11 Abstract Native to Asia, Harmonia axyridis (Pallas) (Coleoptera: Coccinellidae) is 12 considered an invasive alien ladybird in Europe and North America, where it was widely 13 introduced as a biological control agent of aphids and coccids. In Europe, H. axyridis was 14 sold by various biological control companies from 1995 in France, Belgium and the 15 Netherlands, and was also intentionally released in at least nine other countries. It has 16 spread very rapidly, particularly since 2002, and is now regarded as established in thirteen 17 European countries. The established range extends from Denmark in the north to southern

11 Abstract Native to Asia, Harmonia axyridis (Pallas) (Coleoptera: Coccinellidae) is 12 considered an invasive alien ladybird in Europe and North America, where it was widely 13 introduced as a biological control agent of aphids and coccids. In Europe, H. axyridis was 14 sold by various biological control companies from 1995 in France, Belgium and the 15 Netherlands, and was also intentionally released in at least nine other countries. It has 16 spread very rapidly, particularly since 2002, and is now regarded as established in thirteen 17 European countries. The established range extends from Denmark in the north to southern

Species distribution models (SDM) have often been used to predict the potential ranges of introduced species and prioritize management strategies. However, this approach assumes equilibrium between occurrences and environmental gradients, an assumption which is violated during the invasion process, where many suitable sites are empty because the species has not yet reached them. Here we considered the invasive ladybird Harmonia axyridis as a case study to show the benefits of using a dynamic colonization-extinction model that does not assume equilibrium. We used a multi-year occupancy model incorporating environmental, anthropogenic and neighborhood effects, to identify factors that explained spreading variation of this species in France from 2004, when only a few occupied sites were detected, to 2011. We found that anthropogenic factors (urbanization, agriculture, vineyards, and presence/absence of highways) explained more variation in the diffusion process than environmental factors (winter and summer temperatures, wind-speed, and rainfall). The surface of urbanization was the major anthropogenic factor increasing the probability of colonization. The average summer temperature was the main environmental factor affecting colonization, with a negative effect when high or low. The neighborhood effect revealed that colonization was mostly influenced by contributions coming from a radius of 24 km around the focal cell. The contribution of neighborhood decreases over time, suggesting that H. axyridis is reaching its equilibrium in France. This is confirmed by the small discrepancy observed between the performance of our approach and a SDM approach when predicting a single year occupancy pattern at the end of the study period. Our approach has the advantage of explicitly modelling the state of the biological system during the spatial expansion and identifying colonization constraints. This allows managers to explore the effect of different actions on the system at key moments of the invasion process, hence providing a powerful approach to prioritize management strategies