Informe Anual de la Comisión Interamericana del Atún Tropical, 19

20 TUNA COMMISSION
The edited raw data were transformed to logarithms and the individual measurements were
adjusted to those expected for a mean TL of 639 mm by allometric formulae in which the common
within-groups allometric coefficients were used for each of the morphometric measurements. The
transformed data were then subjected to a principal components analysis (PCA) operating on the
total variance-covariance matrix. PCA is a multivariate technique useful for examining
relationships among several variables such as linear measurements. The PCA successfully provided
an overall view of the data. The calculated eigenvalues indicate that the first two 01' three
components provide a good summary of the data. The first, first two, and first three components
explain 58, 71, and 81 percent of the total sample variance, respectively. The first component is a
measure of overall shape. The first eigenvector has high positive values for al] seven variables, and
thus the first principal component appears to be essentially an average of these variables. However,
SAF, SSD, and FDAF, in that order, appear to have the greatest discriminatory powers. (The
measurements are described in Table 13.) The second principal component appears to be acontrast of
the SFD, SSD, and HL, and FDSD, FDAF, and SDAF. The interpretation of the third component is
not obvious.
Cluster analyses have been performed on the adjusted data to assign the fish to groups on a
geographical basis as suggested by the data, rather than doing so on an a priori basis. Eleven
different methods ofthe agglomerative hierarchical clustering procedure were applied to the data.
The number of population clusters for each clustering method was assessed, using three criteria
which have been found to perform best: a pseudo F statistic, a pseudo t2statistic, and the cubic
clustering criteria. Since each of the clustering methods is biased to sorne extent (but in different
ways), a consensus ofthe results ofthe 11 methods with respect to the number of clusters and the
composition within clusters was utilized. In summary, seven of the clustering methods indicate two
clusters, one indicates three, two indicate four, and one indicates five. There is sorne agreement ofthe
composition ofthe c\usters at the two-cluster level, with a north-south dimensiono The cluster which
forms the northern component contains mainly samples from north of18°N, and that which forms
the southern component contains primarily samples from south of 18°N.
Forward stepwise discriminant analyses were used to classify individual fish into groups,
employing the jackknife-validation procedure. The results from the cluster analyses indicating
geographical groups were used as the grouping identification variables in the discriminant analyses.
A cross-validation procedure was employed in which the observations within a group can be
randomly subdivided into two separate groups; then the classification function is estimated from the
first group, and the second group is classified according to the function. The proportion of correct
c1assification for fish from the second group provides an empirical measure of the success of the
discrimination. The results ofthe stepwise discriminant analyses are given in Table 14. The percentcorrect
classification for the data without any subsampling for cross validation was a total of 76.7
percent, with 72.0 percent for the northern group and 78.7 percent for the southern group. The
discriminant function analysis revealed that six of the seven morphometric characters investigated
contributed significantly to the multivariate discrimination between the northern and southern
groups of fish. These were, in order of importance, SDAF, SFD, FDSD, SAF, FDAF, and HL. The F
value computed from the Mahalanobis D2 statistic testing for equality of group means showed a
significant difference between the no:rthern and southern groups (F0.05, [6, 2467) = 153.87, P