Length, Weight, and Yield in Channel Catfish, Lake Diane, MI

Background: Channel catfish (Ictalurus punctatus) are important to both commercial aquaculture and recreational fisheries. Little published data is available on length-weight relationships of channel catfish in Michigan. Though there is no record of public or private stocking, channel catfish appeared in Lake Diane between 1984 and 1995 and it has developed into an excellent fishery. 
Materials and Methods: Sport angling provided 38 samples which were weighed and measured (fork length). Fillets were also weighed. The best fit estimates of parameters a and b in the model, W(L) = aLb, were obtained by both linear least-squares (LLS) regression (log(W) = log(a) + b log(L)) and non-linear least-squares (NLLS) regression. Best-fit parameters of an improved model, W(L) = (L/L1)^b, were also determined by NLLS regression; the parameter L1 is the typical length of a fish weighing 1 kg. The resulting best-fit parameters, parameter standard errors, and covariances are compared between the two models. The average relative weight for this sample of channel catfish is also determined, along with the typical meat yield obtained by filleting. 
Results: NLLS regression yields parameter estimates of b = 3.2293 and a = 0.00522. The improved model yields the same estimate for the exponent, b, and a length estimate (parameter L1) of 45.23 cm. Estimates of uncertainty and covariance are smaller for the improved model, but the correlation coefficient is r = 0.995 in both cases. LLS regression produced different parameter values, a = 0.01356 and b = 2.9726, and a smaller correlation coefficient, r = 0.980. On average, catfish in the sample weighed 106.0% of the standard weight, (Brown et al.) and the linear regression (no slope) of fillet yield vs. total weight suggests a typical fillet yield of 28.1% with r = 0.989.
Conclusion: Most of the fish in the sample were above the standard weight, heavier than the 75th percentile for their length. Channel catfish are doing well in Lake Diane and the population is well matched to the food supply. Management should attempt to maintain current population levels. In this case, the improved length-weight model, W(L) = (L/L1)^b, provided lower uncertainties in parameter estimates and smaller covariance than the traditional model.
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