If you live in a mild climate, where you can overwinter potted yacon in a tunnel or a greenhouse, you might consider taking stem cuttings. They root pretty easily and give you a head start in spring. This is obviously also a good way to multiply up a variety. Between stem cuttings and rhizomes, you could pretty easily turn one yacon plant into fifty.
I take two kinds of stem cuttings from yacon: vertical cuttings on the lower part of the stem where it is still solid and horizontal sections from the upper parts of the stem that are hollow. The reason for the difference is that I had problems with the hollow stems rotting before they would root and the horizontal sections expose the cut interior of the node for rooting, which seems to help. I noticed that lodged yacon stems sometimes reroot on their own, but only where the stem has cracked and split.
I don’t usually take tips for cuttings, although this might be the most tempting approach. The only reason for this is that I try to preserve yacon flowers as long as possible in the hope of getting some seed. Even with lodged plants, I can remove the lower parts of the stem and the put the upper part with the flowers in a bucket of water while they finish. By the time that is done, the stem isn’t in very good condition for taking cuttings.
These are certainly not the only ways to root yacon and they may not even be the best ways. If you have a method that works better, please let us know.
Here’s a brief video that demonstrates both techniques: