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Statistical estimation of mean values of fish stock indicators from trawl surveys

Published online by Cambridge University Press:  17 June 2009

John Cotter*
Affiliation:
Cefas, Lowestoft, NR33 0HT, UK
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Abstract

The mean or average value of a measure or indicator variable used to monitor a fish population can be defined in various ways, each with a correspondingly different statistical estimator for use in the context of a trawl survey. When, as is typical for many species, fish are heterogeneously clustered over space, then scooped in clusters from restricted localities using a trawl, these different estimators can produce different sample mean values with contrasting variations over time, possibly leading to different inferences about the fish population. Two mean parameters and their intuitive estimators, the mean “over fish”, and the mean “over stations”, are discussed and found to present contrasting statistical properties. A third estimator based on fitting a mixed model is proposed which has intermediate properties based on the within-haul correlation. The three estimators are applied illustratively to length data for cod caught in the North Sea by the English groundfish survey from 1992 to 2007. The time series of the mean over stations was smoothest, that for the mean over fish much more variable, and the mixed mean fell between in all years. Variance estimators derived from the fitted mixed model are also put forward. Estimates made from the example suggested that the mixed mean is most efficient. The type of estimator used for the mean should always be considered carefully and mentioned when reporting indicator studies.

Type
Research Article
Copyright
© EDP Sciences, IFREMER, IRD, 2009

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References

Aanes, S., Pennington, M., 2003, On estimating the age composition of the commercial catch of northeast Arctic cod from a sample of clusters. ICES J. Mar. Sci. 60, 297303.
Anonymous, 2004a, Manual for the International Bottom Trawl Surveys. Rev. VII. ICES. http://www.ices.dk/datacentre/datras/NSIBTSmanualRevVIIdraft.pdf
Anonymous, 2004b, Report of the workshop on survey design and data analysis (WKSAD). International Council for the Exploration of the Sea, Copenhagen, ICES CM 2004/B:07, Ref. D.G., www.ices.dk/reports/FTC/2004/WKSAD04.pdf
Anonymous, 2005, Report of the workshop on survey design and data analysis (WKSAD). International Council for the Exploration of the Sea, Sète, France, ICES CM 2005/B:07. www.ices.dk/reports/FTC/2005/WKSAD05.pdf
Anonymous, 2006, Report of the study group on survey trawl standardisation (SGSTS). International Council for the Exploration of the Sea, ICES CM 2006/FTC:05, www.ices.dk/reports/FTC/2005/SGSTS05.pdf
Cochran W.G., 1977, Sampling techniques. J. Wiley & Sons, Inc., New York.
Cotter, A.J.R., 1998, Method for estimating variability due to sampling of catches on a trawl survey. Can. J. Fish. Aquat. Sci. 55, 16071617. CrossRef
Nicholson M.D., Stokes T.K., Thompson A.B., 1991, The interaction between fish distribution, survey design and analysis., ICES CM 1991/D 11.
Pennington, M., Burmeister, L.-M., Hjellvik, V., 2002, Assessing the precision of frequency distributions estimated from trawl-survey samples. Fish. Bull. 100, 7480.
Pennington, M., Vølstad, J.H., 1994, Assessing the effect of intra-haul correlation and variable density on estimates of population characteristics from marine surveys. Biometrics 50, 725732. CrossRef
Pinheiro J.C., Bates D.M., 2000, Mixed-effects models in S and S-plus. Springer, New York.
Searle S.R., Casella G., McCulloch C.E., 1992, Variance components. J. Wiley & Sons, Inc. New York
Sukhatme P.V., Sukhatme B.V., 1984, Sampling theory of surveys with applications. Iowa State University Press, Ames, Iowa.
Thompson S.K., 1992, Sampling. John Wiley & Sons, Inc., New York.
Woillez, M., Poulard, J.C., Rivoirard, J., Petitgas, P., Bez, N., 2007, Indices for capturing spatial patterns and their evolution in time, with application to European hake (Merluccius merluccius) in the Bay of Biscay. ICES J. Mar. Sci. 64, 537550. CrossRef