Pursuit-evasion predator-prey waves in two spatial dimensions

We consider a spatially distributed population dynamics model with excitable predator-prey dynamics, where species propagate in space due to their taxis with respect to each other's gradient in addition to, or instead of, their diffusive spread. Earlier, we have described new phenomena in this model in one spatial dimension, not found in analogous systems without taxis: reflecting and self-splitting waves. Here we identify new phenomena in two spatial dimensions: unusual patterns of meander of spirals, partial reflection of waves, swelling wavetips, attachment of free wave ends to wave backs, and as a result, a novel mechanism of self-supporting complicated spatio-temporal activity, unknown in reaction-diffusion population models.Comment: 15 pages, 15 figures, submitted to Chao

The Community Ecology of Herbivore Regulation in an Agroecosystem: Lessons from Complex Systems

AbstractWhether an ecological community is controlled from above or below remains a popular framework that continues generating interesting research questions and takes on especially important meaning in agroecosystems. We describe the regulation from above of three coffee herbivores, a leaf herbivore (the green coffee scale, Coccus viridis), a seed predator (the coffee berry borer, Hypothenemus hampei), and a plant pathogen (the coffee rust disease, caused by Hemelia vastatrix) by various natural enemies, emphasizing the remarkable complexity involved. We emphasize the intersection of this classical question of ecology with the burgeoning field of complex systems, including references to chaos, critical transitions, hysteresis, basin or boundary collision, and spatial self-organization, all aimed at the applied question of pest control in the coffee agroecosystem