April 6, 1906.] 



SCIENCE. 



549 



SPECIAL ARTICLES. 



A MENDELIAN CHARACTER IN CATTLE. 



Cursory observation led me some years ago 

 to suspect that the polled character in cattle 

 might be a Mendelian unit character. The 

 importance of such fact, should it prove to 

 be a fact, may be inferred when it is remem- 

 bered that every year hundreds of thousands 

 of cattle are dehorned, while certain breeders 

 who are trying to breed polled specimens of 

 the ordinary horned breeds are able to dispose 

 of polled animals at prices double those of 

 horned animals of similar breeding. During 

 the past summer I had the opportunity to col- 

 lect sufficient data on this subject to show 

 that the character is in all probability actually 

 Mendelian, and have worked out rules of 

 procedure for breeders who wish to rid their 

 cattle of horns. The data on which my con- 

 clusions are based are presented below. Be- 

 fore discussing them I wish to call attention 

 to the real meaning of the term ' Mendelian 

 expectation,' which I fear is overlooked by 

 some biologists, who, like myself, are only 

 slightly familiar with the mathematics of the 

 laws of chance. 



Let us consider the case of a cross between 

 a hybrid (DB) with its corresponding reces- 

 sive (B). Suppose the cross results in 4 

 progeny. Ordinarily we would say that the 

 Mendelian expectation is 2 DB and 2 B; or, 

 in greater detail. 



Parents. Gametes. Conjugations. Results. 

 Male DB 2 D and 2R\ j 2 DX-R 2 BK 



Female R 4iJ > I 2IiXIi 2 li 



Here it is an even chance whether a gamete 

 of the female parent shall be fertilized by a 

 D OT an B gamete of the male parent. The 

 four may, therefore, be fertilized in any one 

 of the following five ways: 



Probability 

 of Each Case. 



1. By 4 D gametes and R gametes, 1 



2. By 3 D gametes and 1 R gametes, 4 



3. By 2 D gametes and 2 R gametes, 6 



4. By 1 D gametes and 3 R gametes, 4 

 6. By D gametes and 4 R gametes, 1 



leths. 



The probability of each of these five possible 

 cases depends on the number of ways in which 

 each can occur. Cases 1 and 5 can occur in 

 only one way each; 2 and 4 can occur in four 

 ways each; i. e., the first individual may be 

 B and the remaining 3 DB; the second may 

 be B and the others DB, etc. The third case 

 can occur in six ways. And so on. Alto- 

 gether there are sixteen ways; hence the 

 probabilities shown in the last column. This 

 means that, in sixteen such cases, on the 

 average one case will result in 4 DB progeny, 

 four will result in 3 DB and 1 B progeny, 

 etc.; and this is the real Mendelian expecta- 

 tion. As the combination 2 DB and 2 B 

 would occur oftenest (six in sixteen times) 

 we usually designate it as the Mendelian ex- 

 pectation, but the case 4 DB is also to be 

 expected, though it will not occur so often. 

 It would be more accurate to refer to the 

 combination 2 DB and 2 5 as the highest 

 (but not the only) expectation. Deviations 

 from this highest expectation are to be ex- 

 pected, and the number and character of such 

 deviations can be calculated from the laws of 

 chance. 



In studying the progeny of polled Hereford 

 bulls bred to horned cows, the very interesting 

 fact developed that the polled character is 

 dominant, but the hybrids frequently have 

 imperfectly developed horns, called scurs by 

 breeders. No ease has thus far been found 

 & which a hybrid had fully developed horns. 

 Whether scurs always appear on the hybrids 

 has not been ascertained. Many of the hy- 

 brids examined had no visible scurs, but many 

 of them were calves only a few months old. 

 Breeders state that rather large scurs occa- 

 sionally develop, especially on males, on ani- 

 mals a year or more of age. 



It was not practical to examine all the 

 hybrids observed closely enough to determine 

 the presence or absence of very small scurs. 

 Questions not fully determined, and which 

 warrant further study, are: (1) Do the hy- 

 brids always develop scurs? Final examina- 

 tions should not be made before the animals 

 are about fifteen months old. A breeder re- 

 ports one case in which large scurs developed 

 at fourteen months. (2) Do the hybrids ever 



