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 in fact mathematically equivalent to the Tilman-Levins model in the single species case. But its novel interpretation of a habitat destruction parameter better quantifies seed loss due to edge effects in fragmented habitats and results in different predictions than the Tilman-Levins model. In particular, the seed loss model predicts that species with strong dispersal traits may be most vulnerable to extinction in small habitat fragments.

Author Bio

Mika Cooney, Ben Hafner, Shelby Johnson, and Sean Lee are members of the class of 2022 at Carleton College. They completed the submitted work as part of their senior integrative exercise.