by applying the more critical discriminant func- 

 tion proposed by Fisher (1936b). A similar 

 conclusion has been reached by taxonomists in 

 other groups, for according to Mayr, Linsley, 

 and Usinger (1953:151) 'the mere fact of a 

 (statistically provable) difference between sev- 

 eral populations of a species is therefore of no 

 special interest to the taxonomist; he takes it 

 for granted. Even the lowest recognizable 

 taxonomic category (the subspecies) is normally 

 composed of numerous populations that differ 

 'significantly/' in gene frequencies and in the 

 means of certain variates." 



Thus the conclusion that a statistically 

 significant difference exists between samples 

 becomes a trivial one. It is a necessary pre- 

 liminary in racial studies, but once it is found 

 that significant differences can be expected from 

 the samples that are most closely related in 

 time and space it is no longer useful. As Fish- 

 er (1936a) has pointed out, a test of significance 

 is merely a means of maicing a decision, and 

 once the predetermined level of significance is 

 reached, larger samples and further sampling 

 merely reiterate the conclusion. A test of sig- 

 nificance— decides that there is a difference, 

 and after it is found we become interested in 

 the quantity and direction of the difference. 



A step toward determining the quantity 

 of the difference has been employed by Godsil 

 (1948) and by Schaefer ( 1955), both of whom have 

 determined that differences between samples 

 from widely separated areas are greater (less 

 liKely to occur due to chance) than the difference 

 between samples taken close together. Godsil, 

 using a modified analysis of covariance, showed 

 a much greater difference in the mean square 

 when comparing distant samples than when com- 

 paring "local" samples. Schaefer (1955), using 

 conventional analysis of covariance techniques, 

 came to a similar conclusion with regard to 

 Central American and southeast Polynesian yel- 

 lowfin. Such analyses have shown merely that 

 the differences are much greater but not how 

 much in units that can be readily compared. 



1/ Further discussion of a test of significance 

 will be undertaken in the sections on sampling 

 problems and comparison of tagging and mor— 

 phometric data . 



Another method which gives a direct 

 comparison has been used by Royce (1953), who 

 computed the size of various body parts for yel- 

 lowfin of a given total length . He showed there 

 was an average difference of 1.6 cm. in the 

 head length of a yellowfin tuna 100 cm . long as 

 between the western Caroline Islands and Costa 

 Rica and that the samples of tuna from the in- 

 tervening areas along the Pacific Equator had 

 head lengths of intermediate sizes suggestive of 

 a cline from east to west. A reverse cline was 

 apparent in the height of the anal fin, with dif- 

 ferences of up to 7.2 cm. between Costa Rica 

 and the Caroline Islands. This method provides 

 a ready means of comparison, but it still does 

 not consider the amount of intergradation or 

 overlap . 



CONCEPT OF OVERLAP 



Taxonomists in many fields have used 

 the degree of overlap in studies of inter- and 

 intra -specific variations. Among fish taxono- 

 mists, Ginsburg (1938) postulated that the best 

 means of comparison was the extent of intergrada- 

 tion or the amount of overlapping of principal 

 characters. He gives many examples of meristic 

 or countable characters, and he compares 

 samples by the actual overlap of the percentage 

 distributions. This he computed as a percent 

 (p*) obtained from the sum of the smaller per- 

 cents (%) of the frequency classes in the two 

 samples in the area of overlap. 



p* = S (%1 < %2) +I(%2<%1) (3) 

 2 



Other taxonomists have computed the mean and • 

 standard deviation of such frequency distribu- 

 tions and from them determined a single figure 

 for the distance between the populations which 

 is directly indicative of the amount of non-over- 

 lapping. This figure is simply the absolute 

 value of the difference between the means 

 (x. and x~) divided by the summed standard devia- 

 tions of the two populations (^f and ^2) 



CD. =-'- 



\\ 



1 +^2 



(4) 



It is called a coefficient of difference (CD.) by 

 Mayr et al (1953:146), who give it in a slightly 

 different notation. 



