SELECTION WITHOUT ARTIFICIAL CROSSING. 



39 



of the males are of type DD, two-fourths of type DR, etc., and simi- 

 larly for the females. Now a female of type DD may be fertilized by 

 a male of any of the three types, and the probability that a given 

 female shall be fertilized by a male of a particular type will .depend 

 on the relative number of males of that type. Since one-fourth of 

 the males are of type DD, the chance that any particular female shall 

 be fertilized by a male of type DD is one-fourth. Since one-fourth 

 of the females are of type DD, the chance that in a particular mating 

 the female shall be of type DD is one-fourth. Hence the probability 

 that a given mating shall be of type DD 9 X DD ^ is J X i = Tg^. 

 The possible matings that can occur, and the relative probability of 

 each of these matings, is shown in the left-hand column of Table A. 

 Since the denominator is the same for all these matings, it is omitted 

 for convenience. The products at the right of column 1 represent 

 the relative frequency of each of the matings. Assuming all these 

 matings to be equally productive, these same numbers represent the 

 relative number of progeny from matings of each of the types of 

 matings. 



Table A. — Method of determining the relative proportion of the various types in the 

 progeny produced by the individuals of generation F.^, ivith cross fertilization. 



Matings and their relative frequency. 



Types of progeny and 

 their relative fre- 

 quency from each of 

 the possible matings. 



DD 



DR 



RR 



DD X DD....1 X 1 = 1 ..- 



1 

 1 







DD X DR.. .A X 2= 2 



1 

 1 

 1 

 2 

 1 

 1 

 1 





DD X RR 1 X 1 = 1 





DR X DD 2 X 1 = 2 



1 

 1 





DR X DR.... 2 X 2 = 4 



1 

 1 



DR X RR....2 X 1 = 2 



RR X DD....1 X 1 = 1 





RR X DR 1 X 2 = 2 





1 

 1 



RR X RR....1 X 1 = 1 





Relative proportion in F3 







4 

 1 



8 

 2 



4 



Or 





In the next three columns the relative proportions of the different 

 types of progeny in each of the matings are shown. By adding these 

 columns it is seen that the ratio between the types in Fg is the same 

 as it was in Fg. Hence it will tend to be the same in all subsequent 

 generations, with cross-fertilization. With self-fertilization the 

 results are different, as seen in Table B. 



165 



