STATISTICS IN CLASSIFYING RACES OF SHAD 



281 



population; P is an estimate of the proportion of 

 the sample native to the Connecticut River. 



It is not known which of these estimates would 

 be best for the present problem. A few stray fish 

 will have a greater effect on the first estimate than 

 on the third, particularly if the strays are near one 

 end of the distribution of the discriminant func- 

 tion. In the first type of estimate, they would be 

 weighted more heavily because some of the indi- 

 viduals near the midpoints of the two populations 

 would not be classified. In the third estimate, 

 they would all receive the same weight. In any 

 particular problem, perhaps all three of these 

 estimates should be tried and the various esti- 

 mates compared. If they are not in agreement, 

 the factors causing the differences should be 

 investigated. Plotting the distributions on prob- 

 ability paper may give some clue to the number 

 of strays present in the samples. 



DISCUSSION 



The basic condition necessary for the demon- 

 stration of a distinct population of shad in each 

 river is that the differences between rivers must 

 be large compared to the differences between years. 

 This condition has been met by the data examined 

 in this study: however, some large differences 

 between years have been reported and they are 

 impossible to evaluate completely at this time. 

 Warfel and Olsen (1947) reported average verte- 

 bral counts of 57.042 and 56.837 for 1945 and 1946 

 in the Connecticut River. This difference of 0.2 

 is significant. Raney and de Sylva (1953) also 

 reported some differences between years for 

 striped bass. They made the following statement 

 about these differences: (p. 506) 



In any one river system such as the Hudson River there 

 may be significant variations from year to year in any of 

 the characters investigated. These fluctuations may be 

 caused by differences in water temperature and perhaps 

 other factors during larval life at the time when fin ray 

 number is determined. The assumption is made that 

 fin ray numbers are genetically fixed within narrow limits 

 and the minor fluctuations which occur from year to year 

 are due to different physical and perhaps chemical con- 

 ditions at any one locality or differences in time of spawn- 

 ing, will tend to balance out when samples are taken over 

 a period of several years. 



From the statistical point of view, it does not 

 matter what causes these differences when a mixed 

 population is to be divided into its components. 

 For example, the characters for the Hudson and 



Connecticut Rivers can change considerably from 

 year to year, and the New Jersey catch can still 

 be segregated providing samples are obtained 

 from both rivers and a new discriminant function 

 is calculated each year. Of course, it is essential 

 that the populations be different. 



From the biological point of view, the cause of 

 these differences is important. If these differ- 

 ences are primarily genetic, the different popula- 

 tions should be considered taxonomically as races 

 or even sub-species. Raney and de Sylva (1953) 

 considered striped bass from the Hudson River 

 and Chesapeake-Delaware area to be different 

 taxonomic races and suggested calling them the 

 Hudson race and Chesapeake-Delaware race. 

 Similarly, future research may prove that there 

 are actually taxonomic races (or sub-species) of 

 shad . 



From Rounsefell and Dahlgren's (1932) work 

 on the herring, it appears that temperature, may 

 be one of the most important environmental 

 variables to be studied. A rather simple experi- 

 ment could be set up whereby it would be possible 

 to hatch shad eggs in controlled water tempera- 

 tures. This should produce a response curve 

 between meristic counts and temperature, if such 

 a relation exists. Such an experiment would be 

 useful in evaluating the differences between years 

 and rivers. 



The human errors in making meristic counts 

 should also be investigated. These certainly con- 

 tribute to the total variation; therefore, the mag- 

 nitude of such errors should be known. There 

 are no doubt times when a certain amount of 

 judgment must be used in deciding if a given ray 

 actually should be included in a count. Similarly, 

 gross errors of definition can be made in the 

 counts. These various errors cannot be evalu- 

 ated at this time, but any future work should 

 certainly include a study of this part of the 

 problem. 



Future work with meristic counts will naturally 

 require a great amount of statistical analysis. 

 It is essential, therefore, that the surveys be 

 planned in such a manner that a maximum amount 

 of information can be obtained from them. Of 

 the 1,800 fish collected from 1938 to 1945, only 

 one-third of them could be utilized in a two-way 

 analysis of variance. The surveys should include 

 year classes, sampling dates within a year, differ- 

 ent types of gear and different locations within 



