It may here be remarked that, in his essay on the _Influence of Isolation_, Professor Weismann fails to distinguish between the two kinds of isolation. This essay deals only with one of the many different forms of isolation--the geographical--and is therefore throughout concerned with a consideration of diversity as arising from apogamy alone. But in dealing with this side of the matter Weismann anticipated both Gulick and myself in pointing out the law of inverse proportion, which I have stated in the preceding paragraph in what appears to me its strictly accurate form.
3. Segregate Breeding, or homogamy, which arises under any of the many forms of discriminate isolation, must always tend to be _cumulative_. For, again to quote Mr. Gulick, who has constituted this fact the most prominent as it is the most original feature of his essay, "In the first place, every new form of Segregation[11] that now appears depends on, and is superimposed upon, forms of Segregation that have been previously induced; for when Negative Segregation arises [i. e. isolation due to mutual sterility], and the varieties of a species become less and less fertile with one another, the complete infertility that has existed between them and some other species does not disappear, nor does the Positive Segregation cease [i. e. any other form of isolation previously existing].... In the second place, whenever Segregation is directly produced by some quality of the organism, variations that possess the endowment in a superior degree will have a larger share in producing the segregated forms of the next generation, and accordingly the segregative endowment of the next generation will be greater than that of the present generation; and so with each successive generation the segregation will become increasingly complete." And to this it may be added, in the third place, that where the segregation (isolation) is due to the external conditions of life under which the organism is placed, or where it is due to natural selection simultaneously operating in divergent lines of evolution, the same remarks apply. Hence it follows that discriminate isolation is, in all its forms, cumulative.
[11] This term may here be taken as equivalent to Isolation.