Appendix B. Patch census procedure and the analyses of planthopper distributions in nature.

Patch census procedure and the analyses of planthopper distributions in nature

Appendix A. A description of the sampling methods used to quantify the planthopper's within-patch distribution.

A description of the sampling methods used to quantify the planthopper's within-patch distribution

Appendix F. Results from backward stepwise logistic regression analyses for the effect of cursorial, sit-and-wait and web-building spiders, planthopper density, three landscape variables, and the interaction between patch size and the density of each spider guild on the likelihood of a local planthopper extinction.

Results from backward stepwise logistic regression analyses for the effect of cursorial, sit-and-wait and web-building spiders, planthopper density, three landscape variables, and the interaction between patch size and the density of each spider guild on the likelihood of a local planthopper extinction

Appendix A. Statistical procedures for the among-patch survey of the distribution of spiders and planthoppers and the spider impact experiment.

Statistical procedures for the among-patch survey of the distribution of spiders and planthoppers and the spider impact experiment

Appendix D. Results from a backward stepwise regression analysis for the effect of spider guild density, landscape factors, spider guild density × patch size interaction, and planthopper density at t–1 on current planthopper density.

Results from a backward stepwise regression analysis for the effect of spider guild density, landscape factors, spider guild density × patch size interaction, and planthopper density at t–1 on current planthopper density

Appendix B. Spider guild densities in the three-generation survey and spider impact experiment.

Spider guild densities in the three-generation survey and spider impact experiment

Model code for invasion with spatially varying Allee effects

These files provide the model code in R for exploration of patterns of invasion with spatially varying Allee effects. There are separate files for each landscape type (constant, random, coarse patches, fine patches, gradient). Filenames ending in "detdisp" are the main models discussed in the manuscript, filenames ending in "stoch" are for the alternate model with demographic stochasticity

Appendix E. The correlation (and associated P value) between planthopper and spider density in each of three planthopper generations.

The correlation (and associated P value) between planthopper and spider density in each of three planthopper generations

Appendix C. Descriptive statistics for temporal variation in the synchrony in weather measurements from regions throughout the United States.

Descriptive statistics for temporal variation in the synchrony in weather measurements from regions throughout the United States

Appendix B. Details of the univariate and bivariate wavelet analyses.

Details of the univariate and bivariate wavelet analyses