626 Wil/is .— The Origin of Species by Large , rather than by 
has taken place by sudden mutations covering the whole gap between 
forms. This is the work of Mr. G. Udny Yule and myself upon the 
statistics of evolution. In that paper ( 19 ) we have shown that the evolution 
of new genera out of old follows with quite astonishing exactness the rule of 
compound interest. The close approximation of the logarithm curves 
to straight lines (an exact straight line would mean an exact following of the 
law of compound interest) leaves no room for doubt that this is the rule 
which evolution has followed. After a given time one genus has become 
two, and after another period of time two have become four, and 
so on. Now if genera and species are formed upon such a rule, it 
would seem all but inconceivable that they should have been formed by 
gradual steps, or in any other way than by sudden change. Not only does 
this appear, but it is also clear that the large genera must be the ancestors 
of the small; the genera cannot have arisen from common parents, now 
extinct, as is demanded by the Darwinian theory. The general result of the 
work is to show that evolution has proceeded upon a very definite plan ; 
‘ the manner in which it has unfolded itself has been relatively little affected 
by the various vital and other factors, these only causing deviations this way 
and that from the dominant plan.’ If one accept the idea of gradual 
development of species and genera, in view of this work, then one must 
suppose that all the stages in that gradual development proceeded upon 
definite preordained lines. 
In later papers the thesis which has been briefly indicated here will be 
worked out with greater profusion of illustration. The object now is simply 
to show that the evolution of species from one another by means of large 
mutations is a highly probable occurrence. One species may thus be the 
parent—direct or indirect—of a number of others, found upon the same area, 
or upon portions of it, as both Guppy and myself have shown with regard to 
local endemics. That variation consequently has a tendency to be centrifugal 
is thus rendered extremely probable, and this question will be dealt with 
later in more detail. 
Summary. 
This paper attempts to set forth some of the arguments in favour of the 
origin of species by large mutations, rather than by the gradual accumulation 
of small variation (whether infinitesimal or mutational) that is assumed in the 
Darwinian theory, and for which no proof whatever has yet been given. 
Some compromise between the two extreme suppositions—Special Creation, 
by which species were created with the existing large differences, and 
Natural Selection, by which they were evolved by accumulation of small 
differences—is needful, and it is suggested that the best is the evolution of 
