Sheep's Carbon Footprint - Welsh Hillsides vs. Good Pasture

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I heard a statement on Radio 4 (Costing the Earth, perhaps?) pointing out that sheep on Welsh hillsides have a bigger carbon footprint than the sheep which are reared on good quality pasture. This is on account of the fact that they are actually living longer and doing more in the way of CO2 and methane production. But then I thought - if the sheep weren't up on the hills eating what little grass there was, wouldn't it get eaten by an increasing population of other consumers- rabbits, snails etc., which would also be producing greenhouse gases? Would there, in fact, be less 'gas' produced when you do a total costing of the situation?
Has anyone done the sums?
 
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To do the sums (already a very difficult endeavor), one would need to know EXACTLY what the assertion is, and a loose paraphrase can easily miss important details. It is thus of primary importance that one have access to the original claim, before attempting a calculation. Do you have a link to a video/podcast/transcript or can you somehow quote the exact words of the assertion?
 
I think the remark was made in order to show that things are never as clear cut as people assume.