Non-equilibrium relaxation in a stochastic lattice Lotka-Volterra model

TL;DR

This study uses Monte Carlo simulations to analyze non-equilibrium relaxation and critical phenomena in a stochastic lattice Lotka-Volterra model, revealing universal scaling behaviors near predator extinction thresholds.

Contribution

It demonstrates the critical aging behavior and confirms the directed percolation universality class in a spatial predator-prey model with finite prey capacity.

Findings

Critical slowing-down near extinction threshold

Algebraic decay of predator density at criticality

Universal aging scaling behavior observed

Abstract

We employ Monte Carlo simulations to study a stochastic Lotka-Volterra model on a two-dimensional square lattice with periodic boundary conditions. If the (local) prey carrying capacity is finite, there exists an extinction threshold for the predator population that separates a stable active two-species coexistence phase from an inactive state wherein only prey survive. Holding all other rates fixed, we investigate the non-equilibrium relaxation of the predator density in the vicinity of the critical predation rate. As expected, we observe critical slowing-down, i.e., a power law dependence of the relaxation time on the predation rate, and algebraic decay of the predator density at the extinction critical point. The numerically determined critical exponents are in accord with the established values of the directed percolation universality class. Following a sudden predation rate change to its critical value, one finds critical aging for the predator density autocorrelation function that is also governed by universal scaling exponents. This aging scaling signature of the active-to-absorbing state phase transition emerges at significantly earlier times than the stationary critical power laws, and could thus serve as an advanced indicator of the (predator) population's proximity to its extinction threshold.