# Population boundary across an environmental gradient: Effects of quenched disorder

## TL;DR

This study models how local heterogeneities affect ecological population boundaries across environmental gradients, revealing intermittent dynamics and universal scaling laws that could obscure climate change effects in observations.

## Contribution

It introduces a disordered contact process model with strong-disorder renormalization to analyze population boundary dynamics under environmental gradients, highlighting the impact of quenched heterogeneities.

## Key findings

- Population fronts advance intermittently with long quiescent periods.
- Scaling laws relate the dynamics to the environmental gradient and correlation-length exponent.
- Observations may underestimate long-term climate change effects due to intermittent boundary movements.

## Abstract

Population boundary is a classic indicator of climatic response in ecology. In addition to known challenges, the spatial and dynamical characteristics of the boundary are not only affected by the spatial gradient in the environmental factors, but also by local heterogeneities in the regional characteristics. Here, we capture the effects of quenched heterogeneities on the ecological boundary with the disordered contact process in one and two dimensions with a linear spatial trend in the local control parameter. We apply the strong-disorder renormalization group method to calculate the sites occupied with an $O(1)$ probability in the stationary state, readily yielding the population front's position as the outermost site locally as well as globally for the entire boundary. We show that under a quasistatic change of the global environment, mimicking climate change, the front advances intermittently: long quiescent periods are interrupted by rare but long jumps. The characteristics of this intermittent dynamics are found to obey universal scaling laws in terms of the gradient, conjectured to be related to the correlation-length exponent of the model. Our results suggest that current observations might misleadingly show little to no climate response for an extended period of time, concealing the long-term effects of climate change.