Mathematical analysis of effects of morphometric attributes on body weight for Penaeus vannamei
凡纳对虾形态性状对体重的影响效果分析

The effects of morphometric attributes on body weight for Penaeus vannamei were analyzed. Data for this study were collected from six-month-old 176 Penaeus vannamei in Banqiao Village of Dongfang City , Hainan Province. The body length ( X _1), carapace length ( X _2), carapace width ( X _3), carapace height ( X _4), number of upper frontal eminence spine ( X _5), number of lower frontal eminence spine ( X _6), tail length ( X _7) and body weight (Y) were measured. The correlation coefficients among the attributes were calculated. Tail length was eliminated from the variable data set because it was co-linear with body length ( X _1) and carapace length ( X _2). The first 6 morphometric attributes( X _1~ X _6) were used as independent variables, and body weight( Y ) was used as a dependent variable for path analysis. Path coefficients ( Pi ), determination coefficients ( di) and correlation index ( R ~2) were calculated in path analysis. The results showed that all five correlation coefficients between each morphometric attribute and the weight (0.9446, 0.9262, 0.9102, 0.7923, 0.933) achieved very significant difference ( P <0.01) levels. The path coefficient analysis revealed a truthful relationship between the independent variables and the dependent variable. The path coefficients( Pi ) of the body length ( X _1), carapace length ( X _2), carapace width ( X _3) and number of lower frontal eminence spine ( X _6) to the body weight have all reached a level of significance. These attributes are very indicative of determining the body weight, among them body length ( X _1) weighted the most ( P _1=0.428) to the body weight, it is a key effective factor, carapace length ( X _2) and carapace width ( X _3) weighted the second and third ( P _2=0.2902, P _3=0.2453, significant indirect effect 0.6145, 0.6408 respectively). The number of lower frontal eminence spine ( X _6), carapace height ( X _4), number of upper frontal eminence spine ( X _5), and tail length ( X _7) have insignificant direct effect on the body weight and were neglected. The diversification of determination coefficients ( d_i ) is consistent with that of path coefficients( P_i ). Judging from the result of high correlation index ( R ~2=0.921), the main variables ( X _1, X _2, X _3, X _6) have been selected. The multiple regression equation of the body length ( X _1), carapace length ( X _2), carapace width ( X _3) and number of lower frontal eminence spine ( X _6) to the body weight is obtained to estimate body weight. the regression intercept and partial regression coefficients of the equation are -17.994, 1.477, 4.159, 6.197, and 0.4757. This paper provide a theoretical tool to measure breeding shrimps in aquaculture.