Trees with Roots that don't mind a little disturbance?

I like root crops, and I like trees.

So, let's combine them somehow!

I grow or would like to grow in the future many root crops; carrots, burdock, skirret, jerusalem artichoke, potato, groundnut.

Let's make a list of trees that would be.. relatively unaffected by the cultivation of root crops within a reasonable distance from their trunk. Of course the older the tree, the farther away you must plant things from the trunk to avoid damaging roots. The other variable is the root crop; how much the soil is disturbed by digging it up.

My inclinations are that taprooted trees may accept me growing some root crops pretty close to them.

My feeling is that pioneer species (ideally nitrogen fixers) would be best for this but depending on the species and amount of disturbance, you might end up with a crapload of suckers. I suppose these suckers could be transplanted or chopped and dropped though.

What about growing the root crops under the trees but in large containers? I've grown really nice carrot crops in tree pots for instance. This may be more suited to the homescale/zone 1 rather than any type of commercial solution...

What about growing root crops that don't need to be dug, such as round carrots, short beets, turnips, etc?  And making sure the soil is so soft and mulched that the roots are easily pulled?

there are some trees that will spread and send up hundreds of sucker trees if their roots are damaged so you gotta be careful of those too..

myself..i would put the ROOT crops somewhere else and use your more permanent plantings around your trees, like your herbs, perennials and really shallow rooted plants if you are going to harvest the entire plant..things that the roots can be left behind are ok also like beans, peas, etc..just cut the plant off when you are done harvesting..but not root crops