Developing a size indicator for fish populations


  • Yong Chen School of Marine Sciences, University of Maine
  • Xinjun Chen College of Marine Sciences and Technology
  • Liuxiong Xu College of Marine Sciences and Technology



size-at-age, robust, principal component analysis, minimum volume ellipsoid analysis, size indicator


Monitoring temporal and/or spatial variations in fish size-at-age data can often provide fisheries managers with important information about the status of fish stocks and therefore help them identify necessary changes in management policies. However, due to the multivariate nature of size-at-age data, commonly used single-age-based approaches ignore covariance between sizes of different age groups. Different results may therefore be derived when evaluating temporal variations using different age groups for the comparison. The possibility of atypical errors in size-at-age data due to ageing and measurement errors further complicates the comparison. We propose a two-step approach for developing an indicator for monitoring temporal and/or spatial variation in size-at-age data. A robust approach, minimum volume ellipsoid analysis, is used to identify possible outliers in size-at-age data. Then a weighted principal component analysis is applied to the data with the identified outliers down-weighted. An indicator is defined from the resultant principal components for monitoring temporal/spatial variations in size-at-age data. We illustrate the proposed approach with size-at-age data for cod (Gadus morhua) in the northwest Atlantic, NAFO subdivision 3Ps. The overall size-at-age indicator identified shows that the pre-1980 year classes tend to have a much higher size-at-age than the post-1980 year classes.


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Author Biography

Yong Chen, School of Marine Sciences, University of Maine

College of Marine Sciences and Technology


Beacham, T.D. – 1983. Growth and maturity of Atlantic cod (Gadus morhua) in the southern Gulf of St. Lawrence. Can. Tech. Rep Fish. Aquat. Sci., 1142.

Beverton, R.J.H. and S.J. Holt. – 1957. On the dynamics of exploited fish populations. Fish. Invest. Ser. 2 Mar. Fish. G.B. Minist. Agric. Fish. Food ., 19.

Campbell, N.A. – 1980. Robust procedures in multivariate analysis I: robust covariance estimation. Applied Stats., 29: 231-237. doi:10.2307/2346896

Charnov, E. – 1993. Life History Invariants. Oxford University Press, New York.

Chen, Y. and H.H. Harvey. – 1994. Maturation of white sucker, Catostomus commersoni, populations in Ontario. Can. J. Fish. Aquat. Sci., 51: 2066-2076.

Chen, Y. and H.H. Harvey. – 1995. Growth, abundance, and food supply of white sucker. Trans Am. Fish. Soc., 124: 262-271. doi:10.1577/1548-8659(1995)124<0262:GAAFSO>2.3.CO;2

Chen, Y. and G.S. Mello. – 1999. Growth and maturation of cod (Gadus morhua) of different year classes in NAFO Subdivision 3Ps in Northwest Atlantic. Fish. Res., 42: 87-101. doi:10.1016/S0165-7836(99)00036-3

Chen, Y. and J.E. Paloheimo. – 1998. Can a more realistic model error structure improve the parameter estimation in modelling the dynamics of fish populations? Fish. Res., 38: 9-17. doi:10.1016/S0165-7836(98)00115-5

Chen, Y., D.A. Jackson and J.E. Paloheimo. – 1994. Robust regression approach to analyzing fisheries data. Can. J. Fish. Aquat. Sci., 51: 1420-1429.

Cooley, W.W. and P.R. Lohnes. – 1971. Multivariate Data Analysis. John Wiley and Sons, New York.

Devlin, S.J., R. Gnanadesikan and J.R. Kettenring. – 1981. Robust estimation of dispersion matrices and principal components. J. Am. Stat. Ass., 76: 354-362. doi:10.2307/2287836

Gomes, M.C., R.L. Haedrich and M.G. Villagarcia. – 1995. Spatial and temporal changes in the groundfish assemblages on the northeast Newfoundland/Labrador Shelf, Northwest Atlantic, 1978-1991. Fish. Oceanogr., 4: 85-101. doi:10.1111/j.1365-2419.1995.tb00065.x

Hanson, J.M. and G.A. Chouinard. – 1992. Evidence that size-selective mortality affects growth of Atlantic cod (Gadus morhua L.) in the southern Gulf of St. Lawrence. J. Fish. Biol., 41: 31-41. doi:10.1111/j.1095-8649.1992.tb03168.x

Hilborn, R. and C.J. Walters. – 1992. Quantitative Fisheries Stock Assessment: Choice, Dynamics and Uncertainty. Chapman and Hall, New York.

Hill, R.C., T.H. Fomby and H.H. Johnson. – 1977. Component selection norms for principal component regression. Commun. Stats. Theor. Methods, 6: 309-334. doi:10.1080/03610927708827494

Hutchings, J.A. and R.A. Myers. – 1994. Timing of cod reproduction: interannual variability and the influence of temperature. Mar. Ecol. Prog. Ser., 108: 21-31. doi:10.3354/meps108021

Jackson, D.A. – 1993. Stopping rules in principal component analysis: a comparison of heuristical and statistical approaches. Ecol., 74: 2204-2214. doi:10.2307/1939574

Jackson, D.A. and Y. Chen. – 2003. Robust principal component analysis of ecological data. Environmetrics, 14: 1-11.

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. doi:10.1139/cjfas-53-4-820

Kovtsova, M.V. – 1995. Changes in growth and maturation of the Barents Sea plaice (Pleuronectes platessa L.) in 70s-90s. ICES Council Meeting Papers 12. ICES, Copenhagen (Denmark).

Krohn, M., S. Reidy and S. Kerr. – 1997 Bioenergetic analysis of the effects of temperature and prey availability on growth and condition of northern cod (Gadus morhua). Can. J. Fish. Aquat. Sci., 54 (Suppl. 1): 113-121. doi:10.1139/cjfas-54-S1-113

Krzanowski, W.J. – 1988. Principal of Multivariate Analysis. Clarendon Press, Oxford, UK

Lilly, G.R. – 1996. Growth and condition of cod in Subdivision 3Ps as determined from trawl surveys (1972-1996) and sentinel surveys (1995). DFO Atlantic Fish. Res. Doc., 96/69.

Manly, B.F.J. – 1991. Randomization and Monte Carlo Methods in Biology. Chapman and Hall, New York.

Mason, R.L. and R.F. Gunst. – 1985. Selecting principal components in regression. Stat. Prob. Lett., 3: 299-301. doi:10.1016/0167-7152(85)90059-8

Moreau, J. – 1987. Age and growth of fish. In: R.C. Summerfelt and G.E. Hall [eds.], Fish Growth, pp. 101-143. Iowa State University Press, Ames, Iowa.

Myers, R.A., G. Mertz and P.S. Fowlow. – 1997. Maximum population growth rates and recovery times for Atlantic cod, Gadus morhua. Fish. Bull., 95: 762-772.

Nikolskii, G.V. – 1965. Theory of Fish Population Dynamics. Oliver and Boyd, Edinburgh, U.K.

Paloheimo, J.E. and L.M. Dickie. – 1965. Food and growth of fishes. I. A growth curve derived from experimental data. J. Fish. Res. Bd. Can., 22: 521-542.

Rao, C.R. – 1964. The use and interpretation of principal component analysis in applied research. Sankhya A, 26: 329-358.

Ricker, W.E. – 1975. Computation and interpretation of biological statistics of fish populations. Fish. Res. Board Can., 191.

Roff, D.A. – 1984. The evolution of life history parameters in teleosts. Can. J. Fish. Aquat. Sci., 41: 989-1000.

Rollet, C., J-C. Brêthes and A. Fréchet. – 1995. Spatial and temporal variation in cod length frequencies and length at 50% maturity in Divisions 3Pn, 4RS and 3Ps. DFO Atl. Fish. Res. Doc., 95.

Rousseeuw, P.J. – 1984. Least median of squares regression. J. Am. Stat. Ass., 79: 871-880. doi:10.2307/2288718

Rousseeuw, P.J. – 1985. Multivariate estimation with high breakdown point. In: W. Grossmann, G. Pflug, I. Vincze and W. Wertz (eds.), Mathematical Statistics and Applications (Vol. B), pp. 283-297. Reidel Publishing, Dordrecht, The Netherlands.

Rousseeuw, P.J. and A.M. Leroy. – 1987. Robust Regression and Outlier Detection. John Wiley and Sons Inc. New York.

Rousseeuw, P.J. and B.C. van Zomeren. – 1990. Unmasking multivariate outliers and leverage points. J. Am. Stat. Ass., 85: 633-644. doi:10.2307/2289995

SAS. – 1987. SAS Guide for personal computers. SAS Institute, Cary, North Carolina.

Shelton, P.A., D.E. Stansbury, E.F. Murphy, J. Brattey and G.R. Lilly. – 1996. An assessment of the cod stock in NAFO subdivision 3Ps. DFO Atl. Fish. Res. Doc., 96/91.

Swain, D.P. – 1993. Age- and density-dependent bathymetric pattern of Atlantic cod (Gadus morhua) in the southern Gulf of St. Lawrence. Can. J. Fish. Aquat. Sci., 50: 1255-1264.

Trippel, E.A. – 1995. Age at maturity as stress indicator in fisheries. BioSci., 45: 759-771. doi:10.2307/1312628

Trippel, E.A. – 1998. Egg size and variability and seasonal offspring production of young Atlantic cod. Trans. Am. Fish. Soc., 127: 339-359. doi:10.1577/1548-8659(1998)127<0339:ESAVAS>2.0.CO;2

Vogt, N.B. and K. Kolsett. – 1987. Composition activity relationships _CARE. Part III. Polynomial principal component regression and response surface analysis of mutagenicity in air samples, 1981. Report 87: 747, Chemometrics and Indelligent Lab Systems.




How to Cite

Chen Y, Chen X, Xu L. Developing a size indicator for fish populations. Sci. mar. [Internet]. 2008Jun.30 [cited 2024Feb.29];72(2):221-9. Available from:




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