Using theoretical models to explore dispersal variation and fragmentation in urban environments

Cities are fundamentally changing the environment that plants inhabit, most notably through habitat fragmentation. Urban plant habitat patches are separated by impervious surfaces like buildings and roads and may vary from small, isolated green spaces to large green spaces like parks. Understanding the consequences of this urban fragmentation on seed dispersal is essential to both maintain urban biodiversity and mitigate the spread of unwanted weeds or invasive species but we currently lack enough empirical data to draw generalities. Theoretical reasoning (via both verbal and mathematical models) is well positioned to contribute to this knowledge gap in dispersal by providing useful predictions when empirical data are lacking. Variation in dispersal can easily be captured by models by incorporating different dispersal kernel shapes, and multiple habitat configurations can be examined. Urban environments are rarely considered by mathematical models, and our literature review indicates that most models that include dispersal variation via a dispersal kernel use only one or two shapes, suggesting a gap in the theoretical literature as well. We present a proof-of-concept model of fragmentation in an urban environment illustrating how varying habitat width can lead to different outcomes depending on the dispersal kernel. We also provide some thoughts for future directions on the application of mathematical models in urban areas.