116 REDUCTION OF VARIABILITY. 



this daughter will be pure in respect to one half of the number 

 of these genes, and impure for the rest of them. A plant, het- 

 erozygous for sixteen genes, will have a daughter impure for 

 only eight. The potential variability of an individual plant, 

 which is the number of genes for which it is heterozygous, is 

 one half of that of its mother, and it is double that of its daugh- 

 ter. In every subsequent generation the potential variabihty 

 is on the average cut in half. The reduction in potential var- 

 iability may fluctuate somewhat from generation to gener- 

 ation, it may be 40 % for one generation and 60 % for the 

 next, but it will always average 50 %. If we start with a plant 

 heterozygous for sixteen genes, with a potential variability 

 sixteen, the T. P. V. of its daughter, grand-daughter and so on, 

 will be 8, 4, 2, one, and zero. In a few generations the descen- 

 dants of a plant which is propagated in this way will be with- 

 out potential variabiUty. In other words, it will be a pure 

 line. 



In a population of self-fertihzed plants, a mixture of plants 

 of different biot3rpe, each species included will speedily lose its 

 potential variability. In very few generations we will have a 

 mixture of pure lines, every composing species will have lost 

 its potential variability absolutely. 



But even if all the composing species are genetically wholly 

 pure, the whole, the mixture is still variable, comprising differ- 

 ent strains, different pure lines. WiU this variability persist, 

 or will it also tend to diminish automatically? 



We have a collection of several hundred species of wheats 

 and other small cereals. If we want to keep our collection in- 

 tact, we have to take the trouble of separately harvesting a 

 plant or at least a few seeds of every nmnber. Suppose that 

 for any reason we lose interest in the names and origin of my 

 species, and we simply want to conserve them all to use for 

 possible further breeding-work. Can we harvest all our little 

 plots with one stroke of a harvesting machine, mix the seed 

 thoroughly, and sow a sample? Will we keep the collection, or 

 will numbers get lost? It is very obvious, that such a procedure 



