  We study the non-equilibrium phase transition between survival and extinction
of spatially extended biological populations using an agent-based model. We
especially focus on the effects of global temporal fluctuations of the
environmental conditions, i.e., temporal disorder. Using large-scale
Monte-Carlo simulations of up to $3\times 10^7$ organisms and $10^5$
generations, we find the extinction transition in time-independent environments
to be in the well-known directed percolation universality class. In contrast,
temporal disorder leads to a highly unusual extinction transition characterized
by logarithmically slow population decay and enormous fluctuations even for
large populations. The simulations provide strong evidence for this transition
to be of exotic infinite-noise type, as recently predicted by a renormalization
group theory. The transition is accompanied by temporal Griffiths phases
featuring a power-law dependence of the life time on the population size.
