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The traditional power law model, W(L) = aL^b, is widely applied to describeweight (W) vs. length (L) in fish. The model, W(L) = (L/L1)^b, is proposed asan improvement. The Levenberg-Marquardt non-linear least squares technique isused to determine the best-fit parameters L1 and b. This model has theadvantages that L1 has the same units (length) independent of the value of theexponent and has an easily interpreted physical meaning as the typical lengthof a fish with one unit of weight. This proposed model is compared with thetraditional model on length-weight data sets for black crappie, largemouthbass, chain pickerel, yellow perch, and brown bullhead obtained from StilwellReservoir, West Point, New York. The resulting best-fit parameters, parameterstandard errors, and covariances are compared between the two models. Theaverage relative weight for these species is determined, along with typicalmeat yields for four species. For the five species, using the logarithmicapproach and a linear least-squares, standard errors in the coefficient, a,range from 60.2% to 136.5% for the traditional model. Using a non-linear leastsquares technique to determine best fit parameters, the standard errors for thecoefficient, a, range from 68.5% to 164.0% in the traditional model. In theimproved model, standard errors in the parameter L1 range from 0.94% to 15.0%.The covariance between a and b in the traditional model has a magnitude between0.999 and 1.000 in both linear and non-linear parameter estimation methods. Inthe improved model, the covariances between L1 and b are smaller. The improvedmodel, W(L) = (L/L1)^b, is preferable for weight vs. length in fish, becausethe estimated parameter uncertainties and covariances are smaller in magnitude.Furthermore, the parameters both have consistent units and an easilyinterpreted physical meaning.

Demonstrating an Improved Length-weight Model in Largemouth Bass, Chain  Pickerel, Yellow Perch, Black Crappie, and Brown Bullhead in Stilwell  Reservoir, West Point, New York