130 'SUMMARY OF CURRENT RESEARCHES RELATING TO 



no fin-like margins. Interpretation of these and oilier abnormalities is 

 left for a larger paper. 



Inbreeding.* — II. S. Jennings gives a general formula for the rate 

 at which organisms become homozygotic through continued brother ami 



sister mating. The formula gives "(1) the proportion of individuals that 

 will lie homozygotic for any given character after any number of un- 

 broken generations of such inbreeding ; and (2) the average proportion 

 of the characters of a given individual that will be homozygotic after 

 any number of unbroken generations of such inbreeding. The numerical 

 value obtained may be called the coefficient of homozygosis. 



Let x = the coefficient of homozygosis ; n = the number of inbred 

 generations (the number of times successive brother and sister mating 

 has occurred) : f v / 2 , / 3 , etc. = the successive terms of the Fibonacci 

 series (thus f x = 0, /_> = 1, etc.). Then the formula for the coefficient 

 of homozygosis is — 



2 n-l + f . 2«-S + /„ • 2"- y 



The coefficient of inbreeding on the same lines (brother and sister 

 mating) is — — . The coefficient of inbreeding in self-fertilization 



is — - , and the coefficient of homozygosis is the same. The co- 



on 



2" 

 2" - n - 1 



v « — A V 



efficient of inbreeding in cousin matings is ' — J ', in parent and 

 offspring matings 



Inbreeding.j — Raymond Pearl points out that the values of the co- 

 efficients of inbreeding for a particular pedigree are composed of the 

 following elements : (1) the occurrence of the same individual animals 

 more than once on the sire's side of the pedigree only ; (2) the occur- 

 rence of the same individual animals more than once on the dam's side 

 of the pedigree only; and (8) the re-appearance of animals which, 

 appear first on one side of the pedigree (either the sire's side or the 

 dam's side) on the other side. The occurrence of (3) means that 

 sire and dam are in some degree related, and the question arises what 

 portion of the observed inbreeding is due to this. It appears that an 

 individual may be inbred in ten generations to within two-tenths of one 

 per cent as intensely, measured by the coefficients of inbreeding, if his 

 sire and dam are in no way related, as he would be if his sire and dam 

 were brother and sister. But clearly the germinal constitution of the 

 individual produced would, except by the most remote chance, be quite 

 different in the two cases. Pearl suggests a method for measuring the 

 proportion due to kinship of the parents, and that due to earlier re- 

 duplication. 



* Amer. Naturalist, xliii. (1914) pp. 693-6. 



t Amer. Naturalist, xlviii. (1914) pp. 513-23 (2 figs.). 



