Zoysia versus Bermuda

My neighborhood is mostly zoysia lawns, but there are a couple Bermuda lawns down the street and a fair number of cool-season lawns here too. Pretty much everything goes in the Transition Zone of St. Louis. Lotsa variety of lawns from warm-season to cool-season lawns.
My lawn is 90 percent Zoysia and 10 percent Fine Fescue (I have an area in the backyard which is solely Fine Fescue).
However, in back I also have a few small patches of Bermuda grass here and there. The Bermuda doesn't make up more than 1 percent of my total lawn right now.
When the Zoysia and the Bermuda finally meet, which will win? Right now they're separated by some weeds. Will the zoysia take over the Bermuda or vice versa? Thanks.
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