Nov. 10, 1870} 
NATURE 31 
o 

that every one of these changes must present some advan- 
tage to the species which undergoes it. Now let us apply these 
two principles to the recognised facts of Mimetism ; and for 
this purpose we may take a single instance, one of the most re- 
markable and best authenticated, recorded by Mr. Bates in his 
“Naturalist on the Amazons,” and more fully in his paper on the 
“Lepidoptera of the Amazon Valley,” in the ‘‘ Transactions of 
the Linnean Society.”” There is in South America a tribe of 
butterflies of very gaudy colour, the {eliconide, which appear to 
enjoy exceptional immunity from the attacks of birds, from the 
exudation, when attacked, of a nauseous fluid, and are conse- 
quently extremely abundant. Another South American genus 
of Lepidoptera, the Zeféa/s, belongs structurally to an entirely 
different class, the /ieride, and the majority of its species 
differ correspondingly from the Heéliconide, in their size, 
shape, colour, and manner of flying, being nearly pure white, 
and of the same family as our common cabbage butterfly. 
There is, however, one particular species of Zeféalis, which 
departs widely in externai facies from all its allies, and so 
closely resembles a species of /thomia belonging to the /e/i- 
conide, as apparently not only to deceive the most experienced 
entomologists, but even to take in its natural enemies also, 
and, although perfectly harmless, to share the immunity of the 
butterfly it simulates. Mr. Bates and Mr. Wallace have both 
attempted to show, with great ingenuity and plausibility, that 
this entire change from the normal form to that resembling the 
Ithomia has taken place through the agency of natural selection 
acting through a long series of generations. I believe, however, 
on careful examination, the line of argument will be found to 
break down, and that at its very outset, on the ground that the 
early stages of the transformation will be perfectly useless for 
the protection of the species. 
Applying the rigid test of mathematical calculation to the 
problem, I think it may safely be assumed that it would re- 
quire, at the very lowest calculation, one thousand steps to 
enable the normal Zeféalis to pass into its protective form. 
Mr. Bates indeed assumes that the change may have 
taken place much more rapidly, but this appears a very 
unsafe and unsupported deviation from the sounder prin- 
ciple laid down by Darwin and Wallace. It is indeed obvious 
that any marked variety resulting suddenly must inevitably 
revert, as already observed, more and more towards the 
parent type by crossing, unless, indeed, we are to suppose 
that a pair, male and female, are simultaneously produced with 
a deviation in exactly the same direction, and that their offspring 
keeps itself apart, interbreeding only with itself as a separate 
colony,—an assumption contrary to all experience. At all 
events, we may safely say that within the historic period no 
such change has been effected within a vastly larger number of 
generations, where human agency has not come into play. The 
next step in my argument is, that the smallest change in the 
direction of the /thomia, which we can conceive on any 
hypothesis to be beneficial to the Zeféalis, is at the 
very lowest one-fiftieth of the change required to produce 
perfect resemblance. I believe myself that a very much larger frac- 
tion, say one-fourth or one-third, would be practically useless ; 
as I am told by practical entomologists that birds will distinguish 
‘with accuracy caterpillars suited for their food from other species 
scarcely distinguishable to our eyes, which are not so suitable. 
For the sake of argument, however, I will suppose that a change 
to the extent of one-fiftieth is beneficial to thatsmall extent after 
which natural selection may begin to come into play. Mr. Wal- 
lace, indeed, argues that an infinitesimal and inappreciable dis- 
tinction may make the difference of a slightly longer span of life 
being allowed to the butterfly, to lay its eggs in safety ; but this 
is a deductive piece of reasoning derived from the theory, be- 
cause necessary to it, and not inductive observation from nature ; 
and I altogether decline to be carried further, for the sake of the 
theory, than the limit I have indicated. Suppose a parallel in- 
stance : that our common brown owl has a enchant for mice, 
while moles are abhorrent to its palate ; is it conceivable that, 
supposing a mouse was born approaching a mole by the one- 
hundredth partin external appearance, say with feet a fraction of 
_a line broader, or eyes slightly deeper set, the shortest-sighted of 
owls would fora moment mistake AZus for Za/fa? Or, a still 
more parallel instance: suppose a blue-bottle fly were born 
blessed witha slightly narrower waist, or a faint band of yellow 
on its body, will any one maintain that it stands the least 
chance of escape from destruction by those birds which do 
Not feed on wasps? And no one who has examined. Mr, 


Bates’s or Mr. Trimen’s beautiful drawings, or, still better, the 
insects themselves, will say that I have exaggerrated the extent 
of the passage from the normal to the imitative Zeféadis. 
