A generalized, nonlinear regression approach to the length-weight relationship of European perch (Perca fluviatilis L.) from the Polish coast of the southern Baltic Sea

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Length-weight relationships in fish are important tools in fisheries management. The aim of this study was to estimate the growth curve W=aLb for European perch, Perca fluviatilis L., from the Polish coast of the southern Baltic Sea (ICES Subdivision 25). The data set comprised the total weights and total lengths of 827 specimens caught during the 2011-2013 period. The mean total length (TL) was 169.4 mm (range 100.0-310.0 mm), and the mean total weight was 83.9 g (range 11.3-553.2 g). First, a multiplicative error term and a linear regression approach to loglog-transformed data was considered. The following estimated values for the parameters were obtained: a = exp(-12.5323), b=3.25, s=0.07862. This approach was not successful in solving the common heterogeneity problem of the length-weight data. A generalized nonlinear regression approach to the original data was more suitable in our case. The estimated model was W = 3.83×10-6×L3.238 + ε, with ε~norm(0,0.0281×E[W|L]2×1.242). The estimated 95% confidence interval for b was (3.218, 3.259), and the growth was allometric. The perch from the coastal waters of the Baltic Sea (ICES Subdivision 25) was characterized by slightly better condition than that caught in inland waters and estuaries.

Akaike H. 1973 - Information theory as an extension of the maximum likelihood principle - In: Second International Symposium on Information Theory (Eds) B.N. Petrov, F. Csaki, Akademiai Kiado, Budapest, Hungary: 267-281.

Böhling P., Hudd R., Lehtonen H., Karås P., Neuman E., Thoresson G. 1991 - Variations in year-class strength of different perch (Perca fluviatilis) populations in the Baltic Sea with special to temperature and pollution - Can. J. Fish. Aquat. Sci. 48: 1181-1187.

Byström P., Bergström U., Hjälten A., Ståhl S., Jonsson D., Olsson J. 2015 - Declining coastal piscivore populations in the Baltic Sea: Where and when do sticklebacks matter? - Ambio, 44: 462-471.

Carroll R.J., Ruppert D. 1984 - Power transformations when fitting theoretical models to data - J. Am. Stat. Assoc. 79:321-328.

Cone R.S. 1989 - The need to reconsider the use of condition indices in fishery science - Trans. Am. Fish. Soc. 118:510-514.

Eriksson B.K., Sieben S., Eklöf J., Ljunggren L., Olsson J., Casini M., Bergström U. 2011 - Effects of altered offshore food webs on coastal ecosystems emphasizes the need for cross ecosystem management - Ambio 40: 786-797.

Feldstien M.J., Hersch A.H. 1935 - The 242 determination of genetic constants of relative growth - Am. Nat. 69:344-353.

Fox J., Weisberg S. 2011 - An R companion to applied regression - Thousand Oaks, CA, Sage Publications, 449 p.

Froese R. 1998 - Length-weight relationships for 18 less-studied fish species - J. Appl. Ichthyol. 14: 117-118.

Froese R. 2006 - Cube law, condition factor and weight-length relationships: history, meta analysis and recommendations - J. Appl. Ichthyol. 22: 241-253.

Galstoff P.S. 1931 - The weight-length relationship of the shells of the Hawaiian pearl oyster, Pinctada sp. - Am. Nat. 65: 423-433.

Giannetto D., Carosi A., Franchi E., La Porta G., Lorenzoni M. 2012 - Proposed standard weight (Ws) equation for European perch (Perca fluviatilis Linnaeus, 1758) - J. Appl. Ichthyol. 28: 34-39.

Guy C.S., Brown M.L. 2007 - Analysis and interpretation of freshwater fisheries data - Am. Fish. Soc., Bethesda, Maryland, 996 p.

Huxley J.S. 1924 - Constant differential growth-ratios and their significance - Nature 114: 895-896.

