No. 646] SHORTER ARTICLES AND DISCUSSION 459 



which should be considered in order to distinguish matings which 

 should give. all dominant individuals from those which may pro- 

 duce recessives. 



The theory is of course quite simple. It is assumed that the 

 expected ratio of dominant to recessive is known, and is p : q, 

 where p -)- g = 1. The distribution of the chances of obtaining 

 dominant and recessive individuals in the frequencies n : 0, 

 (n~l) : 1, in—2) : 2, etc., when n individuals are grown is 

 (P + 3)"- To ascertain the probability of securing all dominant 

 individuals in a culture which should show a definite ratio of 

 dominant to recessive offspring we have merely to table p" against 

 n. If this value is very small, it is reasonable to assume that in 

 practice a culture of n individuals all of the dominant type 

 represents a parent or parents capable of producing only off- 

 spring of the dominant type. Thus, for example, if seeds which 

 should produce dominant and recessive individuals in a 5 : 1 

 ratio were sown, a culture of 35 all dominant individuals should 

 be obtained only 17 times in 10,000. Hence, if a sowing is made 

 to distinguish between a mating capable of producing only domi- 

 nants and one which should give recessives in a 5 : 1 ratio, and 

 there results a culture of 35 individuals all of the dominant type, 

 it is altogether reasonable to assume that the mating in question 

 is incapable of producing recessives. 



Tables have been formed to include the 3 : 1 and 1 : 1 ratios 

 familiar in ordinary disomie inheritance, the 2 : 1 and 8 : 1 

 ratios found in trisomic inheritance in the mutant Poinsettia, 

 and the 5 : 1, 11 : 1, and 35 : 1 ratios found in tetraploids in 

 Datura. Some of these ratios are suggested by published data. 

 on (Enothera Lamarckiana and Primula sinensis, and will prob- 

 ably be found ultimately by those studying other forms. 



The tables enable one to decide how large a culture is neces- 

 sary on a probability basis. If it is felt that only 1 chance in 

 1,000 of the mating being capable of producing a recessive is 

 sufficient evidence that the culture represents only dominants, 

 then, to distinguish a mating which can produce only dominants 

 from one which should give a 1 : 1 ratio, a culture of at least 10 

 individuals is necessary. If the 3 : 1 ratio is the one in question, 

 then 24 individuals are necessary ; while if a 35 : 1 ratio is con- 

 sidered, 244 individuals are required. In other words, cultures of 

 10, 24 and 244 individuals are of equal value in distinguishing 

 matings which should produce only dominants from those which 



