Physical Sciences and Mathematics Commons^™

The Effect Of Habitat Fragmentation On Plant Communities In A Spatially-Implicit Grassland Model, Mika T. Cooney, Benjamin R. Hafner, Shelby E. Johnson, Sean Lee

Rose-Hulman Undergraduate Mathematics Journal

The spatially implicit Tilman-Levins ODE model helps to explain why so many plant species can coexist in grassland communities. This now-classic modeling framework assumes a trade-off between colonization and competition traits and predicts that habitat destruction can lead to long transient declines called ``extinction debts.'' Despite its strengths, the Tilman-Levins model does not explicitly account for landscape scale or the spatial configuration of viable habitat, two factors that may be decisive for population viability. We propose modifications to the model that explicitly capture habitat geometry and the spatial pattern of seed dispersal. The modified model retains implicit space and is …