Huxley J.S. 1932 - Problems of relative growth - Metheun, London, UK, 319 p.

Hui D., Jackson R.B. 2007 - Uncertainty in allometric exponent estimation: a case study in scaling metabolic rate with body mass - J. Theor. Biol. 249: 168-177.

Jellyman P.G., Booker D.J., Crow S.K., Jellyman D.J. 2013 - Does one size fit all? An evaluation of length-weight relationships for New Zealand’s freshwater fish species - New Zeal. J. Mar. Fresh. 47: 450-468.

Jenning C.A., Sloss B.L., Lasee B.A., Burtle G.J., Moyer G.R. 2012 - Care, handling, and examination of sampled organism - In: Fisheries Techniques, 3nd edn (Eds) A.V. Zale, D.L. Parrish, T.M. Sutton, American Fisheries Society, Bethesda, Meryland: 163-221.

Karås P. 1990 - Seasonal changes in growth and standard metabolic rate of juvenile perch, Perca fluviatilis L. - J. Fish Biol. 37: 913-920.

Le Cren E.D. 1951 - The length-weight relationship and seasonal cycle in gonad weight and condition in the perch (Perca fluviatilis) - J. Anim. Ecol. 20: 201-219.

Ljunggren L., Sandström A., Bergstrom U., Mattila J., Lappalainen A., Johansson G., Sundblad G., Casini M., Kaljuste O., Eriksson B. K. 2010 - Recruitment failure of coastal predatory fish in the Baltic Sea coincident with an offshore ecosystem regime shift - ICES J. Mar. Sci. 67:1587-1595

Lloret J., Shulman G., Love R.M. 2014 - Condition and health indicators of exploited marine fishes - Wiley Blackwell, West Sussex, UK, 262 p.

Ložys L. 2004 - The growth of pikeperch (Sander lucioperca L.) and perch (Perca fluviatilis L.) under different water temperature and salinity conditions in the Curonian Lagoon and Lithuanian coastal waters of the Baltic Sea - Hydrobiologia 514: 105-113.

Ogle D.H. 2015 - Introductory fisheries analysis with R - Chapman and Hall/CRC, Boca Raton, USA, 317 p.

Olsson J., Bergström L., Gårdmark A. 2012 - Abiotic drivers of coastal fish community change during four decades in the Baltic Sea - ICES J. Mar. Sci. 69: 961-970.

Oscoz J., Campos F., Escala M.C. 2005 - Weight-length relationships of some fish species of the Iberian Peninsula - J. Appl. Ichthyol. 21: 73-74.

Pinheiro J., Bates D. 2000 - Mixed effects models in S and S-Plus - Springer, New York, USA, 528 p.

Pinheiro J., Bates D., DebRoy S., Sarkar D. 2015 - NLME: Linear and nonlinear mixed effects models - R package version 3.1-122, URL http://CRAN.R289project.org/package=nlme.

Quinn T.J., Deriso R.B. 1999 - Quantitative fish dynamics - Oxford University Press, New York, Oxford, 542 p.

R Core Team 2014 - R: A language and environment for statistical computing - R Foundation for Statistical Computing, Vienna, Austria. URL http://www.R-project.org/.

Ritz C., Streibig J.C. 2008 - Nonlinear regression with R - Springer, Berlin, Germany, 150 p.

Sprugel D.G. 1983 - Correcting for bias in log-transformed allometric equations - Ecology 64: 209-210.

Thorpe J.E. 1977 - Synopsis of biological data on the perch Perca fluviatilis Linnaeus, 1758 and Perca flavescens Mitchill, 1804 - FAO Fisheries Synopsis 113, 138 p.

Zar J.H. 1968 - Calculation and miscalculation of the allometric equation as a model in biological data - Bio-Science 18: 1118-1120.

Fisheries & Aquatic Life

The Journal of Stanislaw Sakowicz Inland Fisheries Institute

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