The prevailing thought is that methane production by methanogens happens strictly under anoxic condition, but when oxygen is available, methanotrophs will consume the methane. Therefore, the balance between production and consumption as regulated by oxygen availability determines the net emission from any particular habitat. However, this conventional wisdom is beginning to change because recent research on land as well as in aquatic environments has shown that microbial methane production can actively occur even under oxic condition. For more information, please see the papers:
Angel et al. (2011) Activation of methanogenesis in arid biological soil crusts despite the presence of oxygen. PLOS One (doi: 10.1371/journal.pone.0020453)
Grossart et al. (2011) Microbial methane production in oxygenated water column of an oligotrophic lake. PNAS 108:19657-19661 (doi:10.1073/pnas.1110716108)
Tang et al. (2014) Paradox reconsidered: Methane oversaturation in well-oxygenated lake waters. Limnology & Oceanography 59:275-284 (doi:10.4319/lo.2014.59.1.0275) (open access)