PRODUCTION FUNCTIONS FOR GOLDEN SHINER GROWTH IN DIFFERENT CULTURE SYSTEMS

Lin Xie*, Nathan Stone, and Rebecca Lochmann
Aquaculture/Fisheries Center
University of Arkansas at Pine Bluff
Pine Bluff, AR  71601
xiel@uapb.edu

Two of the most popular production functions - Cobb-Douglas (CD) and the transcendental logarithmic (TL) function - have been widely used in agriculture and aquaculture to predict the production outputs based on a given set of inputs. The CD model is the reduced model to the TL model by excluding the quadratic and interaction terms in the TL model.

This study is based on thirty-two golden shiner feeding experiments conducted at the University of Arkansas at Pine Bluff over the last two decades. Four key production variables (stocking density, duration of culture, protein content of feed, and culture system) were analyzed to determine their effects on the final weight of golden shiner. The TL model has a better fit (RMSE =0.31, adjusted R2=0.81) compared to the CD model (RMSE =0.50, adjusted R2=0.52).  The Likelihood Ratio test is statistically significant, indicating that quadratic and interaction terms in the TL model are significant. A serial of residual analysis for the TL model, Shapiro-Wilk test (P=0.56) for normality and a plot of standardized residual versus predicted values, suggesting the TL model based on the assumption of normality and homogeneity of variance was suitable to describe the growth of golden shiner.  The effect of culture system was statistically significant. Golden shiner grew much better in outdoor culture systems compared to indoor culture systems.