Extinction phase transitions in correlated external noise

We investigate the non-equilibrium phase transition between survival and extinction of biological populations in the presence of global temporal fluctuations of the environmental conditions. Such temporal disorder gives rise to an unusual type of critical point dubbed infinite-noise critical point [1]. It is characterized by enormous density fluctions 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. Here we show that long-range power-law correlations of the environmental noise further increase these effects, i.e., they accelerate the decay of a typical population but slow down the decay of the ensemble average. We determine the complete critical behavior of the extinction transitions, we establish a relation of our results to fractional random walks, and we illustrate them by Monte Carlo simulations.

[1] T. Vojta and J.A. Hoyos, Europhys. Lett. 112, 30002 (2015)