No. 562] THE PROBLEM OF INBREEDING 581 



fertilization, where the number of ancestors reduces to 1 

 in each generation. 



The Measueement of the Degree of Inbreeding 



This brings us to a consideration of a practical and 

 general measure of the degree of inbreeding exhibited in 

 a particular pedigree. This problem has been attacked 

 by a number of other investigators, but so far as I have 

 been able to learn all previous measures have been modi- 

 fications in one form or another of the scheme of Lehn- 

 dorff. This plan 4 took account, as a measure of inbreed- 

 ing, only of the number of generations intervening be- 

 tween that generation in which relatives were bred to- 

 gether, and that generation in which their first common 

 ancestor was found. Thus Lehndorfr says : 5 



I am of opinion, that a horse should only be termed in-bred, when in 

 sum total less than four degrees lay between its parents and their 

 common ancestor; in other words, when the children or grandchildren 

 of a stallion or a mare are mated, I call their produce in-bred; but this 

 term does not apply to the produce of great-grandchildren of the 

 common ancestor. AVe must not forget that in the pedigrees of horses 

 the word brother or sister often means half-brother or half-sister, and 

 that here the definition borrowed from the human family connection is 

 not applicable. 



As breeding within moderate relationship I reckon the mating of 

 stallion and mare that are removed from their common ancestor four, 

 five or six degrees. It is indifferent whether they are on both sides 

 equidistant from, or one of them nearer to the male or female pro- 

 genitor than the other. 



Von Oettingen used a measure exactly the same in 

 principle as this of LehndorfT's. The system of Bruce 

 Low, though somewhat differently stated, comes to essen- 

 tially the same thing, so far as I am able to determine 

 from abstracts, this author's original writings not having 

 been accessible to me. 



All systems based on the number of "free generations" 

 alone do not furnish a precise or reliable measure of the 

 real intensity of inbreeding. The essential reason for 

 this failure, stated baldly, is that they do not take account 



4 Cf. Lehndorff, G., "Horse-breeding Eecollections, " Philadelphia, 1887. 



