TITLE:
Lag-induced critical transitions to extinction in replicating
systems: the \tau-tipping mechanism

AUTHORS:

Edward A. Turner^(1), Francisco Crespo^(2), Joan Gimeno^(3),
Ernest Fontich^(3), Santiago F. Elena^(4,5) and Josep Sardanyes^(6,7)

(1) Facultad de Ciencias Juridicas, Sociales y de la Educacion,
    Universidad Vi\~na del Mar, Chile.

(2) Aerospace Engineering Department, Embry-Riddle Aeronautical University. 
    Daytona Beach, FL 32114, USA.

(3) Departament de Matemàtiques i Informàtica, Universitat de Barcelona (UB).
   Barcelona, Catalonia, Spain.

(4) Institute for Integrative Systems Biology (I2SysBio), 
    CSIC-Universitat de Valencia,
    Valencia, Spain

(5) The Santa Fe Institute,
    Santa Fe, NM87501, USA.

(6) Centre de Recerca Matematica (CRM). 
    Barcelona, Spain

(7) Dynamical Systems and Computational Virology, 
    CSIC Associated Unit I2SysBio-CRM,
    Cerdanyola del Valles, Spain.


ABSTRACT:
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, populations cross an
extinction threshold solely due to replication delays. In a 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 \tau-tipping.