different family of the Nymphalidae, to which there is no evidence for assigning the disagreeable properties of the Danaines. Now the different species of Euralia show remarkably close resemblances to the species of Amauris, which are found flying in the same region, and it is supposed that by "mimicking" the unpalatable forms they impose upon their enemies and thereby acquire immunity from attack. The point at issue is the way in which this seemingly purposeful resemblance has been brought about.
One of the species of Euralia occurs in two very distinct forms (Pl. VI.), which were previously regarded as separate species under the names E. wahlbergi and E. mima. These two forms respectively resemble Amauris dominicanus and A. echeria. For purposes of argument we will assume A. echeria to be the more recent form of the two. On the modern Darwinian view certain individuals of A. dominicanus gradually diverged from the dominicanus type and eventually reached the echeria type, though why this should have happened does not appear to be clear. At the same time those specimens which tended to vary in the direction of A. echeria in places where this species was more abundant than A. dominicanus were encouraged by natural selection, and under its guiding hand the form mima eventually arose from wahlbergi.
According to Mendelian views, on the other hand,
A. echeria arose suddenly from A. dominicanus (or vice versa), and similarly mima arose suddenly from wahlbergi. If mima occurred where A. echeria was common and A. dominicanus was rare, its resemblance to the more plentiful distasteful form would give it the advantage over wahlbergi and allow it to establish itself in place of the latter. On the modern Darwinian view natural selection gradually shapes wahlbergi into the mima form owing to the presence of A. echeria; on the Mendelian view natural selection merely conserves the mima form when once it has arisen. Now this case of mimicry is one of especial interest, because we have experimental evidence that the relation between mima and wahlbergi is a simple Mendelian one, though at present it is uncertain which is the dominant and which the recessive form. The two have been proved to occur in families bred from the same female without the occurrence of any intermediates, and the fact that the two segregate cleanly is strong evidence in favour of the Mendelian view. On this view the genera Amauris and Euralia contain a similar set of pattern factors, and the conditions, whatever they may be, which bring about mutation in the former lead to the production of a similar mutation in the latter. Of the different forms of Euralia produced in any region that one has the best chance of survival, through the operation of natural selection, which resembles the most plentiful Amauris form. Mimetic resemblance is a true phenomenon, but natural selection plays the part of a conservative, not of a formative agent.
It is interesting to recall that in earlier years Darwin was inclined to ascribe more importance to "sports" as opposed to continuous minute variation, and to consider that they might play a not inconsiderable part in the formation of new varieties in nature. This view, however, he gave up later, because he thought that the relatively rare sport or mutation would rapidly disappear through the swamping effects of crossing with the more abundant normal form, and so, even though favoured by natural selection, would never succeed in establishing itself. Mendel's discovery has eliminated this difficulty. For suppose that the sport differed from the normal in the loss of a factor and were recessive. When mated with the normal this character would seem to disappear, though, of course, half of the gametes of its progeny would bear it. By continual crossing with normals a small proportion of heterozygotes would eventually be scattered among the population, and as soon as any two of these mated together the recessive sport would appear in one quarter of their offspring.
A suggestive contribution to this subject was recently made by G. H. Hardy. Considering the distribution of a single factor in a mixed population consisting of the heterozygous and the two homozygous forms he showed that such a population breeding at random rapidly fell into a
stable condition with regard to the proportion of these three forms, whatever may have been the proportion of the three forms to start with. Let us suppose for instance, that the population consists of p homozygotes of one kind, r homozygotes of the other kind, and 2 q heterozygotes. Hardy pointed out that, other things being equal, such a population would be in equilibrium for this particular factor so long as the condition q2 = pr was fulfilled. If the condition is fulfilled to start with, the population remains in equilibrium. If the condition is not fulfilled to start with, Hardy showed that a position of equilibrium becomes established after a single generation, and that this position is thereafter maintained. The proportions of the three classes which satisfy the equation q2 = pr are exceedingly numerous, and populations in which they existed in the proportions shown in the appended table would remain in stable equilibrium generation after generation:—
| p. | 2q. | r. |
| 1 | 2 | 1 |
| 1 | 4 | 4 |
| 1 | 6 | 9 |
| 1 | 8 | 16 |
| 1 | 20,000 | 100,000,000 |
| 1 | 2n | n2 |