They came to their conclusions after combining genome skimming and target DNA capture to sequence the whole chloroplasts and 605 single-copy nuclear regions from 199 specimens representing the sweet potato and all of its crop wild relatives.
They found the data strongly suggested that sweet potato arose after a genome duplication event, and confirmed that no other extant species were involved in the sweet potato's origin.
Phylogenetic analysis of the DNA sequences produced conflicting family trees.
However, the researchers reported, those conflicting patterns could be explained by a dual role for their closest wild relative, Ipomoea trifida.
They found the sweet potato arose from I. trifida and later hybridised with I. trifida to produce another, independent sweet potato lineage.
"We demonstrate that the existence of those two different lineages is the result of an ancient hybridisation between sweet potato and its progenitor," said the study's first author, Pablo Munoz-Rodriguez.
"We conclude that sweet potato evolved at least 800,000 years ago from its progenitor, and then after the two species became distinct, they hybridised."
However, two University of Otago researchers weren't convinced by one of the study's main findings.
Professor Lisa Matisoo-Smith and Dr Michael Knapp, both of the university's Department of Anatomy, said the study answered questions about the sweet potato's evolution well, but it fell short in examining how it came to be widespread in Polynesia before European arrival.
They noted the data used to address the issue of how the sweet potato got to the Pacific consisted of chloroplast and nuclear DNA obtained from a plant specimen collected in 1769 in Tahiti by Joseph Banks and Daniel Solander, who accompanied Captain James Cook during his Endeavour expedition.
"This was a sample held in the Herbarium at the British Museum. While technically only 250 years old, this specimen is not fresh tissue and will have degraded DNA," the two researchers said in a joint statement.
"Any DNA obtained from this sample needs to be treated with all of the precautions of ancient DNA."
Matisoo-Smith and Knapp said there were well accepted and published protocols for the extraction and sequencing of ancient DNA, none of which appear to have been followed by these researchers.
"Not surprisingly, they found an unusual number of DNA mutations in the Banks and Solander sample and from this, they calculated that the Polynesian sample must have been isolated from its source population for over 100,000 years.
"Humans have only been in East Polynesia for just over 1000 years, so the authors conclude that the sweet potato dispersed to Polynesia naturally.
"From there, they conclude that there is no evidence for pre-Columbian contacts between Polynesia and the Americas.
"So, the data that the whole argument is based upon is DNA from one sample that was produced without using standard ancient DNA protocols and analysed without using standard ancient DNA authentication methods.
"The data presented, to an ancient DNA researcher, ring alarm bells and appear very much like damaged and/or contaminated DNA.
"I would want to at least see replication before considering using it in further analyses. There are also technical issues with the actual phylogenetic analyses that would have a major impact on the date of divergence."
Further, they added, much of the discussion regarding the likelihood of the sweet potato being introduced to Polynesia due to human contact, as opposed to naturally, was the strong linguistic evidence.
The Polynesian word, kumara, was derived from the Quechuan word, cumar - and traced particularly to the Gulf of Guayaquil, in Ecuador, one of the centres of sweet potato domestication.
"Such linguistic evidence requires human contact and the authors mention this information but they do not account for it in their argument for natural dispersal," Matisoo-Smith and Knapp said.
"They also lightly brush off or do not mention a significant amount of other anthropological evidence for pre-Columbian contacts.
"While natural dispersal of the sweet potato is certainly possible, the data and argument presented are not convincing.
"Can their DNA result be replicated in an ancient DNA facility?
"There are multiple samples from that same Banks and Solander collection, including plants collected from New Zealand, held in the British Museum Herbarium – do they show the same pattern of genetic divergence?
"Is there any evidence of sweet potato starch, phytoliths or pollen found in soils that are over 10,000 years old, or even more than 1500 years old in Polynesia?
"We would like to see more robust data, ideally from multiple sources, presented before we can accept the data and reconsider the current interpretation that the sweet potato was brought to Polynesia by humans at some point around 1000-1200 AD."
