Waves of larch budmoth outbreaks in the European alps.

Spatially extended population models predict complex spatiotemporal patterns, such as spiral waves and spatial chaos, as a result of the reaction-diffusion dynamics that arise from trophic interactions. However, examples of such patterns in ecological systems are scarce. We develop a quantitative technique to demonstrate the existence of waves in Central European larch budmoth (Zeiraphera diniana Gn.) outbreaks. We show that these waves travel toward the northeast-east at 210 kilometers per year. A theoretical model involving a moth-enemy interaction predicts directional waves, but only if dispersal is directionally biased or habitat productivity varies across the landscape. Our study confirms that nonlinear ecological interactions can lead to complex spatial dynamics at a regional scale.