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There's a 1600-lb animal missing from your calculations.
Here are my calculations, with references, courtesy of google and an hour of my time. Thanks also to the USDA and PBS.
Size of national herd, all cows and calves: 106 million.
http://usda.mannlib.cornell.edu/usda/current/Catt/Catt-07-20-2007.txt
Number on feed (multiplying their GHG impact): 11 million.
(in short, they are only on feed near The End.)
http://www.usda.gov/nass/PUBS/TODAYRPT/cofd0907.txt
Number of bison they ecologically replaced, bison that ALSO produced GHGs:
60 million.
http://www.pbs.org/wnet/frontierhouse/frontierlife/essay8.html
OK, so because of the 11 million on feed, the 106 million cows have the GHG impact of a good 120 million grass-fed, so they have double the "natural" level produced by the bison?
But wait! Or, rather, weight:
Bull bison (37% of herd): 1800-2500 lb.
Cow bison (45%): 900-1200 lb.
Calves (18%) :35 lb up to numbers above
sources:
Herd composition:
http://links.jstor.org/sici?sici=0022-541X(198907)53%3A3%3C593%3ACOBPEW%3E2.0.CO%3B2-R
Weight:
http://www.gunpowderbison.com/Kids%20Corner
So the TONNAGE of natural ruminants on the North American plains can be calculated from the above numbers (giving calves half the average of cow and bull) to be an "average bison" weight of 1559 lb. Times 60M, is 46.8 megatons.
The US herd is lighter because it's mostly younger than a natural one; we slaughter cows at 2 years, bison live 20, so a higher proportion of the total is calves.
My first reference also notes that just 33M of that national herd is over 500 lbs. Conservatively giving them all the full adult weight (from wikipedia, "cattle") halfway between 1300 and 1900 lb, and the average of the other 74M that are under 500lb, conservatively, at 400 lb...we get a total tonnage of beef at 41.2 megtons.
Bottom line: there are fewer tons of beef now than there were of bison in the 19th century. Beef eater's disturbance of the natural methane balance is zero, indeed it may be NEGATIVE.
Maybe not; 41.2MT is only 12% less than 46.8MT and my whole-hour of research may have missed a few things. Also, the amplification of GHG output by the 10% of the herd that's on feed is a factor. I'm willing to call it even, although my weight numbers were quite conservative.
So, there's no GHG impact at ALL, compared to the original, natural state. At least not in North America -- but what was the former methane production everywhere that are now cattle ranches? Most ranching is done where there was an equivalent animal before. And even swamps and rainforests have quite a bit of decomposition that produces methane; smell one some time.
Until you do that part of the calc - the previous GHG load from the former "natural" environment, you don't have a calculation, you have HALF a calculation.
Liz Galst, please do 100% of your homework next article, I'll only do the other half for free this once.