REDUCTION OF VARIABILITY 111 



one or two individuals are impure for a certain gene, these may 

 be included in only one of the two halves 



The potential variability of a group of organisms remains at 

 the same level only for as long as for every gene for which the 

 group is impure there will be individuals, or at least one indi- 

 vidual carrying it, and as long as there will be included at 

 least one individual lacking it, or heterozygous for it. For this 

 reason it is only in peculiar circumstances that the potential 

 variability of a group retains its magnitude. 



Even in those cases where colonization is random sampling, 

 the sample will seldom be wholly representative. Therefore the 

 greatest chance of finding cases, where the potential variability 

 of a group does not decrease is in well-established, common 

 species. In these species the number of individuals which we 

 find to belong to each remains essentially the same from year 

 to year. Let us suppose that we could make a census of the 

 house-flies within the town limits of a given city on midsum- 

 mei day. We would very probably find that from year to year 

 the number did not vary materially. Or if we could make a 

 complete census of the pigs kept on a certain date in a given 

 county, we would probably find their number to be essentially 

 the same for that same date on ten successive years. The en- 

 vironment, the economic conditions are such, that they deter- 

 mine a certain number of flies, a certain number of dandelions, 

 of pigs, of rats. Is this a set of cases in which the potential 

 variability remains the same? Or will it diminish? We have to 

 examine the facts a little more closely. Let us choose the case 

 of the pigs. Last year there were a thousand pigs, and this 

 year there are one thousand, and it is very probable that there 

 will be one thousand next year. We bring these figures to a 

 statistician and he calculates rom them, that on the average 

 every pig has produced one baby pig. Next we turn to the 

 farmers and ask them whether in reality every pig has produced 

 one young pig in the year studied. We are surprised to find, 

 that quite a number of those thousand pigs of last year died 

 without off-spring. In fact, we find that of the five-hundred 



