SHORTER ARTICLES AND DISCUSSION 



THE PROBABILITY ESTABLISHED BY A CULTURE OF 

 GIVEN SIZE THAT A MATING IS CAPABLE OF 

 PRODUCING ONLY DOMINANT 

 INDIVIDUALS 



To distinguish individuals heterozygous from those homozygous 

 for a given dominant factor is a matter of mere inspection when 

 the simplex condition is somatically distinct from the duplex 

 condition, as is the case with the mottling factor in the Adzuki 

 Bean.^ Generally, however, the degree of dominance is such 

 that a breeding test must be resorted to in order to distinguish 

 these two types. A homozj'gous dominant will breed true for the 

 character whether selfed or back-crossed to the recessive, whereas 

 a heterozygous individual will give 3 : 1 and 1 : 1 ratios respec- 

 tively when similarly treated. The common breeding practice 

 is to consider the parent homozygous when, if selfed or back- 

 crossed, it fails to produce any recessive individuals in a reason- 

 ably large number of offspring. 



Just what is to be considered an adequately large number of 

 otfspring has in the past been determined by the personal judg- 

 ment of the individual investigator, and the diflBculty of obtain- 

 ing offspring in large numbers. There has beren no general 

 agreement based on mathematical considerations, probably be- 

 cause large numbers of offspring have not been found necessary 

 in order to distinguish a homozygous dominant from a heterozy- 

 gous parent producing such ratios as 3 : 1 and 1 : 1. The need 

 of a statistical criterion of what is an adequately large number 

 of offspring was realized when it became necessary in tetraploid 

 races of the Jimson Weed (Datura Stramonium) to distinguish 

 between matings which should produce only dominant purple 

 offspring and those which should produce a 35 : 1 ratio of purples 

 to whites. In distributions which are so asymmetrical as those 

 given by sampling from the 35 : 1 ratio, we are hardly justified 

 in using the ordinary theory of probable errors. Special tables 

 have, therefore, been computed for use in work under way at 

 the Station for Experimental Evolution. Since other investiga- 

 tors will probably meet with the need for similar criteria, it 

 seems worth while to give tables showing the number of offspring 



1 Jour. Eered., 8, 125-131, Fig. 10, 1917. 



458 



