Revised Dec 5 2016 with new text and images.
These are difficult taxa to nest:
The tusks of Astrapotherium (Fig. 1; Burmeister 1879; Hatcher 1902) are canines. The premaxilla is missing. The mandible of Astrapotherium really does stick out quite a bit further than the rostrum.
Finally a sister!
I didn’t have one really good enough sister taxon for Astrapotherium. Now I do.
(Figs. 2, 3; Cope 1874; Williamson and Lucas 1992; Middle Eocene 54-38 mya; 25-50 cm long), which Wikipedia describes as a dog-sized herbivore with hooves found as a pack of individuals.
Cooper et al. 2014 nested Meniscotherium with Phenacodus as a condylarth, a possible member of Afrotheria, perissodactyl. They did not test Astrapotherium.
Wible et al. 2007 nested Meniscotherium close to early cetioartiodactyls (an invalid clade) and close to early Carnivora. They, likewise, did not test Astrapotherium.
The LRT nests the clade of Astrapotherium + Meniscotherium between the clade of Edentates and the clade of Phenacodus.
The retention of five fingers and five toes
is key to the phylogenetic nesting of these taxa. More derived taxa start losing digit 1. We can see the genesis of canine tusks in Meniscotherium.
Meniscotherium is the smaller and more plesiomorphic
of the two and is found in earlier strata (Eocene, 50-38 mya) than Astrapotherium (late Oligocene, Middle Miocene, 28-15 mya).
Burmeister 1879. Description physique de al République Agentine, T. III 1879:517.
Cooper LN, Seiffert ER, Clementz M, Madar SI, Bajpai S, Hussain ST, Thewissen JGM 2014-10-08. Anthracobunids from the Middle Eocene of India and Pakistan Are Stem Perissodactyls. PLoS ONE. 9 (10): e109232. doi:10.1371/journal.pone.0109232. PMID 25295875.
Hatcher JB 1901. Report of the Princeton University Expeditions to Patagonia 1869-1899. Mammalia of the Santa Cruz Beds. IV. Astrapotheria. Scott WB ed. Vol. 6, Paleontology 3. Princeton, NJ Stuttgart 1909-1928.
Wible JR, Rougier GW, Novacek MJ, Asher RJ 2007. Cretaceous eutherians and Laurasian origin for placental mammals near the K/T boundary. Nature 447: 1003–1006. doi: 10.1038/nature05854
Williamson TE, Lucas SG 1992. Meniscotherium (Mammalia, “Condylarthra”) from the Paleocene-Eocene of western North America. Bulletin of the New Mexico Museum of Natural History and Science 1: 1–54.