We carry out density functional theory calculations which demonstrate that the electron dynamics in the skyrmion phase of Fe-rich Mn$_{1-x}$Fe$_x$Ge alloys is governed by Berry phase physics. We observe that the magnitude of the Dzyaloshinskii-Moriya
interaction, directly related to the mixed space-momentum Berry phases, changes sign and magnitude with concentration $x$ in direct correlation with the data of Shibata {it et al.}, Nature Nanotech. {bf 8}, 723 (2013). The computed anomalous and topological Hall effects in FeGe are also in good agreement with available experiments. We further develop a simple tight-binding model able to explain these findings. Finally, we show that the adiabatic Berry phase picture is violated in the Mn-rich limit of the alloys.
