MATHEMATICAL CONTRIBUTIONS TO THE THEORY OF EVOLUTION. 315 
physique and organic relationship, or leave these characters uncontrolled by the 
principle of heredity. It seems to me, therefore, that the results of this memoir 
force on us some modification of current views of evolution. The suspension of natural 
selection does not denote either the regression of a race to past types, as the 
supporters of panmixia suggest, or the permanence of the existing type, as others 
have believed. It really denotes full play to genetic or reproductive selection, which 
Avill progressively develop the race in a manner which can be quantitatively predicted 
when once we know the numerical constants which define the characters of a race 
and their relation to racial fertility. In other words, natural selection must not be 
looked upon as moulding an otherwise permanent or stable type ; it is occupied with 
checking, guiding, and otherwise controlling a progressive tendency to change. 
So soon as a species is placed under a novel environment, either artificially or 
naturally, the equilibrium is disturbed, and it will begin to progress in the manner 
indicated by genetic (reproductive) selection, until this progress is checked by the 
development of characters in a manner or to an extent which is inconsistent with 
fitness to survive in the new surroundings. Within a very few generations a novel 
environment, sympathetic so to speak to the progressive tendency indicated by 
reproductive selection, produces the suitable variations without the assistance of 
natural selection. It seems to me that this principle ought to be borne in mind 
when, in laboratory experiments or in artificial breeding, natural selection is wholly 
or largely suspended, or again is altered in type ; the species dealt with is unlikely 
to remain constant for several generations, but will develop in the direction indicated 
by genetic selection. Further, when stable types of life like the English sparrow are 
taken to America, or the English rabbit to Australia, where initially they fill a more or 
less vacant field among living forms, and natural selection is in part suspended, we 
should expect in a few generations a considerable divergence in type.'"' The converse 
aspect of the problem is also of great importance ; namely, the natural selection 
of physical characters must tend to indirectly modify fertility and fecundity, if 
these be correlated with those characters. Variations in the fertility of local races 
need not be looked upon as due directly to environment, but may arise from the 
selection of characters correlated with fertility, combined with the law that fertility 
is itself an inherited character. 
Lastly, the inheritance of fertility involves the “acceleration” of fertility; a 
race, natural selection being suspended, tends not only to increase but to increase 
at an increasing rate. This principle is again full of meaning, not only for the study 
of the manner in which lower types of life rapidly expand under changed envirom 
ment, but also for the problems set to those philosophers who may desire that the 
most social and not the most fertile type of citizen may predominate in our modern 
civilised communities, where the state and public opinion to a greater or less extent 
hinder natural selection from playing the great part it does in wild life. 
* It would be interesting to know wbether the size or frequency of tlie litter ot the Australian 
rabbit is greater than that of the English. 
2 s 2 
