SHOKTER ARTICLES AND DISCUSSION 



STUDIES ON INBREEDING— IV 



On a General Formula for the Constitution of the wth 

 Generation of a Mendelian Population in which 



ALL MaTIXGS ARK OF Bk< ITIIER X SlSTER 1 



I. In a former paper in this series' tin- constitution of a Men- 

 sister type was worked out empirically. The results there pre- 

 sented may be put in the form of a general formula, by means 

 of which the constitution of any generation may be written down 

 from a knowledge of the preceding generation; that is from a 

 knowledge of the n — 1th generation the nth generation may be 



II. This general formula may be developed as follows. A 

 single character pair will be considered. A denoting the dominant 

 character and a the recessive. Kqual fertility for all malings 

 is assumed, the number of individuals per family being taken as 

 2s, of which s are males and x are females. One family will then 

 make 5 mating* and produce x families in the next generation. 

 Each mating is, by hypothesis, of a brother with his sister. 



Starling as before with a pair from a population in which all 

 individuals are of constitution Aa there will be in the next 

 generation one family of the AA -f Aa + aA -f aa type. In all 

 succeeding generations there will be six types of families, viz.: 



(1) AA families. 



(2) AA-\-Aa families. 



(3) Aa families. 



(4) Aa + 2 Aa + aa families. 



(5) Aa^A- aa families. 



(6) aa families. 



Rept. Me. Agr. Expt. Sta. for 191.'?. pp. 191-202. TIL "On the Results 



I'r.niuu, ( 'mi r] n'<i i m>, A m Kii. N at.. Vol. XLVIU. pp. 57-62, 1914. 

 2 Amer. Nat., Vol. XVLIII, pp. 57-62, 1914. 



491 



