You might try the U.S. Department of Agriculture. A market study was conducted for Arizona but that may not be public information. Certification programs are listed at http://www.ams.usda.gov/lsg/certprog/speccomp.pdf and some of them are natural.
The following websites have information on natyral beef production.
http://www.agmrc.org/beef/info/ksunatbeef.pdf
http://www.agmrc.org/beef/info/ksueconbeef.pdf
http://www.agmrc.org/beef/info/naturalbeefmarket.pdf
http://www.fsis.usda.gov/OPPDE/larc/Procedures.htm