182 NATURAL SCIENCE [September 



that in the Lepidopterous Ithania urolina, 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, 1 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, #,300 medium sized ones, M, 

 and 300 large ones, L. Let the 900 females be similarly divided 

 up into the three groups, s, m and I. 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 SI. Again, with 

 reference to the medium sized males, there will be 100 male and 

 female, Ms, Mm, and Ml offspring ; and with reference to the large 

 sized males, 100 male and female, Ls, Lm and LI offspring. Now 

 let it be granted that the offspring SI and Ls 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 Mm, 200 Ml, 100 LI. 



Now let us suppose that the comparative fertility of the various 

 sized individuals is slightly changed, so that the principle of " repro- 

 1 H. W. Bates, Trans. Linn. Soc, 1862, p. 545. 



