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The existence of a feedback between climate and methane (CH4) emissions from wetlands has previously been hypothesized, but both its sign and amplitude remain unknown. Moreover, this feedback could interact with the climate-CO2 cycle feedback, which has not yet been accounted for at the global scale. These interactions relate to (i) the effect of atmospheric CO2 on methanogenic substrates by virtue of its fertilizing effect on plant productivity and (ii) the fact that a climate perturbation due to CO2 (respectively CH4) radiative forcing has an effect on wetland CH4 emissions (respectively CO2 fluxes at the surface/atmosphere interface). We present a theoretical analysis of these interactions, which makes it possible to express the magnitude of the feedback for CO2 and CH4 alone, the additional gain due to interactions between these two feedbacks and the effects of these feedbacks on the difference in atmospheric CH4 and CO2 between 2100 and pre-industrial time (respectively ΔCH4 and ΔCO2). These gains are expressed as functions of different sensitivity terms, which we estimate based on prior studies and from experiments performed with the global terrestrial vegetation model ORCHIDEE. Despite high uncertainties on the sensitivity of wetland CH4 emissions to climate, we found that the absolute value of the gain of the climate-CH4 feedback from wetlands is relatively low (<30% of climate-CO2 feedback gain), with either negative or positive sign within the range of estimates. Whereas the interactions between the two feedbacks have low influence on ΔCO2, the ΔCH4 could increase by 475 to 1400 ppb based on the sign of the C-CH4 feedback gain. Our study suggests that it is necessary to better constrain the evolution of wetland area under future climate change as well as the local coupling through methanogenesis substrate of the carbon and CH4 cycles -- in particular the magnitude of the CO2 fertilization effect on the wetland CH4 emissions -- as these are the dominant sources of uncertainty in our model. [ABSTRACT FROM AUTHOR]