Ghosts in the Origins of Life?

The so-called bottleneck or ghost can appear after a saddle-node bifurcation, leaving a region in phase space by which the flow is attracted although no fixed points are present. Such ghosts, displayed by some dynamical systems, actually cause a delay of the flow. In this paper, we analyze a saddle-node ghost found in a biological model for the two-member hypercycle dynamics. The model predicts a scaling law of the dynamic delay caused by the ghost near the threshold: τ ∼ φ−1/2, consistent with previous results in physical systems. Possible biological meanings for such a dynamical phenomenon are outlined.