BARNETT ET AL.: DISTRIBUTION OF ICHTHYOPLANKTON OFF SAN ONOFRE, CALIF. 



were roughly the same as the actual numbers of eggs 

 and larvae caught, a desirable situation for analysis 

 with transformed data (Murphy and Clutter 1972). 

 These values were transformed by log (X + 1) before 

 analysis for offshore and vertical pattern. The results 

 were back-transformed, resulting in geometric 

 means with asymmetric confidence bounds, and pre- 

 sented as number/1 00m 1 . 



To describe the cross-shelf abundance patterns of 

 ichthyoplankton, a procedure was adopted involving 

 Hotelling's T 2 test and a series of a posteriori '(-tests 

 (Morrison 1976) to divide the 15 strata into groups. 

 These parametric methods allowed us to detect 

 significant differences in mean abundance among 

 components of a pattern and to determine con- 

 fidence bounds on the means. 



Hotelling's T l test was selected over an analysis of 

 variance (ANOVA) because the covariance struc- 

 tures in the data tended not to meet the assumptions 

 of standard ANOVA models (i.e., errors were not 

 independent; the abundances of neighbor strata 

 were likely to be correlated). The T 2 -test allows this 

 correlation by using the sample covariance matrix, 

 rather than (as in ANOVA) assuming a specified 

 covariance pattern (Winer 1971; Morrison 1976). 



With a significant T 1 test result obtained (P< 0.05), 

 a posteriori multiple (-tests were used to separate 

 strata into groups having significantly different 

 abundances. The strata were contrasted in a series of 

 (-tests using the Bonferroni statistic, ((0.05),,, where 

 k — potential number of contrasts, s = number of 

 sampling periods — 1, and 0.05 = overall type / (a) 

 error. The value of k was set as the number of all poss- 

 ible contrasts among m strata plus 5, for further tests 

 employing combinations of the initial strata: i.e., 

 (m)(m-l) 



k 



+ 5. Bonferroni (-values were taken 



After the initial series of (-tests of all possible com- 

 parisons, strata found not to differ significantly were 

 pooled into initial groups. The time-averaged abun- 

 dance of each stratum was used to calculate the initial 

 groups' mean abundance 



Zj = 



z 



Z,/n 



where Z, is the initial group mean, n is the number of 

 strata in the initial group, and Z, are the means of 

 individual strata. Further (-tests (the total of all tests 

 <k) were made to contrast the resulting initial 

 groups. If more than one final grouping was possible, 

 the final set of groups selected was that which max- 

 imized the (-statistic. 



Both the Hotelling T 2 and the (-test assume nor- 

 mally distributed data. Excessive zero values in a 

 data set violate this assumption in a way that cannot 

 be corrected by transformations. The methods used 

 here were robust with respect to zero values in 

 zooplankton data (Barnett et al. 12 ); nevertheless, 

 some sampling dates for 1 2 of the 1 9 ichthyoplankton 

 taxa analyzed were deleted in one of two ways in 

 order to reduce the number of zero observations. The 

 preferred method, useful for eight seasonally abun- 

 dant taxa, was to eliminate from analysis all consecu- 

 tive samples taken when the annual abundance cycle 

 was lowest. In these cases, the number of survey 

 dates was <57 (Fig. 3), and means and confidence 

 bounds presented (Table 1) apply to the "season of 

 abundance". The second method, used for four 

 sporadically abundant taxa, was to include only those 



from Myers (1972, table A-12). 



l; Barnett, A. M., A. E. Jahn, and P. D. Sertic. 1980. Long term 

 average spatial patterns of zooplankton off San Onofre and their 

 relationship to the SONGS cooling system, ME CO 1380994. Marine 

 Ecological Consultants of Southern California, 531 Encinitas 

 Boulevard, Encinitas, CA 92024. 



Table 1. -Geometric mean abundance (no./100m 3 ) with 96% confidence bounds (C.B.) for the 15 larval fish taxa 

 showing statistically significant cross-shelf patterns off San Onofre, Calif. Groups of strata which differ significantly in 

 mean abundance are ranked from highest to lowest. Refer to Figure 3 for locations of these groups. 



101 



