Affiliate Marketing Secrets

I apologize for this being so long.
So I’m doing this independent research for AP Biology and it involves growing, identifying, and testing sensitivity to antibiotics for bacteria. Yes it was originally 3 parts, and I finished them all and was about to write the report and get the presentation ready, when I noticed that a fungus was growing on one of the dishes and no bacterial colony growth was visible near it. I did some tests and some observation and based on the results and appearance I concluded that it was Absidia corymbifera or Mycocladus corymbifera as they sometimes call it. Now this got me thinking about Gause’s Competitive Exclusion Principle and I thought maybe I should add a 4th part to my experiment studying the competition between these two organisms given they can only occupy the same niche ie: use the same agar.
My question is, does yeast out-compete bacteria in Lysogenic broth (regular agar) or vice-versa?
I would believe that being eukaryotes and requiring less nutrients (most yeast can grow on sugar water) the yeast would out-compete the bacteria but are there any studies supporting my idea?