THE CASE OF _PAPILIO POLYTES_ (_cont._)
It was suggested in the last chapter that if a new variation arose as a
sport--as a sudden hereditary variation--and if that variation were,
through resemblance to a different and unpalatable species, to be more
immune to the attacks of enemies than the normal form, it was conceivable
that the newer mimetic sport would become established, and in time perhaps
come to be the only form of the species. We may suppose, for example, that
the A female of _P. polytes_ arose suddenly, and that owing to its likeness
to the presumably distasteful _P. aristolochiae_ it became rapidly more
numerous until in some localities it is the commonest or even the only
form. However, before discussing the establishing of a mimetic form in this
manner we must first deal with certain general results which may be
expected to follow on a process of selection applied to members of a
population presenting variations which are inherited on ordinary Mendelian
lines.
Let us suppose that we are dealing with the inheritance of a character
which depends upon the presence of the genetic factor X; and let us also
suppose that the heterozygous form () is indistinguishable {94} from the
homozygous form () in appearance. In other words the character dependent
upon X exhibits complete dominance. With regard to X then all the members
of our population must belong to one or other of three classes. They may be
homozygous (XX) for X, having received it from both parents, or they may be
heterozygous (Xx) because they have received it from only one parent, or
they may be devoid of X, _i.e._ pure recessives (xx). An interesting
question arises as to the conditions under which a population containing
these three kinds of individuals remains stable. By stability is meant that
with the three kinds mating freely among themselves and being all equally
fertile, there is no tendency for the relative proportions of the three
classes to be disturbed from generation to generation. The question was
looked into some years ago by G. H. Hardy, who shewed that if the mixed
population consist of p XX individuals, 2q Xx individuals and r xx
individuals, the population will be in stable equilibrium with regard to
the relative proportions of these three classes so long as the equation pr
= q^2 is satisfied[48].
Now let us suppose that in place of equality of conditions selection is
exercised in favour of those individuals which exhibit the dominant
character. It has been shewn by Mr Norton that even if the selection
exercised were slight the result in the end would be that the recessive
form would entirely disappear. The total time required for bringing this
about would {95} depend upon two things, (1) the proportion of dominants
existing in the population before the process of selection began, and (2)
the intensity of the selection process itself. Suppose, for example, that
we started with a population consisting of pure dominants, heterozygotes,
and recessives in the ratio 1:4:4. Since these figures satisfy the equation
pr = q^2, such a population mating at random within itself is in a state of
stable equilibrium. Now let us suppose that the dominant form (including of
course the heterozygotes) is endowed with a selection advantage over the
recessives of 10%, or in other words that the relative proportion of the
recessives who survive to breed is only 90% of the proportion of dominants
that survive[49]. It is clear that the proportion of dominants must
gradually increase and that of the recessives diminish.
At what rate will this change in the population take place? Mr Norton has
worked this out (see App. I) and has shewn that at the end of 12
generations the proportions of pure dominants, heterozygotes, and
recessives will be 1:2:1. The population will have reached another position
of equilibrium, but the proportion of recessives from being four-ninths of
the {96} total is now reduced to one-quarter. After 18 more generations the
proportions 4:4:1 are reached, the recessives being only one-ninth of the
total; after 40 further generations of the process they become reduced to
one-fortieth. In other words a selective advantage of 10% operating against
the recessives will reduce their numbers in 70 generations from nearly
one-half of the population to less than one-fortieth.
With a less stringent selective rate the number of generations elapsing
before this result is brought about will be larger. If, for example, the
selective rate is diminished from 10% to 1% the number of generations
necessary for bringing about the same change is nearly 700 instead of
70--roughly ten times as great. Even so, and one can hardly speak of a 1%
selective rate as a stringent one, it is remarkable in how brief a space of
time a form which is discriminated against, even lightly, is bound to
disappear. Evolution, in so far as it consists of the supplanting of one
form by another, may be a very much more rapid process than has hitherto
been suspected, for natural selection, if appreciable, must be held to
operate with extraordinary swiftness where it is given established
variations with which to work.
