[nonbel]

I think you are underestimating how much methane there is under there.

>"There is a huge amount of carbon stored in permafrost. Right now, the Earth's atmosphere contains about 850 gigatons of carbon. (A gigaton is one billion tons—about the weight of one hundred thousand school buses). We estimate that there are about 1,400 gigatons of carbon frozen in permafrost." https://nsidc.org/cryosphere/frozenground/methane.html

The beavers are going to do their thing and create comfortable habitats for themselves, which is melting the permafrost. So it looks like this gas is coming out one way or the other.