REDUCTION OF VARIABILirV. 117 



would lose us several of the numbers. If we sow all the seed 

 that is harvested and continue sowing everything, the poten- 

 tial variability of our collection wiU be kept at its original 

 level. Very soon, however, some numbers would take the upper 

 hand, their seeds would far-out-number the seeds of others. It 

 caimot be expected that a wheat like "de I'extr^me sud Alg6- 

 rien" would produce more than five percent of the number of 

 seeds of a "Squarehead." And as soon as sowing all the seed 

 becomes a practical impossibhty, even dividing the bulk fairly 

 in half would probably mean the loss of a few numbers. Let us 

 examine a hypothetical example of great simplicity, and see 

 what wiU happen if the number of individuals remains the 

 same from generation to generation, in a mixture of species. 

 In continuing our collection, we need only produce one indiAdd- 

 ual of every kind in every generation. If a collection consists 

 of three species, and the number of individuals in every genera- 

 tion is three, the chances that without ^ny selection three seeds 

 will again reproduce the three kinds is 3 x (3 — 1) : 3^ or 

 6 : 27. The greater the number of tjrpes, corresponding to the 

 number of individuals produced in every generation, the smaller 

 becomes the chance of preserving the collection intact. The 

 greater becomes the chance of losing one. 



The chance that a lot of n individuals taken at random wiU 

 represent n species, or clones, which existed in a mixture con- 

 taining equal quantities of each is n (n — 1) (n — 2) (n — 3) 

 etc. : N°. 



If a population consists of ten pure lines, or ten pure clones, 

 and we know that they are each represented by the same 

 nmnber of individuals, the chance of getting the original di- 

 versity if we plant only ten seeds, ten tubers, is 3.628.800 : 

 100.000.000.000, or 1 : 27527. As soon as in such a case one 

 type is not included, it is lost for ever, and not only that, but 

 the relative preponderance of some types brought about by 

 chance alone, wiU make the chance for others to get lost very 

 much greater than it originally was. 



There is a strong tendency to automatic reduction of the 



