# Boundary Effects on Population Dynamics in Stochastic Lattice Lotka-Volterra Models

## TL;DR

This study uses Monte Carlo simulations to explore how boundary effects influence predator-prey dynamics in a stochastic lattice Lotka-Volterra model, revealing localized predator density enhancements and complex oscillation behaviors.

## Contribution

It introduces a novel two-domain simulation approach to analyze boundary effects in stochastic predator-prey models, highlighting how domain boundaries impact population densities and correlations.

## Key findings

- Predator density is enhanced at domain boundaries.
- Predator correlation length shows a minimum at the boundary.
- Boundary effects diminish with smaller domain sizes.

## Abstract

We investigate spatially inhomogeneous versions of the stochastic Lotka-Volterra model for predator-prey competition and coexistence by means of Monte Carlo simulations on a two-dimensional lattice with periodic boundary conditions. To study boundary effects for this paradigmatic population dynamics system, we employ a simulation domain split into two patches: Upon setting the predation rates at two distinct values, one half of the system resides in an absorbing state where only the prey survives, while the other half attains a stable coexistence state wherein both species remain active. At the domain boundary, we observe a marked enhancement of the predator population density. The predator correlation length displays a minimum at the boundary, before reaching its asymptotic constant value deep in the active region. The frequency of the population oscillations appears only very weakly affected by the existence of two distinct domains, in contrast to their attenuation rate, which assumes its largest value there. We also observe that boundary effects become less prominent as the system is successively divided into subdomains in a checkerboard pattern, with two different reaction rates assigned to neighboring patches. When the domain size becomes reduced to the scale of the correlation length, the mean population densities attain values that are very similar to those in a disordered system with randomly assigned reaction rates drawn from a bimodal distribution.