TAXONOMIC CHARACTERS 



Any morphological character may be ex- 

 pressed either as a count or as a measurement. 

 Counts are made of the number of body parts: 

 fin rays, vertebrae, scales, etc . The presence 

 or absence of a part, e.g., a barbel, fin, or 

 scales on a certain part, may be considered as 

 a special kind of count which is either 1 or 0. 

 All other things may be measured: distance, 

 area, volume, weight, angle, etc . We shall not 

 be concerned with non -morphological characters, 

 but such things as color, physiology, and fertil- 

 ity may usually be measured too . 



In any search for distinctive characters, 

 we seek those which reflect inheritable genetic 

 differences regardless of sex, size, nutrition 

 and environment. If a character is a function of 

 any of the latter factors, then we may either 

 compare samples which are identical with re- 

 gard to these factors (e.g., all the same sex) 

 or introduce a mathematical adjustment that re - 

 moves the non -inheritable difference. In this 

 paper we should be concerned with characters 

 that are related to size, but it should be noted 

 that the other factors may be considered in 

 similar ways . 



Any morphological character may be a 

 function of total size, but usually counts are not 

 and they are generally used as though independ- 

 ent. On the other hand, measurements of fish 

 almost always are related to body size. This 

 makes it obvious that the effect of body size 

 must be eliminated, and fish taxonomists usually 

 have attempted this by using ratios. However, 

 ratios are difficult to use (Marr 1955) because 

 parts are seldom related to body size in a simp- 

 le constant ratio. This has led Ginsburg (1939) 

 to doubt the value of measured characters (dis- 

 tances) and Parr (1949) to propose a relatively 

 complicated formula for dealing with them . 



Another approach was made in the first 

 studies of the morphometric characteristics and 

 relative growth of yellowfin tuna by Godsil (1948) 

 and by Schaefer (1948), who used regression 

 analysis to describe the size of body parts . Both 

 of these authors found that body proportions or 

 ratios of the size of a part to total length were 

 unsatisfactory except in the rare instance where 



the ratio had a constant relation to the total 

 length or, in other words, where the growth of 

 the part was exactly proportional to the growth 

 of the fish . When the data are subj ected to re- 

 gression analysis this is the unique case in 

 which the regression line is straight and passes 

 through the origin . Godsil found that not only 

 did the regression lines rarely pass through the 

 origin but that in most cases when a large amount 

 of data was available a slight curvilinearity was 

 obvious, and he fitted his regression lines with 

 the formula ^. 



Y = a + bX + 



(1) 



in which a, b, and c are constants, X is the fork 

 length of the fish, and Y is the estimated length 

 of the character measured. Schaefer, on the 

 other hand, found a satisfactory fit using a 

 straight -line regression method for most char- 

 acters A 



Y = a + bX (2) 



but with the length of the pectoral, second dor- 

 sal, and anal fins he found it necessary to trans- 

 form either the fin length or fork length or both 

 to logarithms in order to obtain a sufficiently 

 straight regression line. Marr (1955) points out 

 that transformations are usually satisfactory and 

 are much easier to analyse than curvilinear 

 regressions. 



TESTS OF SIGNIFICANCE 



After determining the regression line 

 which gives a satisfactory fit, most authors have 

 used a test of significance to decide whether two 

 or more samples could have been drawn from 

 the same population. Godsil (1948) compared 

 Central American, Japanese, Hawaiian, and 

 Peruvian yellowfin and found that with one or 

 more characters there were highly significant 

 statistical differences between areas. Schaefer 

 and Walford (1950) found similar differences be- 

 tween yellowfin of Central America and Angola, 

 Africa . These methods have been followed in 

 subsequent papers, all of which indicate highly 

 significant statistical differences between areas. 

 Such statistical differences have been found so 

 consistently that Royce (1953) concluded that, 

 even with samples from closely related stocks, 

 highly significant statistical differences could 

 always be found by increasing the size of the 

 sample, by considering enough characters, or 



