Abstract Lagrangian-mean wave activity diagnostics are applied to the nonlinear baroclinic eddy life cycle in a simple general circulation model of the atmosphere. The growth of these instabilities through baroclinic conversion of potential temperature gradients and their subsequent barotropic decay can exhibit two distinct life cycles. One life cycle results in equatorward propagation of the growing eddy, anticyclonic wave breaking, and a poleward shift of the mean jet. The second life cycle is distinguished by limited equatorward propagation and cyclonic wave breaking on the poleward flank of the jet. Using a conservative finite-amplitude, Lagrangian-mean wave activity (negative pseudomomentum) to quantify wave growth and propagation reveals more details about the life cycles than could be discerned from eddy kinetic energy (EKE) or other Eulerian metrics. It is shown that the distribution of pseudomomentum relative to the latitude of the axis of the jet can be used to provide a clear distinction between the two life cycles at an early stage in their development and, hence, a prediction for the subsequent shift of the jet. This suggests that the distribution of pseudomomentum may provide some predictability for the atmospheric annular modes.