We may now consider the bearing of these theoretical deductions upon the
case of _Papilio polytes_ in Ceylon. Here is a case of a population living
and breeding together under the same conditions, a population in which
there are three classes depending upon the presence or absence of two
factors, X and Y, {97} exhibiting ordinary Mendelian inheritance. For the
present we may consider one of these factors, X, which involves the
proportion of mimetic to non-mimetic forms. It is generally agreed among
observers who have studied this species that of the three forms of female
the M form is distinctly the most common, while of the other two the H form
is rather more numerous than the A form. The two dominant mimetic forms
taken together, however, are rather more numerous than the recessive M
form. The most recent observer who studied this question, Mr Fryer,
captured 155 specimens in the wild state as larvae. When reared 66 turned
out to be males, while of the females there were 49 of the two mimetic
forms and 40 of the M form, the ratio of dominants to recessives being
closely 5:4[50]. Now as has already been pointed out the ratio 5:4 of
dominants and recessives is characteristic of a population exhibiting
simple Mendelian inheritance when in a state of stable equilibrium. The
natural deduction from Mr Fryer's figures is that with regard to the factor
that differentiates the mimetic forms from the non-mimetic, the _polytes_
population is, for the moment at any rate, in a position of stable
equilibrium. This may mean one of two things. Either the population is
definitely in a state of equilibrium which has lasted for a period of time
in the past {98} and may be expected to endure for a further period in the
future, or else the population is in a condition of gradual change as
regards the numerical proportion of mimetics and non-mimetics, progressing
towards the elimination of the one or the other, the present state of
equilibrium being merely transitory and accidental. In this connection a
few scraps of historical evidence are of interest. Of the various forms of
_P. polytes_ the A form of female was the first to be described in 1758,
and not long after (1776) the H form was registered as a species under the
name of _Papilio Eques Trojanus romulus_. Later on the female resembling
the male found its way into the literature as _Papilio pammon_. From the
fact that the mimetic forms were known before the non-mimetic, it is
unlikely that they can have been scarce a century and a half ago. As _P.
polytes_ certainly produces at least four broods a year in Ceylon this
period of time represents something like 600 generations in the life of the
species, and we have already seen that even if the mimetic forms have but a
1% advantage over the non-mimetic the proportion of the latter would
decrease from nearly equality down to but 1 in 40 in about 700 generations.
Actually for _P. polytes_ the decrease would not be so marked because the
male is non-mimetic. Owing to this peculiar feature the rapidity of change
in the proportion of the different forms is reduced to about one-half of
what it would be if the males were also mimetic. Nevertheless the change
from nearly equality to about one non-mimetic in 40 would have taken place
{99} during the time _P. polytes_ has been known if a 2% selection
advantage had operated during that period in favour of the mimetic. If
there has been any appreciable selection going on during that time mimetics
must have been far rarer when the species was first discovered, but the
fact that both the mimetic forms made their way into collections before the
non-mimetic tells distinctly against this supposition. Nor is there any
reason to suppose that the non-mimetic form has been dwindling in numbers
relatively to the mimetics during the last half century. Moore[51] in 1880
records an earlier observation of Wade's that "These three butterflies are
very common, especially those of the first form; the second being perhaps
least so." The first form alluded to is the M form, and the second is the A
form, so that at the time Wade wrote the relative proportions of these
three forms must have been very much what they are to-day. Even during half
a century and with such a relatively weak selection rate as 2% in favour of
the mimetics, the proportion of non-mimetics should drop from about 4:5
down to about 1:5. Therefore we must either infer that in respect of
mimetic resemblances natural selection does not exist for _P. polytes_ in
Ceylon, or else we must suppose its force to be so slight that in half a
century certainly, and perhaps in a century and a half, it can produce no
effect appreciable to the necessarily rough method of estimation employed.
