituto di Tecnologia della Pesca e del Pescato, Mazara del Vallo, Italy.

Chapman D. G. (1961). Statistical problems in dynamics of exploited fisheries populations. In ‘Proceedings of the 4th Berkeley Symposium of Mathematics, Statistics and Probability, Vol. 4’. pp. 153–168. (University of California Press: Berkeley, CA.)

Dawe, E. G. , and Beck, P. (1997). Population structure, growth and sexual maturation of short-finned squid (Illex illecebrosus) at Newfoundland. Canadian Journal of Fisheries and Aquatic Sciences 54, 137–146.
Crossref | GoogleScholarGoogle Scholar | Dawe E. G., and Natsukari Y. (1991). Light microscopy. In ‘Squid Age Determination Using Statoliths. Proceedings of the International Workshop, Mazara del Vallo, Italy, 9–14 October 1989’. (Eds P. Jereb, S. Ragonese and S. von Boletzky.) pp. 83–96. N.T.R.-I.T.P.P. Special publications, No.1. Istituto di Tecnologia della Pesca e del Pescato, Mazara del Vallo, Italy.

Dawe, E. G. , O’Dor, R. K. , O’Dense, P. H. , and Hurley, G. V. (1985). Validation and application of an ageing technique for short-finned squid (Illex illecebrosus). Journal of the Northwest Atlantic Fishery Science 6, 107–116.
Forsythe J. W., and Van Heukelem W. F. (1987). Growth. In ‘Cephalopod Life Cycles, Vol. II. Comparative Reviews’. (Ed. P. R. Boyle.) pp. 135–156. (Academic Press: London.)

Forsythe, J. W. , DeRusha, R. H. , and Hanlon, R. T. (1994). Growth, reproduction and life span of Sepia officinalis (Cephalopoda: Mollusca) cultured through seven consequtive generations. Journal of Zoology 233, 175–192.
Lipinski M. R. (1978). The age of squids, Illex illecebrosus (LeSueur, 1821) from their statoliths. ICNAF Res. Doc., No. 78/II/15, Ser. No. 5167. International Commission for the Northwest Atlantic Fisheries, Dartmouth, Nova Scotia.

Lipinski M. R. (1979). Universal maturity scale for the commercially-important squids (Cephalopoda: Teuthoidea). The results of maturity classification of the Illex illecebrosus (LeSueur, 1821) populations for the years 1973−1977. ICNAF Res. Doc., No. 79/II/38, Ser. No. 5364. International Commission for the Northwest Atlantic Fisheries, Dartmouth, Nova Scotia.

Lipinski, M. R. (2001). Growth of cephalopods: a conceptual model. Abhandlungen der Geologischen Bundesanstalt 57, 133–138.
Mangold K. (1987). Reproduction. In ‘Cephalopod Life Cycles, Vol. II. Comparative Reviews’. (Ed. P. R. Boyle.) pp. 157–200. (Academic Press: London.)

Natsukari, Y. , and Komine, N. (1992). Age and growth estimation of the European squid, Loligo vulgaris, based on statolith microstructure. Journal of the Marine Biological Association of the UK 72, 271–280.
Peters R. H. (1983). ‘The Ecological Implications of Body Size.’ (Cambridge University Press: Cambridge.)

Richards, F. J. (1959). A flexible growth function for empirical use. Journal of Experimental Botany 10, 290–300.
Ricker W. E. (1979). Growth rates and models. In ‘Fish Physiology, Vol. III, Bioenergetics and Growth’. (Eds W. S. Hoar, D. J. Randall and J. R. Brett.) (Academic Press: New York.)

Sakamoto Y., Ishiguro M., and Kitagawa G. (1986). ‘Akaike Information Criterion Statistics.’ (KTK Scientific Publishers: Tokyo.)

Schnute, J. (1981). A versatile growth model with statistically stable parameters. Canadian Journal of Fisheries and Aquatic Sciences 38, 1128–1140.
Seber G. A. F. (1973). ‘The Estimation of Animal Abundance and Related Parameters.’ (Hafner Press: New York.)

Semmens, J. M. , Pecl, G. T. , Villanueva, R. , Jouffre, D. , Sobrino, I. , Wood, J. B. , and Rigby, P. R. (2004). Understanding octopus growth: patterns, variability and physiology. Marine and Freshwater Research 55, 367–378.
Crossref | GoogleScholarGoogle Scholar |

Spratt, J. D. (1978). Age and growth of the market squid, Loligo opalescens Berry, in Monterey Bay. Fish Bulletin of the California Department of Fish and Game 169, 35–44.


Sweeney, M. J. , Roper, C. F. E. , Mangold, K. M. , Clarke, M. R. , and von Boletzky, S. (1992). ‘Larval’ and juvenile cephalopods: a manual for their identification. Smithsonian Contributions to Zoology 513, 1–282.


Tinbergen, L. , and Vervey, J. (1945). Zur biologie von Loligo vulgaris Lam. Archives Néerlandaises de Zoologie 7, 213–286.


Uozumi, Y. , and Ohara, H. (1993). Age and growth of Nototodarus sloanii (Cephalopoda: Oegopsida) based on daily increment counts in statoliths. Nippon Suisan Gakkai Shi 59, 1469–1477.


Verrill, A. E. (1881). The cephalopods of the northeastern coast of America. Part II. The smaller cephalopods including the squid and octopus, with other allied forms. Transactions of the Connecticut Academy of Science 5, 260–446.


West, G. B. , Brown, J. H. , and Enquist, B. J. (2001). A general model for ontogenetic growth. Nature 413, 628–631.
Crossref | GoogleScholarGoogle Scholar | PubMed |

Yang, W. T. , Hixon, R. F. , Turk, P. E. , Krejci, M. E. , Hulet, W. H. , and Hanlon, R. T. (1986). Growth, behavior, and sexual maturation of the market squid, Loligo opalescens, cultured through life cycle. Fishery Bulletin (Washington, D.C.) 84, 771–798.