KATZ ET AL.: DELINEATION OF TILEFISH STOCKS 



with two exceptions: Barbel length was mea- 

 sured from its posterior tip to the junction with 

 the lower lip, and the suborbital depth was mea- 

 sured from the lower margin of the infraorbitals 

 to the junction of the articular and interopercu- 

 lar bones. Morphometric characters were mea- 

 sured to the nearest millimeter with dividers and 

 a tape measure. These characters were chosen on 

 the basis of a preliminary study of two specimens 

 of tilefish by Bigelow and Schroeder (1947) and 

 a systematic study of the Branchiostegidae by 

 Dooley (1978). 



Morphological data was determined from fish 

 of dissimilar lengths (Fig. 2), so we used analysis 

 of covariance to remove the size effects as sug- 

 gested by Atchley et al. (1976). A linear relation- 

 ship to standard length (SL) was determined for 

 most morphological characters with the excep- 

 tion of adipose flap length where an additional 

 coefficient of standard length squared was in- 

 cluded in the model because of allometry. For the 

 final size-corrected comparisons between sam- 

 ple locations we used sample location least square 

 means for each morphological character ( Barr et 



J- 



_L 



200 400 600 800 1000 200 400 600 800 1000 



Standard Length (mm) 



Figure 2.— Length-frequency histograms of tilefish samples 

 used to conduct the morphological analysis. See Figure 1 for 

 approximate locations. 



al. 1976). Least square means are estimates of 

 arithmetic means that would be predicted had 

 samples with the same size composition been ob- 

 tainable from each sampling location. 



We conducted analysis of covariance on each 

 morphological character to test for differences 

 between sampling locations. Sex, sample loca- 

 tion, and all interactions were initially included 

 in the covariance model, but all nonsignificant 

 (P<0.01) interactions were removed from the 

 final model. The difference between sample loca- 

 tion least square means for each morphological 

 character for each sex was tested by comparison 

 with the west Hudson Canyon sample using a t 

 test. Significant differences were determined 

 conservatively, using a high significance level 

 (P<0.001), because the possibility of finding dif- 

 ferences increases with the number of tests run. 



To further test for differences between sample 

 locations we used discriminant function analysis 

 (Jolicoeur 1959; Seal 1964) to determine the level 

 of distinctness of fish from each location. The 

 discriminant function was computed using both 

 raw and size-corrected data for males and fe- 

 males separately, because the analysis of covari- 

 ance indicated sexual dimorphism. Only linearly 

 related morphological characters were used in 

 the raw discriminant function (Seal 1964). Size 

 correction of morphological characters was ac- 

 complished using the average value of standard 

 length (SL) of all samples, and linear and quad- 

 ratic regression coefficients (Bi, B 2 ) obtained 

 from covariance analysis for each morphological 

 character according to the following formula: 



corrected = raw - B x (SL-SL) - B 2 (SL-SL) 2 . 



This correction removed size effects by displac- 

 ing each morphological observation towards the 

 average, while allowing sample location and in- 

 teraction effects to remain. 



RESULTS 



Electrophoretic Data 



The genetic basis of protein variation in tile- 

 fish was implied from the electrophoretic band- 

 ing patterns. IDH showed a dimeric pattern 

 (heterozygote was three banded) with medium, 

 slow, and fast bands. The rare fast form occurred 

 only as a heterozygote in 10 out of 226 fish in the 

 Mid- Atlantic Bight samples; therefore it has 

 been left out of the statistical analysis. The EST 



43 



