From _Food in Antiquity_ by Don Brothwell and Patricia Brothwell. 1998.

The sweet potato is widely grown in South America, in the West Indies and
all over the Pacific area. Early trans-Pacific migration most likely caused
it to be carried from its home in America by man, resulting in its
widespread cultivation under its Peruvian name, kumara. Recent studies show
it to have been cultivated in Peru during the Formative period of
agriculture, and dried remains of it were found in the necropolis at
Paracas of about the same date. Columbus, on his arrival in the West
Indies, found it very much in evidence. He was given the tubers which he
likened to large radishes and also bread which he called aje-bread -- aje
or axi being the local name for sweet potato. On Santo Tome he was received
by the king and given a feast at which three or four varieties were served.

At this same feast he also tasted cassava bread. If the sweet potato was a
mainstay of the diet so also was and is cassava, particularly among the
inhabitants of north-eastern South America. Flour is prepared from the
manioc root by first shredding and soaking it to remove the toxic
qualities, a technique probably already long-established by the time of the
Spanish conquest. Indeed what are believed to be traces of manioc have been
detected in one of the levels of the Tamaulipas caves in Mexico dating from
about 2300-1800 BC.

The removal of toxins is also necessary in the case of the yam, a valuable
food in three major areas of the world. Different species have been
cultivated and gathered wild in Africa, South East Asia and the Atlantic
drainage areas of South America, particularly the Guianas and the West
Indies, since pre-European contact times. Even if we concede that Columbus
got his botanical names confused, it seems possible that he did recognize
the yam there. It has been suggested that the American yam came originally
from Africa on the grounds that if people could sail between America and
Polynesia, why not, following the Equatorial current, from Africa; a single
find of one kind of yam in the Marquesas Islands has in fact been declared
a close relative to -- if not identical with -- the African variety,
Dioscorea cayenensis.