A different view seems to me more probable. As the cases are curious and not numerous, I will briefly give all that I have been able to find.
In one section of the genus Turnix, quail-like birds, the female is invariably larger than the male (being nearly twice as large in one of the Australian species), and this is an unusual circumstance with the Gallinaceae. In most of the species the female is more distinctly coloured and brighter than the male (14. For the Australian species, see Gould's 'Handbook,' etc., vol. ii. pp. 178, 180, 186, and 188. In the British Museum specimens of the Australian Plain-wanderer (Pedionomus torquatus) may be seen, shewing similar sexual differences.), but in some few species the sexes are alike. In Turnix taigoor of India the male "wants the black on the throat and neck, and the whole tone of the plumage is lighter and less pronounced than that of the female." The female appears to be noisier, and is certainly much more pugnacious than the male; so that the females and not the males are often kept by the natives for fighting, like game-cocks. As male birds are exposed by the English bird-catchers for a decoy near a trap, in order to catch other males by exciting their rivalry, so the females of this Turnix are employed in India. When thus exposed the females soon begin their "loud purring call, which can be heard a long way off, and any females within ear-shot run rapidly to the spot, and commence fighting with the caged bird." In this way from twelve to twenty birds, all breeding females, may be caught in the course of a single day. The natives assert that the females after laying their eggs associate in flocks, and leave the males to sit on them. There is no reason to doubt the truth of this assertion, which is supported by some observations made in China by Mr. Swinhoe. (15. Jerdon, 'Birds of India,' vol. iii. p. 596. Mr. Swinhoe, in 'Ibis,' 1865, p. 542; 1866, pp. 131, 405.) Mr. Blyth believes, that the young of both sexes resemble the adult male.
[Fig. 62. Rhynchaea capensis (from Brehm).]
The females of the three species of Painted Snipes (Rhynchaea, Fig. 62) "are not only larger but much more richly coloured than the males." (16. Jerdon, 'Birds of India,' vol. iii. p. 677.) With all other birds in which the trachea differs in structure in the two sexes it is more developed and complex in the male than in the female; but in the Rhynchaea australis it is simple in the male, whilst in the female it makes four distinct convolutions before entering the lungs. (17. Gould's 'Handbook to the Birds of Australia,' vol. ii. p. 275.) The female therefore of this species has acquired an eminently masculine character. Mr. Blyth ascertained, by examining many specimens, that the trachea is not convoluted in either sex of R. bengalensis, which species resembles R. australis so closely, that it can hardly be distinguished except by its shorter toes. This fact is another striking instance of the law that secondary sexual characters are often widely different in closely-allied forms, though it is a very rare circumstance when such differences relate to the female sex. The young of both sexes of R. bengalensis in their first plumage are said to resemble the mature male. (18. 'The Indian Field,' Sept. 1858, p. 3.) There is also reason to believe that the male undertakes the duty of incubation, for Mr. Swinhoe (19. 'Ibis,' 1866, p. 298.) found the females before the close of the summer associated in flocks, as occurs with the females of the Turnix.
The females of Phalaropus fulicarius and P. hyperboreus are larger, and in their summer plumage "more gaily attired than the males." But the difference in colour between the sexes is far from conspicuous. According to Professor Steenstrup, the male alone of P. fulicarius undertakes the duty of incubation; this is likewise shewn by the state of his breast- feathers during the breeding-season. The female of the dotterel plover (Eudromias morinellus) is larger than the male, and has the red and black tints on the lower surface, the white crescent on the breast, and the stripes over the eyes, more strongly pronounced.