tuating variability from going any further. The existence of such limits compels us to acknowledge that there is no possibility that species might arise in nature according to the same plan by which certain breeds originate under artificial selection.
On this point de Vries and Wallace differ essentially. The latter is convinced that the fluctuating variability is the only source from which new species have gradually originated; de Vries, however, is quite justified in claiming that the examples of the increase and the accumulation of certain variable characters do not prove that a new species or subspecies has ever arisen in that way in its natural environment.
But in addition to the fluctuating variability we have now to consider another variability, regarding which both Darwin and Wallace have collected numerous data, the so-called 'single variations,' which do not follow the Galton curve. They are not connected with their starting-point by very gradual transformations, but are separated from it by a measurable distance which they have overcome, not by degrees, but by starts. They have, therefore, been named 'sports' or 'saults,' the leap being in different cases larger or smaller.
We have seen that fluctuating variability leads to slow changes and furnishes farmers with the material to improve the races of animals and plants. The 'chance variations' in their turn are valued quite especially by horticulturists and nursery-gardeners.
The English name 'single variations' expresses very well, indeed, the difference between the two kinds of variability. Fluctuating variability shows us simultaneously all the different degrees between extremes, as represented by the descendants of a single parental pair. The single variations, on the contrary, stand isolated; they are discontinuous; between them and the original parent form we do not observe any gradation. This difference has long been noticed, and on several occasions the difference between these 'single variations' and fluctuating' or 'oscillating variations' has been insisted upon.
De Vries has accepted the name 'mutation' and has submitted the phenomenon to a severe experimental test. The chief result of this has been the conclusion which has at the same time become the basis of his own mutation theory—that by means of fluctuating variability certain local and improved races may indeed be bred, but that in nature new species never arise through its agency. These latter owe their origin exclusively to mutation, to 'discontinuous' variability. He is here entirely opposed to Wallace, who looked upon fluctuating variability as the real source from which species gradually originated. With Darwin, de Vries is less at variance, and a quotation from the 'Origin of Species' leaves no doubt that Darwin fully appreciated the value of the single variations for the formation of new species. We read on page 66 of the edition of 1872: