Biological Invasions in Heterogeneous Environments: The Coupled Map Lattice Framework

Department of Mathematics, Federal University of Santa Maria, Santa Maria, RS, Brasil.

^⋆ Corresponding author. E-mail: dcmistro@gmail.com

Abstract

Spatial heterogeneity greatly affects the population spread. Although the theory for biological invasion in heterogeneous spatially continuous habitats have received considerable attention, spatially discrete models have remained outside of the mainstream. In this study, we formulate and analyze a Coupled Map Lattice model for a single species population invading a two dimensional heterogeneous environment. The population growth rate and dispersal coefficient depend on the site quality. We first find an analytical criterium for the spread success in terms of the population growth rate and the dispersal coefficient in unfavorable regions. We then implemented our model for two distinct spatial configurations: periodical stripe-like and randomized environments. The spread rate is computed numerically and it shows a decrease with an increase of the fraction of the hostile sites. However, we observed that invasion success does not depend on the fraction of favorable sites but crucially depends on the connectivity of favorable regions.