CHAPTER VIII
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 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 = q2 is satisfied[1].
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 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 = q2, 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[2]. 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 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, 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[3]. 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 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 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[4] 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.
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 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 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[5]. 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[6]. 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[7]. 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 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.
- ↑ Science, July, 1908.
- ↑ If for example there were 5000 dominants and 4000 recessives, and if only half of the population survives to mate, then we should be left with 2500 dominants and 2000 recessives as parents of the next generation. But if there were also a 10% selective disadvantage working against the recessives, their numbers would be further reduced from 2000 to 1800 and the proportion of dominants to recessives would be changed from 5:4 to 25:18.
- ↑ As these larvae were for the most part found simply over a considerable time it follows that they are the offspring of different females and represent the relative proportions of the three forms in the general population.
- ↑ The Lepidoptera of Ceylon, 1880.
- ↑ From the experience of breeders it would appear that the melanic form is somewhat hardier, at any rate in captivity.
- ↑ Intermediates may also occur in some strains (cf. Bowater, Journal of Genetics, vol. 3, no. 4, 1914).
- ↑ An interesting case of a similar nature has recently been published by Hasebroek (Die Umschau, 1913, p. 1020). A melanic form of the moth, Cymatophora or, suddenly appeared near Hamburg in 1904. This new form, to which the name albingensis was given, rapidly became the predominant one. In 1911-1912 over 90% of the moths reared from caterpillars taken in the open were of the albingensis form; nor were any intermediates found between it and the typical form. Some experiments were also made which shew that the albingensis form behaves as a dominant to the original type form.