METHODS 



Measurements - -Six characters were 

 measured. Standard length, predorsal dis- 

 tance, head length, and caudal -peduncle depth 

 conform to the descriptions of Hubbs and Lag- 

 ler (1947). The following measurements were 

 also made: body depth, the distance between 

 the origin of the first dorsal fin and the origin 

 of the pelvic fin; prepelvic distance, the dis- 

 tance between the anterior base of the pelvic 

 fin and the most anterior tip of the lower jaw. 



Measurements up to 150 mm. were 

 made to 0. 1 mm . with dial calipers. The larg- 

 er specimens were measured to 0. 1 mm . with 

 trammel points (used in the carpentry trade) 

 and the distances between the points were ascer- 

 tained with a steel ruler . 



Comparison of data - -The standard length 

 was used as the independent variable in all com- 

 parisons; all other characters measured were 

 employed as dependent variables. Therefore, 

 five reg^ressions were determined for the speci- 

 mens from each locality. Representative 

 samples of the data were plotted for an indica- 

 tion of the relations of the various dependent 

 variables on the independent. Throughout the 

 size range investigated, all relations were 

 found to be linear. It was also noted that the 

 variances of the dependent variables increased 

 as the standard length increased. The regres- 

 sion assumption of homogeneous variances was 

 not justified and a transformation had to be per- 

 formed. The correlation between means and 

 variances was removed by transforming the 

 original data into logarithms, as suggested by 

 Mottley (1941). The transformations and the 

 sums of squares were compiled on a Card Pro- 

 gram Computer. Natural logarithms were used, 

 since the machine performs this transformation 

 more rapidly. A linear relation was still pres- 

 ent after transformation. 



The statistical procedure used in com- 

 paring the regression is similar to that employed 

 by Martin (1949). Homogeneity of regression 

 is posed as the null hypothesis and is tested by 

 the appropriate F-test in an analysis of covari- 

 ance . The regression coefficients are first 

 tested for homogeneity, and if a nonsignificant 

 "F" value is found the intercepts are subjected 



to analysis. When the slopes are found hetero- 

 geneous the intercepts are not tested for the 

 populations have already been found different . 

 Throughout the text, when reference is made to 

 values being significant or not significant the 

 1 -percent level is implied. The 5-percent level 

 is not considered biologically significant, how- 

 ever, in the tables, "F" values found significant 

 at that level are labelled as such. Unless speci- 

 fied otherwise, statistical significance is 

 designated in the tables as follows: N.S. - not 

 significant; * - significant at the 5 -percent level; 

 ** - significant at the 1 -percent level. The 

 statistical methods outlined in Snedecor (1946) 

 were followed. 



Individual comparisons among samples 

 from nearby geographic areas were made in an 

 attempt to find out whether the samples differed, 

 and other comparisons were made to check dif- 

 ferences found by other workers who used 

 different characters . Therefore, all individual 

 comparisons were meaningful and need not be 

 orthogonal (independent) . 



The term "population", as used through- 

 out the text, is employed in a restricted sense. 

 Its meaning is synonomous with the definition 

 that Mayr, Lindsley, and Usinger (1953; p.308) 

 give to "local population". Since it is common 

 practice to use the term "population" when refer- 

 ring to the results of statistical tests and in so 

 doing imply a restricted meaning, the term was 

 always employed in that way for the sake of 

 consistency. 



The locations studied were limited to 

 areas from which large specimens were available. 

 All specimens obtained in an area were assumed 

 to have had their origin there . Different year 

 classes were combined and the resulting regres- 

 sions represent averages for that locality. 



It was assumed that sexual dimorphism 

 was not present. 



RESULTS 



Body Depth - - Using body depth as the 

 dependent variable and standard length as the in- 

 dependent, the covariance test for the homogeneity 

 of regression coefficients over all areas studied 

 (table 1) resulted in an "F" value that was 



