Synopsis: Methane levels in atmosphere are not caused by level of CO2 in atmosphere.
Source here. "Methane (CH4) is a potent greenhouse gas. An enhanced CO2 environment has been shown to have “neither positive nor negative consequences” on atmospheric methane concentrations. Higher temperatures have been shown to result in reduced methane release from peatbeds. Methane emissions from cattle have been reduced considerably by altering diet, immunization, and genetic selection."