If, therefore, this reasoning is sound, one thousand steps being 
necessary to effect this change in external appearance, and one- 
fiftieth of the whole change, or twenty steps, being the smallest 
amount that is really profitable to the animal, it follows that the 
first twenty steps of the transformation are not due to natural 
selection, but must have taken place by an accumulation of 
chances. Let us investigate the value of this chance. Suppose 
there are twenty different ways in which a Zeffalis may vary, 
one only of these being in the direction ultimately required, the 
chance of any individual producing a descendant which will take 
its place in the succeeding generation varying in the required 
. . . I . . . 
direction, is 553 the chance of this operation being repeated in 
I I 
the same direction in the second generation is —, or — ; 
g zon 0 4003 the 
chance of this occurring for fez successive generations (instead 
I 
of twenty, as I have assumed above) is Bow OF about one in 
ten billions. Now another factor comes into the calculation, and 
that is the number of individuals among which this chance is 
distributed. Mr. Bates and Mr. Wallace agree in stating that 
both in South America and in the Malay Archipelago the imi- 
tative species are always confined to a limited area, and are 
always very scarce compared with the imitated species. We 
will assume that the number of individuals of the imitative 
Leptalis existing at any one time is one million; the chance of 
there being among these million a single individual approaching 
the /thomia to the extent of one-hundredth is qtr eooo 
or the chance against it is ten million to one. 
It will be seen that in the above calculation I have endeavoured 
to throw every advantage into the scale of the natural selectionist. 
I believe myself, and I think most naturalists will agree with me, 
that vastly more than a thousand generations, each characterised 
by a small change, must be conceded; and that, on the other 
hand, a change to the extent of even greatly more than one- 
fiftieth would be absolutely useless. This idea receives great 
confirmation from observing the most wonderful identity of the 
marking in the mimicked and mimicker. If a rough imitation 
is so useful, it must be a mere freak of Nature to produce so 
absolute an identity, and we are landed in the dilemma that the 
Jast stages are comparatively useless. If, again, I had carried 
I Toes 
on the calculation to 30% instead of =, it would have been 
201 
difficult to have stated the result in figures ; and if, on the other 
hand, it is objected that a million is too low an estimate of the 
number of individuals existing at one time, and a hundred 
million or a thousand million is substituted (an altogether in- 
conceivable estimate for a rare conspicuous butterfly limited to 
a small area”), the result will not be materially affected. For, 
supposing the chance is reduced from one in ten million to one 
in ten thousand—and it is said that the world has existed quite 
long enough to give a fair chance of this having occurred once— 
it is not a solitary instance that we have. Mr. Bates states that, 
in a comparatively small area, several distinct instances of such 
perfect mimicry occur; Mr. Wallace has a store in the Malay 
Archipelago ; Mr. Trimen records several of wonderful beauty 
and exactness in South Africa ; and the more attention is turned 
to the subject, the more numerous do , instances of inimicry 
become. 
I have left out of account altogether those still more remark- 
able instances, which are even more difficult to explain on the 
theory of natural selection (as the number of steps must be in- 
finitely greater), in which animals not only imitate others be- 
longing to entirely different natural orders, as Diptera mimicking 
Hymenoptera, and caterpillars snakes, but where they resemble 
inanimate objects. The weird and uncanny resemblance of the 
Phasmata and Mantides to dry leaves and sticks has long been 
known: not only is the veining of the leaves accurately repro- 
duced, but the attacks of parasitic fungi are simulated ; and 
Mr. Wallace records instances of larvze bearing the most minute 
resemblance to the droppings of birds, and spiders to the axillary 
buds of plants. ‘Through what countless generations must these 
transformations have been effected ! and by what mathematical 
formula could we express the chance against their occurrence, if 
* The latter number would give 150 individuals per acre over an area 100 
miles square, or 50 per acre for an area as large as Ireland. 
