September 27, 



[917] 



NATURE 



75 



THE STATISTICS OF THE DAIRY. 



DR. RAYMOND PEARL is one of the younger 

 generation of American biologists. He belongs 

 to that school of naturalists who pursue, to begin with, 

 the critical study of evolution, dealing not with its 

 results alone but with its actual phenomena, who 

 inquire into the essential facts and ways of working 

 of selection, and who investigate accordingly all the 

 problems, mathematical and other (especially those re- 

 lating to "probability"), which are associated with 

 variation and heredity. He belongs, that is to say, 

 to the twin brotherhood of the experimentalists and 

 Mtisticians, and like others of his school he has of 

 -■ turned his investigations into very practical lines. 

 . batch of Dr. Pearl's recent papers has come to 

 hand, mostlv on work done in connection with the 

 Agricultural Experiment Station of the State of Maine. 

 One — a very interesting one — is a general' review of 

 "The Selection Problem." Others deal with statistical 

 and biometric methods — for instance with class-fre- 

 quencies, with the gamma function, and with other 

 matters connected with "curve-fitting." The rest of 

 the batch are for the most 

 lit experimental studies, on 

 -;:; -production or " inherit- 

 ■ iice of fecundity" in the 

 common fowl, and on various 

 problems of productiveness 

 ami of race-inheritance in 

 cattle. Let us consider one 

 only of these papers (or rather 

 a part of one), which deals 

 with " Animal Husbandry 

 Investigations," and in par- 

 ticular with the " Study and 

 Analysis of Milk Records." ^ 

 This is a very practical sub- 

 ject indeed, and all the more 

 so at present, when questions 

 of efficiency in food production 

 are of the highest and most 

 obvious importance. 



The essential problem before 

 us is the comparison of two 

 dairies, or two herds, w^ith 

 regard to milk production; 

 how are we to say, or to dis- 

 cover, which herd is the 

 better of the two? Simple as 

 the case at first sight seems 

 to be, it really involves a 



curious and puzzling statistical problem ; for the 

 yield of each individual cow not only depends 

 on its own intrinsic "quality," but is very 

 largely influenced by two distinct factors, namely 

 by the animal's age and by the time which has elapsed 

 since calving. The cow is at her best when about 

 five to si.x years old ; her yield of milk increases up to 

 that age, and slowly falls away afterwards. Whether 

 she be old or young, her yield is at a maximum shortly 

 after calving, and month by month it gradually and 

 slowly diminishes. We must find some means of 

 equaiitij^ our two sets of data for the two herds, when 

 none of the individual data are directly comparable, 

 for the cows in our two herds will differ, at haphazard, 

 in age and in the period elapsed since parturition. We 

 must, in other words, discover some system of 

 "weighting" for these factors, or (what comes to the 

 same thing) some way of adjusting the actual yield 

 to a standard condition of age and period. It is 



1 Report of Progress on Animal Hu»bandr5' Investigations in 1915 ; Maine 

 Agricultural Experiment Station, Orono, Maine. (Papers from the Bio- 

 logical Laboratory, No. 92.) 



NO. 2500, VOL. 100] 



obvious, then, that any such calculation must be pre- 

 ceded by a long and comprehensive experimental in- 

 vestigation. After this experimental basis is obtained 

 (and for practical purposes Dr. Pearl has now suffi- 

 ciently achieved it — unless, perchance, there turn out 

 to be significant differences in the case of Jerseys or 

 other special breeds), the rest is easy ; but I have tried 

 (with Dr. Pearl's approval) to simplify his own very 

 lucid account still further, and to employ for this pur- 

 pose a simple chart or diagram. 



As the outcome of all his previous investigations, Dr. 

 Pearl gives us a table of percentage efficiencies in 

 dairy cattle, of which the following is an abbreviation 

 or abstract. We shall not, by the way, carry our dis- 

 cussion beyond the period of ten or eleven months after 

 calving, after which time (provided the cow does 

 not calve again) the yield may still continue a long 

 while, diminishing very s'owly in quantity; we must 

 also remember that, for cows ending their lactation 

 in earlier months, the curve will drop somewhat 

 abruptly to zero ; and we must not forget that this is a 

 quantitative study only, and that the quality or rich- 

 ness of the milk must be dealt with separately. 



MonJths sinc e Calving or Freshenin g. 

 3579 



I L \ \ L 



Perce ntage-effici«ncy chart of milk production. Two herds, A and B, are supposed to have been 

 plotted on the blank chart #, cows of Herd A ; O, cows of Herd B. 



Table of Percentage Efficiencies. 



Stage of lactation, in months 



From this, or from the full table, we may now 

 prepare our diagram, in which the several contour-lines 

 denote percentages of the maximum or ideal efficiency, 

 90 per cent., 80 per cent., etc., and the spaces or 

 zones between them represent, therefore, average per- 

 centage efficiencies of 95 per cent., 85 per cent., etc., as 

 compared with the standard of maximum— this latter 

 being what we should expect were the cow five to six 



