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THE AMERICAN NATURALIST [Vol. XLVIII 



Thus, if the number of inbreedings (n) is 3 

 x = — = 1/2, or 50 per cent. 

 If »=4 



-f Q.2 7 + 1. 2° + 1.2-- + 2.2 1 + 3.2 3 + 5.2 2 + 8.2 1 + 13.2 

 = 457/512, or 89.26 per cent. 



If n=16 



_ 63819 

 * 65536 



97.38 per cent. 



As these examples show, the formula gives the results that 

 were Obtained by Pearl in the detailed working out (so far as 

 this was carried), as given in Pearl's table I (2, p. 62). (It will 

 be noted that Pearl counts as generation 1 the one before inbreed- 

 ing has occurred, so that his generation 10, for example, is that in 

 which there have been 9 inbreedings (n = 9).) 



If one is working out the values of the coefficient x for a series 

 of generations, the above formula may be expressed as a simple 

 rule, applicable after the value for w=l is obtained. This 



The value of the coefficient of homozygous x for any term (as 

 the nth) is obtained by doubling the numerator and denominator 

 of the fraction expressing the value for the previous term, and 

 adding to the numerator the corresponding (n — 1th) term of 

 the Fibonacci series. 



Or, in view of the peculiar nature of the Fibonacci series, the 

 rule may be expressed as follows : 



Double the numerator and denominator, and add to the nu- 

 merator the sum of the last two numbers so added. 



Thus, since 



x for 1 inbreeding =1/2 



