7022 - Laserfiche WebLink

Home Browse Search

822 COPEIA, 1991, NO. 3 However, the proportions were used for char- acter gap-coding prior to phylogenetic analysis. For purposes of species discrimination and identification within the genus Ptychocheilus an array of multivariate statistical techniques were used. These included principal component analysis (PCA), canonical variate analysis (CVA) and multivariate analysis of variance (MANO- VA). PCA was performed on a covariance ma- trix of log-transformed measurements and served to reduce the dimensionality of the data set while retaining as much variance as possible (Joliffe, 1986). CVA was used for both discrim- ination and classification (Johnson and Wich- ern, 1982). The CVA was performed essentially as a two-step PCA, with the first, a standard PCA described above, summarizing the major components of over-all variance, and the second describing between-group variance (Campbell and Atchley, 1981). A problem known to occur with CVA is over- determination (Gittins, 1985), in which any groups chosen by the user appear to separate widely. This can happen with datasets contain- ing many measurement variables (W. Rainboth, pers. obs.). To avoid overdetermination, prin- cipal component scores were used to create an effective summary of measurement information in fewer dimensions and at the same time to eliminate random error associated with taking each measurement. Reducing overdetermina- tion assured that randomness in identification (misclassifications) would be visible in scatter- plots and quantifiable by one-way MANOVA. Using scores of PCA on a correlation matrix of meristics gave essentially the same result in CVA as using original meristics and did not appear to be subject to overdetermination. Conse- quently, original meristics were used, simplify- ing CVA interpretation. CVA is scale-invariant, unlike PCA (Mardis et al., 1979), and rescaling variables causes no change in canonical scores. Therefore, standardized scores for the princi- pal axes and counts were used to allow inter- pretation of relative contribution of each vari- able to the between-group variance described by each discriminant function. The significance of the classification was test- ed by subjecting the CVA scores to one-way MANOVA using Bartlett's chi-square approx- imation to Wilk's likelihood ratio statistic (Tat- suoka, 1971; James, 1985). Calculation of de- grees of freedom followed Tatsuoka (1971) and calculation of the significance (a-level) followed Anscombe (1981). To make certain which pop- TABLE 1. MORPHOMETRIC MEASURES AND COUNTS. Characters standardized by division by standard length (SL): I. Prepea.I length 2. Preoccipital length 3. Occiput to pectoral insertion 4. Dorsal origin to pectoral insertion 5. Dorsal on into occiput 6. Predorsal length 7. Dorsal origin to pelvic insertion 8. Pelvic insertion to occiput 9. Pelvic insertion to pectoral base 10. Pelvic insertion to anal origin 11. Dorsal origin to anal origin 12. Dorsal base length (dorsal fin origin to insertion) 13. Dorsal insertion to pelvic insertion 14. Dorsal insertion to anal origin 15. Anal base length (anal fin origin to insertion) 16. Anal insertion to dorsal origin 17. Anal insertion to dorsal insertion 18. Dorsal insertion to upper caudal principal ray base 19. Upper caudal principal ray base to anal insertion 20. Upper caudal principal ray base to lower caudal principal ray 21. Lower caudal principal ray base to dorsal insertion 22. Lower caudal principal ray base to anal insertion 23. Dorsal fin height 24. Caudal fin length 25. Anal fin height 26. Pelvic fin length 27. Pectoral fin length Characters standardized by division by prepectoral length (PPL): 28. Snout to supraorbital 29. Occiput to supraorbital 30. Interorbital width 31. Supraorbital to opercular cleft 32. Occiput to opercular cleft 33. Opercular cleft to opercular cleft 34. Left opercular cleft to left pectoral insertion 35. Left opercular cleft to right pectoral insertion 36. Pectoral insertion to pectoral insertion 37. Orbital width 38. Orbital height 39. Left supraorbital to left pectoral insertion 40. Left supraorbital to left maxilla 41. Gape width 42. Left pectoral insertion to left maxilla 43. Left toraI insertion to right maxilla 44. Maxilla to snout tip 45. Lower jaw length Counts: 46. Lateral-line scales 47. Dorsal rays 48. Anal rays 49. Pectoralrays 50. Pelvic rays 51. Gill rakers ulations belonged in the combined groups (spe- cies), cross-validation was performed. For cross- validation, each population was paired with all others in all possible combinations. The least random classification had the greatest signifi- cance (highest chi-square, lowest a) in MANO- VA and became the final choice. It was these groupings which served as our species identifi- cations. Rather than merely listing the signifi- cance of group differences we have provided visual displays of CVA scatterplots with 95% bivariate sample prediction ellipses for each group (Owen and Chmielewski, 1985). Linear regression and calculation of sample prediction intervals were performed according to Morri- son (1983). All computer programs for statis-