Lag-induced critical transitions to extinction in replicating systems: the τ-tipping mechanism.

Replicating systems sustained by error-prone enzymatic amplification can undergo critical transitions between persistence and extinction. In RNA viruses, such transitions are classically governed by mutation rates and fitness landscape topographies, giving rise to error thresholds and lethal mutagenesis. Motivated by experimental evidence that polymerase-targeting antivirals limit replication, we analyze replicating systems with explicit time lags in replication-enzyme availability by means of delay differential equations. Our approach is not equivalent to a simple renormalization of the rate of replication, since explicit delays introduce memory and temporal nonlocality into the dynamics. We identify a lag-induced critical transition driven by the loss of temporal coordination between genome expression and replication. At fixed mutation and replication rates ensuring persistence, populations cross an extinction threshold solely due to replication delays. In our delay-extended quasispecies model, the timing of replicase availability emerges as an independent dynamical control parameter, defining a route to extinction that is fundamentally distinct from transitions driven by mutation rates or replicative fitness. These results further suggest that perturbing the temporal coordination of viral replication may provide an alternative antiviral strategy for driving viral populations toward collapse. More generally, we propose that the extinction mechanism described here constitutes a form of lag-time-induced tipping, which we denote as τ-tipping.