The question constantly comes up in both pro-permaculture and permaculture-skeptical literature. Finally, here's a chance to generate published scientific data on yield/land use for permaculture food producers!
If you have a mature permaculture operation, and produce lots of food (especially for sale to the surrounding community), I'd love to talk to you about including your operation in my thesis research. I hope to generate a case study on at least 3 solid operations. The result will be a sustainable development MSc thesis, which will hopefully be published in a scientific journal.
I'll happily work with producers on any continent. If you get in touch, I can explain the methodology a little more thoroughly. It will require significant record-keeping, but I think the benefits (global awareness, and hopefully scientific validation for permaculture and forest gardening yield sustainability) will be worth the effort!!