HISTORY OF ZOOLOGY 45 



the fewer, the farther they be removed from the middle value. From the 

 figures of the statistics which express the relative frequency of each grade of 

 peculiarity there can usually be constructed a curve (Gallon's curve) with regular 

 ascending and descending limbs. 



If now the extreme plus or minus variants of such an animal or plant popula- 

 tion be bred and the peculiarities under investigation be studied in the descend- 

 ants, there is found a 'regression,' the descendants of the plus or minus variants 

 approaching the mean fixed for the population. For example, very large parents 

 have on the average, offspring smaller than themselves, diminutive ancestors 

 children larger than they. But since the return to mean is not complete, there 

 appears a possibility, by continued selection to establish the variation from the 

 mean as a permanent character. 



Again there are the cases where 'pure strains' are employed in breeding, 

 where the descendants from one and the same parents, or better, from a her- 

 maphrodite plant, are used and the plus and minus variants are continually 

 inbred. There then follows a complete reversion; the descendants of the plus 

 variants give the same curve, with the same mean and the same limbs as the 

 minus variants and the same as the pure strain. "Within the pure strain there is 

 therefore a certain 'genotypic character,' revealed by Gallon's curve, equally ap- 

 plicable, whether plus or minus variants or mean forms be employed for breeding; 

 against which selection is powerless. From these results, drawn certainly from 

 insufficient empiric material, many have concluded that the fluctuating variations, 

 on which Darwin's theory lays such stress, cannot be taken into account in the 

 origin of new species. 



The breeding of pure strains has given another important conclusion regard- 

 ing the nature of variations: that mutations, that is pure-breeding, sharply cir- 

 cumscribed variations, are much more common than had been thought. There 

 are mutations, which on account of the inconspicuousness of the character are 

 easily to be regarded as fluctuating variations, and very likely some of these were 

 regarded by Darwin as such. If different field crops (wheat, oats, vetches, 

 alfalfa) or many meadow grasses be cultivated in pure strains, there are found 

 among the descendants of the same ancestors not a few varieties, which differ 

 by such slight characters that the eye of the trained breeder is necessary to 

 recognize them; yet, by prolonged pure cultures, they show themselves constant 

 and furnish most favorable material for artificial and natural selection. 



Mendelism. In a third way these studies of pure strains have been remark- 

 ably fruitful. These are the researches which have followed the experiments of 

 the Abbe Mendel upon inheritance, by crossing varieties, races and species. 

 Since the explanation of the complicated phenomena involved will be given in 

 a later section, it need only be said here that if in certain cases races be crossed 

 and inbred for several generations, there arises a multiplicity of forms which 

 have the appearance of newly arisen varieties. But more accurate study shows 

 that these are not new forms but are only the grouping of manifold characters 

 which were indeed present in the parents, often in a latent state. These 'analytic 

 varieties' called forth by crossing are in part constant and can furnish material 

 for new varieties. 



The importance of all of these researches cannot be estimated too highly; 

 not because they have already given a final decision on the significance ot the 

 various kinds of variability but because they have brought the problem of 

 species formation from the region of much sterile theoretical speculation into 

 the clear light of exact experimental investigation. 



Migration Theory. To explain how characters formed by variation 

 become fixed, and do not disappear again through crossing with differently 



