STATISTICAL COMPARISON OF 

 MORPHOLOGICAL DATA 



By 



William F. Royce-' 



1/ 



Taxonomists concerned with the smaller 

 taxonomic units in all fields have used a great 

 variety of quantitative methods together with 

 various kinds of qualitative evidence to arrive 

 at decisions on the relationships of species and 

 subspecies. Generally, the quantitative meth- 

 ods have been sparingly used to substantiate a 

 conclusion already reached from the qualitative 

 evidence . We may infer that the qualitative 

 evidence has usually been considered adequate 

 and that quantitative methods are not always 

 necessary. With small forms which may be ar- 

 ranged in a laboratory and directly compared it 

 is easy to find the best characters which will 

 distinguish groups one from the other, and if 

 clear differences are found, then no statistical 

 methods are needed nor desirable . 



If, on the other hand, it is not possible 

 to see and compare many specimens at one time, 

 it is necessary to quantify the characters, and 

 the search for the best characters become much 

 more difficult. The often subtle evidence of 

 allometric or isometric growth must be sought 

 before considering a character . The multiple 

 sensory impressions that are so useful when 

 things are compared side by side become un- 

 certain and unreliable. Such a situation has 

 confronted biologists who have been concerned 

 with the races of tunas, a group in which it is 

 not possible to compare directly most of the 

 specimens. It has been necessary to guess at 

 the distinguishing characters, to measure them 

 in the field, and to compare them statistically 

 in the laboratory. 



Then when the data are at hand the usual 

 statistical methods in current use by fish tax- 

 onomists are not adequate. It is not possible to 



1/ Assistant Administrator in Charge of Re- 

 search, Alaska Commercial Fisheries, U.S. 

 Fish and Wildlife Service, Box 2021, Juneau, 

 Alaska. Formerly Fishery Research Biologist, 

 Pacific Oceanic Fishery Invs., Honolulu, T. H. 



compare directly frequency distributions be- 

 cause the characters used in this group have 

 been mostly the size of body parts, which are of 

 course related to the size of the fish. Such 

 measurements usually have been compared as 

 ratios, but ratios too are related to the size of 

 the fish because of the prevalence of allometric 

 growth. Even the regression analyses which 

 have been used especially for tunas have not 

 fully allowed for the complex allometric growth. 

 Then there has been a tendency to make compar- 

 isons by means of tests of significance, a 

 method which does not make full use of the data. 

 Neither has there been a satisfactory method of 

 comparing two groups while using more than 

 one character at a time . 



Tuna biologists also have an important 

 objective in addition to the usual taxonomic ones. 

 They want to know the amount of intermingling 

 of the stocks of tuna, not just whether they are 

 distinct enough to deserve different specific or 

 subspecific names. Studies based on taxonomic 

 principles provide answers to these problems 

 that supplement direct evidence of intermingling. 



I have prepared this paper with the 

 special objective of developing methods of an- 

 alysis suitable for racial studies of tunas. It 

 will also have obvious applications to intra - 

 specific studies of many groups, especially those 

 in which measurement data are used. In it I 

 will briefly review the quantitative methods in 

 current use. These include averages, ratios, 

 and the more precise regression analysis. I 

 will (1) consider the relative merits of the test 

 of significance and the measurement of overlap, 

 (2) discuss how to determine overlap of counted 

 characters and show how to find the overlap of 

 measured characters through regression analysis, 

 and (3) show the relation between overlap and a 

 concept of the distance between the means and 

 then apply a generalized distance function to 

 measure simultaneously the overlapping of sever- 

 al characters. 



