concrete example, is it not self-evident that the farmer who separated his stock into two or more parts indiscriminately, would not effect any more change in his stock than if he had left them all to breed together?

Well, although at first sight this seems self-evident, it is in fact untrue. For, unless the individuals which are indiscriminately isolated happen to be a very large number, sooner or later their progeny will come to differ from that of the parent type, or unisolated portion of the previous stock. And, of course, as soon as this change of type begins, the isolation ceases to be indiscriminate: the previous apogamy has been converted into homogamy, with the usual result of causing a divergence of type. The reason why progeny of an indiscriminately isolated section of an originally uniform stock—e.g. of a species—will eventually deviate from the original type is, to quote Mr. Gulick, as follows:—"No two portions of a species possess exactly the same average character, and, therefore, the initial differences are for ever reacting on the environment and on each other in such a way as to ensure increasing divergence as long as the individuals of the two groups are kept from intergenerating[5]." Or, as I stated this principle in my essay on Physiological Selection, published but a short time before Mr. Gulick's invaluable contributions to these topics:—

As a matter of fact, we find that no one individual "is like another all in all"; which is another way of saying that a specific type may be regarded as the average mean of all its individual variations, any considerable departure from this average being, however, checked by intercrossing.... Consequently, if from any cause a section of a species is prevented from intercrossing with the rest of its species, we might expect that new varieties should arise within that section, and that in time these varieties should pass into new species. And this is just what we do find[6].

The name which I gave to this cause of specific change was Independent Variability, or variability in the absence of overwhelming intercrossing. But it now appears to me that this cause is really identical with that which was previously enunciated by Delbœuf. Again, in his important essay on The Influence of Isolation, Weismann concludes, on the basis of a large accumulation of facts, that the constancy of any given specific type "does not arise suddenly, but gradually, and is established by the promiscuous intercrossing of all individuals." From which, he says, it follows, that this constancy must cease so soon as the condition which maintains it ceases—i. e. so soon as intercrossing (Panmixia) between all individuals ceases, or so soon as a portion of a species is isolated from its parent stock. To this principle he assigns the name of Amixia. But Weismann's Amixia differs from my Independent Variability in several important particulars; and on this account I have designedly abstained from adopting his term. Here it is enough to remark that it answers to the generic term Isolation, without reference to the kind of isolation as discriminate or indiscriminate, homogamous or apogamous. On the other hand, my Independent Variability is merely a re-statement of the so-called "Law of Delbœuf," which, in his own words, is as follows:—

One point, however, is definitely attained. It is that the proposition, which further back we designated paradoxical, is rigorously true, A constant cause of variation, however insignificant it may be, changes the uniformity [of type] little by little, and diversifies it ad infinitum. From the homogeneous, left to itself, only the homogeneous can proceed; but if there be a slight disturbance ["léger ferment"] in the homogeneous, the homogeneity will be invaded at a single point, differentiation will penetrate the whole, and, after a time—it may be an infinite time—the differentiation will have disintegrated it altogether.

In other words, the "Law," which Delbœuf has formulated on mathematical grounds, and with express reference to the question of segregate breeding, proves that, no matter how infinitesimally small the difference may be between the average qualities of an isolated section of a species compared with the average qualities of the rest of that species, if the isolation continues sufficiently long, differentiation of specific type is necessarily bound to ensue. But, to make this mathematical law biologically complete, it ought to be added that the time required for the change of type to supervene (supposing apogamy to be the only agent of change) will be governed by the range of individual variability which the species in question presents. A highly stable species (such as the Goose) might require an immensely long time for apogamy alone to produce any change of type in an isolated portion of the species, while a highly variable species (such as the Ruff) would rapidly change in any portion that might be indiscriminately isolated. It was in order to recognize this additional and very important factor that I chose the name Independent Variability whereby to designate the diversifying influence of merely indiscriminate isolation, or apogamy. Later on Mr. Gulick published his elaborate papers upon the divergence of type under all kinds of isolation; and retained my term Independent, but changed Variability into Generation. I point this out merely for the sake of remarking that his Independent Generation is exactly the same principle as my Independent Variability, and Delbœuf's Mathematical Law.

Now, while I fully agree with Mons. Giard where he says, in the introductory lecture of his course on The Factors of Evolution[7], that sufficient attention has not been hitherto given by naturalists to this important factor of organic evolution (apogamy), I think I have shown that among those naturalists who have considered it there is a sufficient amount of agreement. Per contra, I have to note the opinion of Mr. Wallace, who steadily maintains the impossibility of any cause other than natural selection (i.e. one of the forms of homogamy) having been concerned in the evolution of species. But at present it is enough to remark that even Professor Ray Lankester—whose leanings of late years have been to the side of ultra-Darwinism, and who is therefore disposed to agree with Mr. Wallace wherever this is logically possible—even Professor Ray Lankester observes:—

Mr. Wallace does not, in my judgement, give sufficient grounds for rejecting the proposition which he indicates as the main point of Mr. Gulick's valuable essay on Divergent Evolution through Cumulative Segregation. Mr. Gulick's idea is that ... no two portions of a species possess exactly the same average character, and the initial differences will, if the individuals of the two groups are kept from intercrossing, assert themselves continuously by heredity in such a way as to ensure an increasing divergence of the forms belonging to the two groups, amounting to what is recognized as specific distinction. Mr. Gulick's idea is simply the recognition of a permanence or persistency in heredity, which, caeteris