CHANGE OF BALANCE 239 



or frequency of chiasma formation at meiosis. The application of 

 this method will now be considered. 



(iv) Secondary Polyploidy. Since new allo-polyploids already 

 behave at meiosis to a great extent like diploids, it follows that 

 polyploid species which have changed since their origin can be 

 identified only by more or less circuitous inferences. And although 

 such inferences can be drawn without much hesitation for the 

 bulk of species in the angiosperms, there remains an interesting 

 group of doubtful cases. 



Where, as in one section of Rumex, species occur with " haploid " 

 or gametic numbers of 10, 20, 30, 40, 50, 60 and 100, and the 

 chromosomes are comparable in size, it is natural to assume without 

 further evidence that the higher-numbered species arise through 

 multiplication of a " basic " set of 10 chromosomes such as that 

 found in the lowest-numbered ones. The inference is less direct in 

 such genera as Dahlia (n = 16, 32) and Digitalis (n = 28, 56). 

 These numbers are multiples respectively of 8 and 7 which are found 

 in related genera. The conclusion that 8 and 7 are the basic 

 numbers, however, requires the support of other evidence. Still 

 less direct is the inference in those genera in which uneven multiples 

 occur. Many of these, such as Papaver (n = y, 11), are not yet 

 elucidated, and in the hybrid Nicotiana longiflora (10) x A^. alata (9) 

 (9" + i\ Goodspeed and Clausen, 1927 h), it is not clear whether 

 the extra chromosome arises from fragmentation or reduplication. 

 Others can be understood as the result of " fusion " between non- 

 homologous chromosomes after the occurrence of polyploidy. 

 Thus Cardamine pratensis (Lawrence, 1931, n = 15) is a tetraploid 

 with an original basic number of 8, two chromosomes having fused, 

 and Nicotiana longiflora (n = 10) is probably derived by fusion from 

 a species with a haploid number of 12 (Ch. III). Others, again, 

 show no evidence of fusion or other structural change, and it would 

 appear that they result from the unbalanced multiplication of the 

 basic set, two or three of the chromosomes occurring once more 

 often than the rest. It is in relation to these supposed " secondary 

 polyploids " that the criteria of polyploidy require to be strictly 

 examined. 



The evidence has been most fully adduced in the Pomoideae 



