The detection of atmospheric methane on Mars implies an active methane source. This introduces the possibility of a biotic source with the implied need to determine whether the methane is indeed biotic in nature or geologically generated. There is a clear need for robotic algorithms which are capable of manoeuvring a rover through a methane plume on Mars to locate its source. We explore aspects of Mars methane plume modelling to reveal complex dynamics characterized by advection and diffusion. A statistical analysis of the plume model has been performed and compared to analyses of terrestrial plume models. Finally, we consider a robotic search strategy to find a methane plume source. We find that gradient-based techniques are ineffective, but that more sophisticated model-based search strategies are unlikely to be available in near-term rover missions.