46 
GENETICS: H. S. JENNINGS 
constitutions (AA, Aa, or aa) remain the same for all generations. Ex- 
amples are: 
(1) Random mating when the parents are at the beginning either all 
Aa; or half AA, half aa; or when the parental proportions are AA-f-2Aa 
+aa. In these cases after any number of generations the resulting 
progeny show the proportions AA+2Aa+aa. 
(2) Random mating, parental proportions, rAA to /aa. Constant 
proportion in offspring: f2AA+2r/Aa+/^aa. 
(3) Random mating, parental proportions, AA+Aa. Constant re- 
sult, 9AA+6Aa+aa. 
(4) Random mating, parental proportions, rAA+^Aa. Constant 
result, (s-{-2r) ^AA + 2^ (5 + 2r) Aa + ^^aa . 
(5) Inbreeding, daughters bred back to father: both parents Aa. 
Constant result, AA-l-2Aa+aa. 
(6) Sex-linked factors; random mating; original parents rAA-{-rA — h 
/aa+/a — , in equal numbers. Constant later proportions: males, 
rA — h/a— ; females, r2AAH-2r/Aa+/2aa. Males and females in equal 
numbers. 
B. In some complex cases the population changes from generation, 
and the best we can do is to obtain a formula which shall, when we know 
the proportions in a given generation n, give us the proportions in the 
next following generation 
Examples : 
(7) Random mating, population in nth generation: rAA+^Aa+/aa. 
Population in generation n+1 = (s-\-2ryAA + 2 (5 -1-2/') (5+ 2/) Aa +' 
(5+2/)2aa. 
(8) Assortative mating; population in the generation n is rAA-f 
5Aa-l-/aa. In the next generation (n+1) the population is (2r-\-syAA+ 
(4rs -f 2^2) Aa -f (s^ -f M + 45/) aa . 
(9) Selection of dominants; parental population in generation n is 
rAA-f ^Aa-f-Zaa. Population in the next generation (w-|-l) is {2r-\-sy 
AA-F25(2r-f5)Aa-f-52aa. 
C. In many cases the constitution of the population changes from 
generation to generation, as long as the given system of breeding lasts, 
and it is possible to give a simple formula in terms of n, the number of 
generations that the given system has been followed, from which for^' 
mula the proportions in generation n can be directly computed. 
Examples : 
(10) Assortative mating (dominants with dominants, recessives with 
recessives) ; original parents are progeny of the cross AA X aa, so that 
their proportions are AA-h2Aa-haa. After n assortative ma tings the 
proportions are: (/z-}-l)AA-|-2Aa-f-(/^-t-l)aa. 
