# Extinction phase transitions in a model of ecological and evolutionary dynamics

## TL;DR

This study investigates how environmental fluctuations influence the extinction transition in ecological models, revealing a novel infinite-noise universality class driven by temporal disorder.

## Contribution

It demonstrates that temporal disorder causes an exotic infinite-noise phase transition, contrasting with the standard directed percolation class in static environments.

## Key findings

- Extinction transition in static environments belongs to directed percolation universality class.
- Temporal disorder induces a logarithmically slow decay and large fluctuations in populations.
- Evidence supports the transition being of infinite-noise type, with temporal Griffiths phases.

## Abstract

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.