276 



FISHERY BULLETIN OF THE FISH AND WILDLIFE SERVICE 



While the differences between rivers are not signifi- 

 cant for anal rays, they are for the other four 

 characters, so it can be safelv concluded that 

 there are differences from river to river for four 

 characters. 



The F values for differences between years are 

 rather large for anterior scutes and posterior 

 scutes, and both are significant at the 10 -percent 

 level {F, ,,20=2.75). At the present time, it is 

 impossible to say definitely whether there are 

 differences from year to year for these two charac- 

 ters. It is apparent that t his is one phase of the 

 problem that should be studied in more detail. 



The fact that there may be differences from 

 year to year for some characters does not disprove 

 the racial theory. The magnitude of the differ- 

 ences between years relative to the differences 

 between rivers is the essential quantity to be con- 

 sidered in this problem. If the differences between 

 years arc small in comparison to the differences 

 between rivers, races can still be distinguished. 

 In terms of the model presented on page 274, the 

 river-effects (a,) should be considerably larger than 

 the year-effects (/?,). An estimate of the relative 

 magnitude of these two effects can be obtained 

 from the analysis of variance tables. Since none 

 of the interactions was significant, the interaction 

 mean square has been pooled with the error mean 

 square to obtain an estimate of the error (a 2 ). 

 It has been assumed that both the years and the 

 rivers are a, sample from a large number of years 

 and rivers. Therefore, the a, and ,8, obtained from 

 the data are samples from some larger population 

 of a, and (3j which have variance o- R and o- Y . 

 From the mean squares in the fourth column 

 of table 5, estimates of <tr and try can be ob- 

 tained. For anterior scutes: o- 2 =0.488, o-y = 0.01 12. 

 and o- R = 0.0414; for posterior scutes: o- 2 =0.633, 

 £y=0.0131, and o- R = 0.1154. Thus, the variation 

 between years for anterior scutes is about one- 

 fourth as large as the variation between rivers. 

 Similarly, for posterior scutes, the variation be- 

 tween years is about one-ninth the variation 

 between rivers. 



These analyses present evidence that there are 

 no differences between years for anal rays, pectoral 

 rays, and vertebrae. There may be differences 

 between years for anterior and posterior scutes, 

 but if they do exist, they are small compared to 

 the variation between rivers. These analyses of 

 variance have approached the racial problem in a 



Table 5. — Analysis of variance with interaction tenn pooled 

 with error term 



more direct manner than in previous studies and 

 have given further support to the racial theory. 



DISCRIMINANT FUNCTION ANALYSIS 



There are numerous ways of using the data from 

 meristic counts to construct discriminant func- 

 tions. Raney and de Sylva (1953) constructed 

 such a function by adding the number of dorsal, 

 anal, and pectoral rays for each fish. They called 

 this a "character index," but actually it is a 

 simple form of a discriminant function. By plot- 

 ting a frequency histogram of this character index 

 for several areas and a series of years, they were 

 able to differentiate to some extent between 

 striped bass from the Hudson River and from 

 Chesapeake Bay. There was considerable over- 

 lap in these distributions, and if one were presented 

 with a fish of unknown origin, it would be difficult 

 to assign it to a particular population with any 

 certainty. 



For illustration purposes, a discriminant func- 

 tion of this type has been constructed using data 

 on shad from the Connecticut River and the 

 Hudson River. It is unfortunate that the data 

 for the Hudson River were collected in 1939 and 

 1940 (tables 11 and 12, appendix) while the Con- 

 necticut data were collected in 1945 (table 13. 

 appendix), but since it has been shown that the 

 characters are consistent from year to year, the 

 data can be used for discrimination. The dis- 

 criminant function, 



Z=X,+Xo+X 3 +X 4 +X 5 +X 6 



where X, is the number of anterior scutes, X L . the 

 number of posterior scutes, X 3 the number of dor- 

 sal rays, X 4 the number of anal rays, X 5 the num- 

 ber of pectoral rays, and X 6 is the number of 



