182 NATURAL SCIENCE [September 
that in the Lepidopterous Jthania wrolina, an insect found in the 
Amazon valley, small individuals were slightly more fertile with 
other small individuals than with larger individuals, whilst these 
were also more fertile inter se, then it would follow that fewer 
individuals of intermediate size would be produced, and in course of 
time the species would be split up into a small and a large variety. 
These varieties would continue to diverge as long as the principle 
of “reproductive divergence” was acting, till at length they might 
become differentiated into two mutually sterile species. Supposing, 
on the other hand, this variation in fertility were correlated with 
slight differences of colour, then in course of time varieties differing 
in respect of colour would be produced, or if it were correlated with 
both size and colour, varieties differing in respect of both charac- 
teristics might be produced. As a matter of fact, this insect does 
actually occur as four distinct varieties, differing in colour, form and 
size,, though whether in consequence of the operation of repro- 
ductive divergence, it is of course impossible to say. 
| It will be observed that the theory enunciated is made up of 
| two parts, the first of which can only be verified by experiment, 
_ whilst the second is the statement of a fact, which is capable of 
mathematical demonstration. This we will now proceed to afford. 
Let a certain number of individuals of a species, say 900 males 
and 900 females, be divided up into three groups, according to their 
size. Let there be 300 small males, S, 300 medium sized ones, JZ, 
and 300 large ones, Z. Let the 900 females be similarly divided 
up into the three groups, s,m and/. In order to maintain the 
number of individuals constant in each generation, let it be granted 
that any number of males and females breeding together give rise 
to the same number of males and females. Then if these 900 
males and females be allowed to breed together, on an average 100 
small males, S, will breed with 100 small females, s, and 100 male 
and female offspring, Ss, will arise. Similarly also there will be 
100 male and female offspring, Sm, and 100 S/. Again, with 
reference to the medium sized males, there will be 100 male and 
female, Ms, Mm, and M1 offspring; and with reference to the large 
sized males, 100 male and female, Zs, Lm and Zi offspring. Now 
let it be granted that the offspring S/ and Zs are of the same size 
as Mm, and that Sm and Lm are respectively of the same size as 
Ms and Ml. Then as the result of the chance breeding of the 900 
males and females, we shall have the following numbers of individuals 
of each sex formed :— 
100 Ss, 200 Sm, 300 Mn, 200 Mi, 100 ZI. 
Now let us suppose that the comparative fertility of the various 
sized individuals is slightly changed, so that the principle of “ repro- 
1H. W. Bates, Zrans. Linn. Soc., 1862, p. 545. 
