It used to be that a simple "site:edu" search would provide quick answers from cooperative extension and the research universities. Lately, colleges have been allowing their students to have personal webpages hosted by the school. So . . . you have John & Mary talking about their backyard garden and showing pictures of Fluffy playing with Fido

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I once read a master's thesis on companion planting. Note, I said that was "read" not "wrote." I found the research sound and the writing good and enjoyed it. It's somewhere online - Massachusetts' scholar if I remember right. His conclusion was that good companions are plants that benefit and plants that are not seriously inconvenienced.
That seemed to make great sense to me

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There are plants that suppress other plants - they are all "trying" to do that since they are all competing for sunlight, nutrients, water. Some, exude chemicals from their roots in the effort - I was surprised to see oats listed as one of those with these allelopathic
skills. We really should be aware that sunflowers do this but, of course, sunflowers are large plants with robust growth. Those big leaves shade any shorter plants growing near them. They are really tough neighbors for most anything but how far those roots travel horizontally, I don't know. I'm not going to worry if a plant is 6 feet away from a sunflower. I believe Thistlebloom has some experience with decomposing sunflower material interfering with a new season's planting.
Yes, that comes as anecdotal information. Like Ridgerunner, I'm open to information on experiences. -
Somewhat Off Topic - I was just reading how "financial experts" have real problems understanding market irrationality. Isn't it odd how we turn to people who know their numbers and expect all the answers about a social institution?? Even the historians are usually ignored so we have trouble just learning from past mistakes.
Anyway, along with plants living together and "not seriously inconveniencing" each other, there are the benefits of "confusing the pests"

. I think it could not be better proven that if you have LOTS of one plant - you risk attracting pests of that plant. If you have a mix of plants, the pests have trouble finding and moving from one host plant to another. Companion planting - as gardeners, I don't think we need a better reason to do it.
Those old notions about crystallizing and such, wow! I don't think we need to go back 80 years and base our beliefs on how much color comes thru a microscope when looking at compost tea . . .
Here is a short pdf file from Oklahoma State University that gives us a quick look at allelopathy and provides a list of companions. It doesn't much go into the "why's" but we can find a list just like this from NDSU, Cornell and other places.
Cultural Controls, OSU
Steve