Supplementary material:
Bjørnstad, O.N. , M. Peltonen, A.M. Liebhold, W.Baltensweiler. 2002. Waves of Larch Budmoth Outbreaks in the European Alps. Science 298: 1020-1023.

Figure S1. Movie of historical defoliation caused by the Larch Budmoth, Zeiraphera diniana in the European Alps, 1961-1998. Inset graph shows the proportion of all areas that were defoliated in each year. Defoliation polygons were aggregated to form raster estimates of the proportion of 20 x 20 km grid cells that were defoliated. Bubbles are proportional to the amount of defoliation in each cell in each year. Visual inspection of the movie suggests the existence of repeated outbreak waves moving from west to east.





Figure S2. Time series of larch budmoth larval density (average of 5 permanent sites) and defoliation (all Alps). Derived from data in Baltensweiler & Rubli (1). This figure shows that defoliation time series very closely track time series in actual population density and thus serves as an adequate proxy to population density.

Model Supplement

Figure S3. Animations of the behaviour of the coupled map lattice models (eqns 2-4 in the main text) illustrate the possible types of spatiotemporal dynamics (skecthed in fig. 3 in the main text) with (A) non-directional (isotropic) dispersal and (B) in the presence of advective dispersal. Click on links to see sample web-movies. Y-axis is parasitoid dispersal rates, X-axes

  (A) Isotropic dispersal        (B) 30% advection

[phase-locking] [radial waves] [spatial chaos] [directional waves] [anti-directional waves] [partial phase-locking]

Figure S4. Animations of the behaviour of the coupled map lattice models (eqns 2-4 in the main text) illustrate the possible types of spatiotemporal dynamics (skecthed in fig. 3 in the main text) in the presence of advective dispersal or a (e-w) gradient in habitat quality:
 

      Gradient

[phase-locking] [directional waves]

Literature cited:
1.    W. Baltensweiler, D. Rubli, Forest Snow and Landscape Research 74, 1-153 (1999)