Effect of Mating on Variability 195 



been increased or decreased? In the original stocks the two 

 sets of parents were diverse in all their characters, while in 

 their grandchildren, although there are 81 sets instead of 

 two, they show all possible intermixtures and gradations. 

 It may be maintained therefore that the result of mating has 

 been to reduce the degree of diversity. And if we find the 

 "coefficient of variation" for the two sets, which is a measure 

 of how much on the whole the individuals differ from the 

 average intermediate condition, we shall doubtless find this 

 to be much greater for the two original stocks, where none 

 of the individuals are like the average of the two sets, than 

 for their grandchildren. By this measure, therefore, varia- 

 tion will be found reduced by mating. Walton (1915) has 

 shown that precisely this is what occurs when diverse stocks 

 of certain higher organisms are mated ; from which he argues 

 that mating decreases variation. The whole is an excellent 

 illustration of the way in which average measures (like the 

 coefficient of variation) may conceal important biological 

 facts. What has happened is the production of many di- 

 verse hereditary combinations bridging the gap between the 

 two that first existed. This is an increase of variation, if 

 one means thereby an increase in the number of hereditarily 

 diverse stocks ; it is a decrease of variation, if one means by 

 .ariation the average diversity from the intermediate con- 

 dition. But this superficial increase or decrease of variation 

 is merely a consequence of the underlying fact, the pro- 

 ductions of new combinations through mating. 4 



4 Mast (1917) studied this phenomenon of increase or decrease in 

 variability of the fission rate as a result of mating in the infusorian 

 Didinium. He was not able to detect with certainty any consistent 

 increase or decrease in the coefficient of variation as a result of mating. 

 This need not surprise us, in view of the points brought out above; but 

 Mast's data were in any case hardly such as to give dependable results 

 on the matter. The study of variation was made on the results of 

 experiments designed for entirely different purposes, so that the num- 

 bers of cases were too small to give significant data. Most of his coeffi- 



