  The effect of diffusively correlated spatial fluctuations on the
proliferation-extinction transition of autocatalytic agents is investigated
numerically. Reactants adaptation to spatio-temporal active regions is shown to
lead to proliferation even if the mean field rate equations predict extinction,
in agreement with previous theoretical predictions. While in the proliferation
phase the system admits a typical time scale that dictates the exponential
growth, the extinction times distribution obeys a power law at the parameter
region considered.
