Smoothly vanishing density in the contact process by an interplay of disorder and long-distance dispersal

TL;DR

This study investigates how spatial heterogeneity and long-distance dispersal influence the contact process, revealing a smooth density decline at extinction and a discontinuous local persistence, indicating complex transition behaviors.

Contribution

It combines Monte Carlo simulations and renormalization group analysis to show that density vanishes smoothly at the extinction threshold in models with disorder and long-range dispersal.

Findings

Density vanishes smoothly at the extinction threshold.

Local persistence shows a discontinuous transition.

Transition behavior is characterized as an infinite-order transition.

Abstract

Realistic modeling of ecological population dynamics requires spatially explicit descriptions that can take into account spatial heterogeneity as well as long-distance dispersal. Here, we present Monte Carlo simulations and numerical renormalization group results for the paradigmatic model, the contact process, in the combined presence of these factors in both one and two-dimensional systems. Our results confirm our analytic arguments stating that the density vanishes smoothly at the extinction threshold, in a way characteristic of infinite-order transitions. This extremely smooth vanishing of the global density entails an enhanced exposure of the population to extinction events. At the same time, a reverse order parameter, the local persistence displays a discontinuity characteristic of mixed-order transitions, as it approaches a non-universal critical value algebraically with an exponent $\beta_p'<1$.