February 7, 1913] 



SCIENCE 



227 



A record of the entire breeding history of a 

 rather remarkable ewe, of which I made a 

 note some time ago for another purpose, illus- 

 trates this law in so clear a manner that it 

 seems desirable to publish it with some dis- 

 cussion, particularly since the place of orig- 

 inal appearance of the record is neither readily 

 accessible nor likely to come to the attention 

 of the biologist. 



The record referred to was contributed to 

 the New England Farmer^ by Mr. Chas. Mat- 

 toon, of Lenox, Mass. The ewe in question 

 was owned by one of his neighbors, Colonel 

 Nathan Barrett, who, at the request of Mat- 

 toon, drew up the following account : 



I hereby certify that I have owned a native ewe 

 sheep, for the space of nineteen years, lacking a 

 few days; having retained her usual vigor for 

 seventeen years. But in the fall of 1822, I ob- 

 served for the first time, and with no small degree 

 of interest, that she slackened her pace, and went 

 in the rear instead of front, which she continued 

 to do for one year. After which, having nearly 

 lost use of her eyes, and teeth, I took her under 

 my immediate care for the last six months, until 

 March, 1824, when she died with old age — having 

 given me nineteen fleeces of wool, and borne me 

 thirty-six full-grown lambs, viz. : 



Lambs 



April , 1806 1 1815 ... 



1807 1 1816 . .. 



1808 2 1817 ... 



Apr. 3, 1809 3 1818 . . . 



Mar. 29, 1810 3 1819 ... 



Making 6 lambs in 11 1820 ... 



months and 26 days. 1821 . . . 



1811 3 1822 ... 



1812 3 1823 ... 



1813 3 1824 ... 



1814 3 Total 



The general accord of this case with the 

 law discussed by Marshall is obvious. Begin- 

 ning with the minimum degree of fecundity 

 possible (excluding absolute sterility) there is 

 a rather rapid increase to a maximum, which 

 is maintained for a time. This is followed 

 by a decline in fecundity more gradual than 

 the rise, ending finally in absolute sterility. 



•Vol. III., June 3, 1825, p. 353. 



The case is of especial interest in the present 

 connection because of the fact that it is a 

 completed record, carried to the natural end 

 of life of the individual. Such completed 

 breeding records are rare for higher animals. 



It is of interest to make certain biometric 

 computations from these data. K the age of 

 the ewe is taken as abscissa and the number 

 of lambs born as ordinate one can calculate 

 by the ordinary methods the arithmetic mean 

 point of this animal's total fecundity period, 

 and certain other constants of interest. The 

 only diiSculty in making such calculations 

 arises from the fact that no precise statement 

 is made as to the age of the ewe at the time 

 when the published lambing record begins. It 

 is altogether reasonable to assume, however, 

 that (a) the first lamb recorded is the first one 

 borne by this ewe, and (h) that she was about 

 one year old when this lamb was born. These 

 assumptions will be made in the calculating, 

 and further it will be assumed that the abscis- 

 sal classes throughout center at even years of 

 life. 



Making these assumptions I find: 



(a) That the arithmetic mean point of this 

 ewe's effective breeding life was at 8.57 years. 



(b) That the median point in her breeding 

 career was at 8.17 years. That is, she pro- 

 duced one half of her offspring before that age 

 and one half after it. 



(c) That the modal breeding point* (i. e., 

 the point of maximum fecundity per unit of 

 time) was at 7.34 years. 



Taking into account the 17 years in which 

 some young were born I find the following 

 constants regarding the number of lambs per 

 birth : 



Mean number of lambs per birth . 2.12 lambs. 

 Standard deviation in number of 



lambs per birth 76 lambs. 



Coefficient of variation in number 



of lambs per birth 35.78 per cent. 



These are intra-individual constants based 

 on an unusually long and completed breeding 



* Calculated by the approximate relation that the 

 distance from mean to mode is three times the dis- 

 tance from mean to median. 



