Comparison of Multivariate Allometric Coefficients in Red-Spot Prawn (Metapenosis barbata) from Adjacent Waters off Taiwan

Abstract

Multivariate allometric coefficients of red-spot prawn sampled from the adjacent waters of Tashi, Keelung, Taichung and Kaohsiung were estimated and compared to examine whether (1) allometry can be used to elucidate the genetic variation among groups and (2) the assumption that those groups compared share a common allometric pattern in some multivariate statistic method, e. g. Burnaby's method and shearing principal component analysis (PCA) for size correction, or common PCA and multiple-group PCA for multiple-group ordination, can be satisfied. The specimens were sampled during November and December in 1995. A total of 11 measurements was made for each individual. The first eigenvector extracted from the covariance matrix of log-transformed data was used to reflect the multivariate allometric coefficients. The bootstrap method was used to assess the accuracy of estimates. The dendrogram of four areas was constructed by unweighted pair-group method with arithmetic means (UPGMA) by using the angles between four first eigenvectors by sex. The results show that four areas were clustered into two distinct groups for each sex, one group included Tashi, Keelung and Kaohsiung; the other included Taichung. The hypothesis of one common multivariate allometric pattern was clearly rejected. This indicates that some multivariate statistic methods should not be used with out testing this assumption. The geographic clusters are different from the one derived from shape analysis, so the examination in genetic variation among populations by multivariate variate allometric comparison may be not suitable for this species. Different water masses in winter and flow patterns of coastal current around sampling areas may be the main factors to result in the differences of allometric coefficients between two clusters.