  We analyze the influence of long-range correlated (colored) external noise on
extinction phase transitions in growth and spreading processes. Uncorrelated
environmental noise (i.e., temporal disorder) was recently shown to give rise
to an unusual infinite-noise critical point [Europhys. Lett. 112, 30002
(2015)]. It is characterized by enormous density fluctuations that increase
without limit at criticality. As a result, a typical population decays much
faster than the ensemble average which is dominated by rare events. Using the
logistic evolution equation as an example, we show here that positively
correlated (red) environmental noise further enhances these effects. This
means, the correlations accelerate the decay of a typical population but slow
down the decay of the ensemble average. Moreover, the mean time to extinction
of a population in the active, surviving phase grows slower than a power law
with population size. To determine the complete critical behavior of the
extinction transition, we establish a relation to fractional random walks, and
we perform extensive Monte-Carlo simulations.