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It may, however, be argued that even an exceedingly low selection rate is
able to bring about the elimination of one or other type provided that it
acts for a sufficiently long time. This is perfectly true. A selective rate
of .001% would reduce the proportion of recessives to dominants from 4:5
down to 1:40 in the course of about 1,400,000 generations where the mimetic
resemblance is already established. Such a form of selection entails the
death of but one additional non-mimetic in 100,000 in each generation. If,
however, the mimetic resemblance is not fully established and the mimic
bears only what supporters of the mimicry theory term a "rough" resemblance
to the model, it is clear that it will have far less chance of being
mistaken for the model. Its advantage as compared with the non-mimetic form
will be very much less. Even supposing that the slight variations concerned
are inherited, an intensity of selection which would produce a certain
change in 1,400,000 generations where a mimetic resemblance is already
established must be supposed to take an enormously greater time where an
approach to a model has to take place from a "rough" resemblance.
From the data as to the relative proportions of the polymorphic females of
_P. polytes_ during the past and at present, and from the behaviour of
their different forms in breeding, the following conclusions only can be
drawn. Either natural selection, from the point of view of mimicry, is
non-existent for this species in Ceylon, or else it is so slight as to be
unable in half a {101} century to produce an appreciable diminution in the
proportion of non-mimetic females. For even if the mimetic resemblance
brings about but the survival of one additional protected form in 100 as
compared with the unprotected, this means a marked diminution in the
proportion of M females in 50 years--a diminution such as there are no
grounds for supposing to have taken place.
It has been argued that in populations exhibiting Mendelian heredity even a
relatively low selection rate must bring about a rapid change in the
constitution of a mixed population. Have we any grounds for supposing that
populations of this sort can undergo such rapid changes? In cases where
mimetic resemblances are involved we have no examples of the sort. But some
interesting evidence as to the rate at which a population may change is to
be gathered from the study of melanism in certain moths. It is well known
that in some parts of England the common peppered moth, _Amphidasys
betularia_ has been almost entirely supplanted by the darker melanic form
_doubledayaria_. It first made its appearance near Manchester in 1850, and
from that centre has been gradually spreading over northern England, the
Midlands, and the south-eastern counties. At Huddersfield, for instance,
fifty years ago only the type form _betularia_ existed; to-day there is
nothing but _doubledayaria_. In Lancashire and Cheshire the type is now
rare. On the continent, too, there is the same story to be told. The
melanic form first appeared in Rhenish {102} Prussia in 1888; to-day it is
much more abundant than the older type. There, too, it is spreading
eastwards and southwards to Thuringia, to Saxony, to Silesia. What
advantage this new dark form has over the older one we do not know[52].
Some advantage, however, it must have, otherwise it could hardly supplant
_betularia_ in the way that it is doing. From our present standpoint two
things are of interest in the case of the peppered moth--the rapidity with
which the change in the nature of the population has taken place, and the
fact that the two forms exhibit Mendelian heredity, _doubledayaria_ being
dominant and _betularia_ recessive[53]. Moreover, mixed broods have been
reared from wild females of both sorts, and so far as is known the two
forms breed freely together where they co-exist. This case of the peppered
moth shews how swiftly a change may come over a species[54]. It is not at
all improbable that the establishing of a new variety at the expense of an
older one in a relatively short space of time is continually going on,
especially in tropical lands where {103} the conditions appear to be more
favourable to exuberance of variation and where generations succeed one
another in more rapid succession. At present, however, we are without data.
A form reported by an old collector as common is now rare; a variety once
regarded as a great prize is now easily to be found. Such to-day is the
sort of information available. For the solution of our problem it is, of
course, useless. The development of Mendelian studies has given us a
method, rough perhaps but the best yet found, of testing for the presence,
and of measuring the intensity, of natural selection. Much could be learned
if some common form were chosen for investigation in which, as in _P.
polytes_, there are both mimetic and non-mimetic forms. Large numbers
should be caught at stated intervals, large enough to give trustworthy data
as to the proportions of the different forms, mimetic or non-mimetic, that
occurred in the population. Such a census of a polymorphic species, if done
thoroughly, and done over a series of years at regular intervals, might be
expected to give us the necessary data for deciding whether the relative
proportion of the different forms was changing--whether there were definite
grounds for supposing natural selection to be at work, and if so what was
the rate at which it brought the change about.
* * * * *
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