Appendix S1 Analysis of invasion data with GAMs.

Appendix S2 Analysis of area change: detailed methods.

Appendix S3 Model of per capita population growth rate.

Figure S1 Distribution of super-polygon areas (a) and residual densities (b) over the 12 years of data.

Figure S2 Comparison of models for population persistence. (a) AIC. (b) Proportion of deviance explained.

Figure S3 Contour plots for the effect of latitude and longitude on population persistence and partial dependence plots for the effects of area and residual density in the 12 pairs of years.

Figure S4 Relationship between population area and rate of area change for each year of analysis.

Figure S5 Relationship between population density and female mating probability from simulated data and fitted mathematical function.

Figure S6 Relationship between critical radius and density (a), survival rate (b), fecundity (c) and dispersal distance (d).

Table S1 Number of seed polygons and superpolygons for each year of analysis.

Table S2 Parameter values and range for the mechanistic model of growth rate.

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