Predicted number of beetles established as a function of propagule size and traveling time. Plots present the number of individuals of Harmonia axyridis (left column) and Cheilomenes lunata (right column) that would survive the transport and establishment stages in a cold b medium and c warm environments (see assumptions, and starvation and fitness data collection in text). One thousand repeats were used and starting propagule size (1 to 100) and travel time (1 to 20 days) were randomly selected for each run. Outcomes of the iterations are shown as red points. Surface regression planes were obtained using locally estimated scatterplot smoothi.