No. 587] SHORTER ARTICLES AND DISCUSSION 



707 



THE VALUE OF INTER-ANNUAL CORRELATIONS 



If x 1} x 2 , x 3 • • • x n be measures taken on the n individuals of a 

 series in a given year and x/, x 3 ' ■ • • x n ' be similar measures 

 taken in a subsequent year, the correlation between the first and 

 second measures on the same individual r xx ', may be designated 

 as a direct inter-annual correlation. 1 The purpose of this review 

 is to illustrate the usefulness of such constants, with a view to 

 extending their application, by bringing together examples of 

 inter-annual correlations from various fields. 



The immediate value of such coefficients may be purely scien- 

 tific, economic, or both theoretical and practical. 



Practically such means of prediction as correlation and regres- 

 sion formulas should find wide application in breeding operations 

 where it is desirable to weed out or send to the butcher at the 

 earliest possible moment those individuals which can not be kept 

 with the maximum profit. If the correlation between the egg 

 production of a fowl in her pullet year and her laying capacity 

 in any subsequent year be high, it is clear that those which on the 

 average are to prove unprofitable may be sent to the pot when 

 most desirable for that purpose, and before they have consumed 

 two or more years' feed without yielding the maximum return in 

 eggs. If, on the contrary, there be no correlation, the labor of 

 selection in the pullet year is an unnecessary expense. If a cow's 

 milking capacity be closely correlated with her milking record in 

 her heifer year, the culling of dairy herds may be profitably 

 carried out in the first year. In plant breeding experiments, 

 involving either sexual or vegetative reproduction, selection of 

 individuals for future propagation must be made, and at as early 

 a date as possible. If the future yield per plant of hay can be 

 estimated with considerable accuracy from a first year's culture 

 the process of selecting clonal strains can be carried out with far 

 greater rapidity than if one must wait for the results of subse- 

 quent years' tests. In all such cases the finality of a first judg- 

 ment must depend in large degree upon the closeness of correla- 

 tion between the results of successive experiments — in short upon 

 the value of the inter-annual correlation coefficient. 



i Cross inter-annual correlations in which the measures taken are of a 

 different sort are sometimes useful, but examples of such are not consid- 

 ered in this review. 



