Numerical simulations of wave propagation in a two-dimensional stratified magneto-atmosphere are presented for conditions that are representative of the solar photosphere and chromosphere. Both the emergent magnetic flux and the extent of the wave source are spatially localized at the lower photospheric boundary of the simulation. The calculations show that the coupling between the fast and slow magnetoacoustic-gravity (MAG) waves is confined to thin quasi-one-dimensional atmospheric layers where the sound speed and the Alfvén velocity are comparable in magnitude. Away from this wave conversion zone, which we call the magnetic canopy, the two MAG waves are effectively decoupled because either the magnetic pressure (B 2 =8) or the plasma pressure (p ¼ Nk B T) dominates over the other. The character of the fluctuations observed in the magneto-atmosphere depend sensitively on the relative location and orientation of the magnetic canopy with respect to the wave source and the observation point. Several distinct wave trains may converge on and simultaneously pass through a given location. Their coherent superposition presents a bewildering variety of Doppler and intensity time series because (1) some waves come directly from the source while others emerge from the magnetic canopy following mode conversion, (2) the propagation directions of the individual wave trains are neither co-aligned with each other nor with the observer's line of sight, and (3) the wave trains may be either fast or slow MAG waves that exhibit different characteristics depending on whether they are observed in high-or low-plasmas ( 8p=B 2 ). Through the analysis of four numerical experiments a coherent and physically intuitive picture emerges of how fast and slow MAG waves interact within two-dimensional magneto-atmospheres.