Difficult Cases of Mimicry

Abstract

I HAVE received from Mr. Thos. Blakiston, of Tokio, Japan, a communication to the Japan Mail by himself and Prof. Alexander, commenting on my article in NATURE, vol. xxvi. p. 86, and pointing out some errors as to the estimated advantage derived by the mimicking butterflies. On referring to my article, I find that I have, by an oversight, misstated the mathematical solution of the problem as given by Dr. Fritz Müller and confirmed by Mr. Meldola, and have thus given rise to some confusion to persons who have not the original article in the Proceedings of the Entomological Society to refer to. Your readers will remember that the question at issue was the advantage gained by a distasteful, and therefore protected, species of butterfly, which resembled another distasteful species, owing to a certain number being annually destroyed by young insectivorous birds in gaining experience of their distastefulness. Dr. Müller says: “If both species are equally common, then both will derive the same benefit from their resemblance—each will save half the number of victims which it has to furnish to the inexperience of its foes. But if one species is commoner than the other, then the benefit is unequally divided, and the proportional advantage for each of the two species which arises from their resemblance is as the square of their relative numbers.” This is undoubtedly correct, but in my article I stated it in other words, and incorrectly, thus: “If two species, both equally distasteful, resemble each other, then the number of individuals sacrificed is divided between them in the proportion of the square of their respective numbers; so that if one species (a) is twice as numerous as another (b), then (b) will lose only one-fourth as many individuals as it would do if it were quite unlike (a); and if it is only one-tenth as numerous, then it will benefit in the proportion of 100 to 1.”