Metastability is a common phenomenon. Many evolutionary processes, both natural and artiÿcial, alternate between periods of stasis and brief periods of rapid change in their behavior. In this paper an analytical model for the dynamics of a mutation-only genetic algorithm (GA) is introduced that identiÿes a new and general mechanism causing metastability in evolutionary dynamics. The GA's population dynamics is described in terms of ows in the space of ÿtness distributions. The trajectories through ÿtness distribution space are derived in closed form in the limit of inÿnite populations. We then show how ÿnite populations induce metastability, even in regions where ÿtness does not exhibit a local optimum. In particular, the model predicts the occurrence of "ÿtness epochs" -periods of stasis in population ÿtness distributions -at ÿnite population size and identiÿes the locations of these ÿtness epochs with the ow's hyperbolic ÿxed points. This enables exact predictions of the metastable ÿtness distributions during the ÿtness epochs, as well as giving insight into the nature of the periods of stasis and the innovations between them. All these results are obtained as closed-form expressions in terms of the GA's parameters.
An analysis of the Jacobian matrices in the neighborhood of an epoch's metastable ÿtness distribution allows for the calculation of its stable and unstable manifold dimensions and so reveals the state space's topological structure. More general quantitative features of the dynamics -ÿtness uctuation amplitudes, epoch stability, and speed of the innovations -are also determined from the Jacobian eigenvalues. The analysis shows how quantitative predictions for a range of dynamical behaviors, that are speciÿc to the ÿnite-population dynamics, can be derived from the solution of the inÿnite-population dynamics. The theoretical predictions are shown to agree very well with statistics from GA simulations. We also discuss the connections of our results with those from population genetics and molecular evolution theory.