Wheat to Rye Starter?

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Just curious if it is reasonable to make a rye starter using my wheat starter? If I feed some of my sourdough wheat starter with rye flour for a few days will I get something that resembles a rye starter?

For what it is worth, I've had a rye starter in the past but it tends to slowly loose its potency in the back of the fridge over the summer when I don't use it as much.

You use a bit of one starter to build another one.

I keep a white starter and build whole wheat or rye ones from the white, but you could build from a wheat too.