The Atoll Achyranthes was described in 1979 as a part of a genus monograph, it is known from several specimens, the oldest of which dates from 1896, which were formerly thought to represent another taxon, the Round-leaved Shining Chaff Flower (Achyranthes splendens var. reflexa Hillebr.) [currently Achyranthes splendens var. rotundata Hillebr.].
The species is thought to have been endemic to the northwestern part of the Hawaiian island chain, it is known from at least four of the atolls/islands: from Kure, Laysan, from Midway as well as from the Pearl and Hermes Reef.
“There are no collection of this species from the southeastern islands of the chain, even on those with an atoll ring surrounding a volcanic core. This species is a part of the native flora of four of the northwestern atolls of the Hawaiian leeward group. It still occurs on Kure, and on Pearl and Hermes. On Midway it was collected in 1902; on Laysan in 1903, and it is doubtless extinct on these two islands.” 
The species, if it is one, was a 1 to 2 m tall shrub with all parts covered with very fine hairs. The elliptic to obovate leaves were 2 to 5,2 cm long and 1,2 to 3,8 wide, the base were cuneate, the apex obtuse or subacute. 
The island of Laysan has lost all of its vegetation due to the stupid intentional introduction of Guinea Pigs (Cavia porcellus (L.)) and Rabbits (Oryctolagus cuniculus (L.)) at the beginning of the 20th century, which simply consumed all of the plant material in existence. On the other atolls and islands named above the species disappeared apparently due to human activities, for example the building of military bases.
It was last collected on the Kure Atoll in 1964 and in 1969 on the Pearl and Hermes Atoll. 
A last remark: the author of this species has actually named a lot of species, many, I mean perhaps most of them are now no longer accepted as being valid, this may well also apply to the Atoll Achyranthes, which after all may indeed someday turn out to be nothing but a Round-leaved Shining Chaff Flower (Achyranthes splendens var. rotundata Hillebr.).
 Harold St. John: Monograph of the Hawaiian species of Achyranthes (Amaranthaceae). Hawaiian plant studies 56. Pacific Science 33(4): 333-350. 1979
This species is known only from two collections that were made in 1905 and 1906 on the Isla Santiago in the Galápagos Islands.
The Santiago Amaranth was very well adapted to the dry habitats of its home island, it was a small profusely and compactly branched shrub and had small, needle-like leaves. 
The species disappeared due to the appetite of introduced donkeys, pigs and especially goats, whose numbers on Isla Santiago alone were estimated in 1980 as being as high as 80000 to 100000! 
 I. Loren Wiggins; D. M. Porter; E. F. Anderson: Flora of the Galápagos Islands. Stanford University Press 1971  F. Cruz; V. Carrion; K. J. Campbell; C. Lavoie; C. J. Donlan: Bio-Economics of Large-Scale Eradication of Feral Goats from Santiago Island, Galápagos. The Journal of Wildlife Management 72(2): 191-200. 2009
The Mangarevan Chaff Flower, which was discovered in the year 1934 at the Mt. Mokoto at an elevation of about 290 m, in contrast to most other species of its genus was not a shrub but a small tree, and could reach a height of up to 5 m.
The local names of the plant were Pukawapuataratara, Tarake, and Teone pa akura.
The species was most closely related to the still extant Marquesas Chaff Flower (Achyranthes marchionica F. Br.) from the Marquesan Islands.
 K. Suessenguth: Amaranthaceae of southeastern Polynesia. Bishop Museum Occasional Papers 12(2): 1-10. 1936
This species, which always was found growing around salt lakes, is considered extinct, after a collection from the year 1987, assigned to this species, was identified in the year 2000 as representing a distinct species, Fitzgerald’s Mulla-Mulla (Ptilotus fasciculatus W. Fitzg.).