Check it out for yourself. http://www.ctahr.hawaii.edu/bnf/Downloads/Dissertations/Chaudhary%20Dissertation.htm
By combining crops, weed control is reduced dramatically since two crops can be planted in one field and the low growing beans shade the sol and reduce weed pressure. I've seen this over and over in the intercropping research trials I've read. Corn is a popular trial crop, partly because results are gained in a short period of time. What about intercropping trees, shrubs, herbs vines, roots, and veggies? I doubt there are many intensive intercropping research trials due to the time needed to collect results and the challenge of scientifically gathering data--there are too many variables. Agroforestry research increases the species diversity a bit, but funding is almost always based commodity production.
I offer this glimpse gained from my experiences and communicating with creators of successful intensive intercrop systems: Weeding can be reduced incredibly with effective installation of a groundcover and trees and shrubs. Since weed control is one of the largest expenses/labor for farms and gardens, more ground can be cultivated. Complex systems fill the various ecological niches and provide products and services such as deep roots that break up compaction and hardpans, better drainage, better nutrient cycling, less leaching, less erosion, creation of in situ organic matter, the main crop, short term pay while long term tree crops grow, and the potential develop niche crops that command a premium(most are forest products since they are not as quick and "simple" as annuals).
Many native plants are slow to germinate and are swamped by weeds or hurt by weed control. I have found that uncommon native plants can germinate and grow in complex intercrop systems because the soil is not tilled or weeded. A bit of subsoil mixed in with topping mix for seedlings and also added to the broadcast seed mix is a simple way to encourage native plants. Pretty simple. The legumes teach us to leave a place bette than when we found. Natural Systems Cultivation offers a way for us to do that.
Please feel free to share any studies that you find so I can post it on the site. Here is a hint for targeting your websearches--search by crop name and the different terms for agroforestry. For example, I would do different searches such as Papaya agroforestrytrials, Papaya multcrop trials, Papaya poylculture trials....intercrop trials....