484 



THE AMERICAN NATURALIST [Vol. XLIX 



of individuals that must be present to give an equal chance 

 for the presence or absence of an individual of every type 

 is 4", where n represents the number of allelomorphic 

 pairs. This being true, if differences in all of the chro- 

 mosomes are predicated in tobacco and in pea crosses, the 

 maximum numln-r of individuals necessary in the F 2 gen- 

 eration to allow for one reproduction of each of the grand- 

 parental forms is 4 24 in the first case and 4 7 in the second 

 case. It is clear that there is an absolutely overwhelming 

 difference in the difficulty of recovering the grandpar- 

 ental forms in the two examples. 



Now this is about what one wishes to do in many plant- 

 breeding problems. It is desired to combine one or two 

 characters from one parent with all of the other qualities 

 of the second parent. And such has been my experience 

 that I believe that this maximum possible difficulty in the 

 operation as predicated by qualitative differences in all of 

 the chromosomes often occurs. There can be no question 

 on these grounds of the importance of determining the 

 number of chromosomes in a species before beginning 

 a complex plant-breeding problem, and thus being able to 

 comprehend the maximum possible difficulties that may 

 be encountered. How greatly these difficulties vary may 

 be seen in the very incomplete list of chromosome counts 

 in common plants that is given below. 



