Friday, August 10, 2007

PS 72-90: Stage-structured reaction-diffusion-competition model of shrub invasion in New Mexico

Etsuko Nonaka, University of New Mexico

In semiarid landscapes of SW USA, invasion of creosotebush (Larrea tridentata) into northern Chihuahuan desert grassland has been a concern for land managers and ranchers. It is believed that the shrub species has spread toward central New Mexico (NM) from Mexico in the last 150 years. The major reasons discussed include intensive grazing, drought, fire suppression, and climate change. Although historical accounts and photographs seemingly suggest rapid spread of the species, quantitative data are very limited. To examine spatial dynamics of this shrub invasion, we developed a stage-structured reaction-diffusion model with competition terms. The model was formulated by known ecology of creosotebush and grass species and parameterized by published data and some expert knowledge. Periodic droughts hit SW every ~50 years, and the shrub is known to be benefited by reduced competition under harsh environment for grass. We incorporated the periodic disturbance by introducing a pulse function in the model. We focused on investigating whether creosotebush literally invaded novel habitat or existed already 150 years ago and rapidly increased in density in central NM. We used hypothetical simple landscapes (“flat” or smooth gradient) and a realistic 2D landscape of NM to run simulations. For simple landscapes, we obtained traveling wave like solutions with a constant propagation speed. Creosotebush almost completely replace grass as they progress. The density of shrub saplings is highest just behind the invasion front, consistent with literature. When smooth gradients are introduced, a long range of coexistence of shrub and grass is achieved. When initial populations are introduced, the propagation speed was much greater, closer to what actually happened on the landscape. The results suggest that some small founding populations of creosotebush probably existed already, serving as invasion sources and that long-distance dispersal needs to be considered.

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