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

Background: The traditional power law model, W(L) = aL, is widely applied to describe weight (W) vs. length (L) in fish. The exponent, b, is independent of the system of units and has an easily interpreted physical meaning as related to isometric growth (b = 3). In contrast, the coefficient, a, depends strongly on both the exponent and the system of units, and its physical meaning is difficult to interpret. It has been suggested that unit conversions and lack of a physical meaning may have contributed to errors in length-weight parameters at FishBase.org and other widely cited sources. Materials and Methods: The model, W(L) = (L/L1), is proposed as an improvement. The Levenberg-Marquardt non-linear least squares technique is used to determine the best-fit parameters L1 and b. This model has the advantages that L1 has the same units (length) independent of the value of the exponent and has an easily interpreted physical meaning as the typical length of a fish with one unit of weight. This proposed model is compared with the traditional model on length-weight data sets for black crappie, largemouth bass, chain pickerel, yellow perch, and brown bullhead obtained from Stilwell Reservoir, West Point, New York. The resulting best-fit parameters, parameter standard errors, and covariances are compared between the two models. The average relative weight for these species is determined, along with typical meat yields for four species. Results: For the five species, using the logarithmic approach 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 least squares technique to determine best fit parameters, the standard errors for the coefficient, a, range from 68.5% to 164.0% in the traditional model. In the improved 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 between 0.999 and 1.000 in both linear and non-linear parameter estimation methods. In the improved model, the covariances between L 1 and b are smaller. The average relative weights for each species were black crappie (92.0%), largemouth bass (91.8%), yellow perch (69.3%), chain pickerel (88.1%), and brown bullhead (100.4%). The average meat yield in fillets as a percentage of total weight were largemouth bass (34.5%), yellow perch (34.9%), chain pickerel (41.9%), and brown bullhead (22.5%). Conclusion: In this study, the improved model, W(L) = (L/L1), is preferable for weight vs. length in fish, because the estimated parameter uncertainties and covariances are smaller in magnitude. Furthermore, the parameters both have consistent units and an easily interpreted physical meaning.