Ecological Invasion, Roughened Fronts, and a Competitor's Extreme Advance: Integrating Stochastic Spatial-Growth Models

TL;DR

This paper models biological invasions using stochastic spatial-growth models, analyzing the invasion front's roughness and the position of the most advanced invader to understand invasion dynamics.

Contribution

It introduces a unified stochastic modeling framework that captures universal invasion features and links habitat size to invasion speed and front dynamics.

Findings

Universal characteristics across different invasion models

Invasion velocity depends on habitat size

Distribution of the front-runner's position is characterized

Abstract

Both community ecology and conservation biology seek further understanding of factors governing the advance of an invasive species. We model biological invasion as an individual-based, stochastic process on a two-dimensional landscape. An ecologically superior invader and a resident species compete for space preemptively. Our general model includes the basic contact process and a variant of the Eden model as special cases. We employ the concept of a "roughened" front to quantify effects of discreteness and stochasticity on invasion; we emphasize the probability distribution of the front-runner's relative position. That is, we analyze the location of the most advanced invader as the extreme deviation about the front's mean position. We find that a class of models with different assumptions about neighborhood interactions exhibit universal characteristics. That is, key features of the invasion dynamics span a class of models, independently of locally detailed demographic rules. Our results integrate theories of invasive spatial growth and generate novel hypotheses linking habitat or landscape size (length of the invading front) to invasion velocity, and to the relative position of the most advanced invader.