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The polyphagous Asian vinegar fly Drosophila suzukii (spotted wing Drosophila) is a native of Eastern and Southeastern Asia. It emerged as an important invasive insect pest of berries and stone fruits in the Americas and Europe beginning in 2008. Species distribution models are commonly used for analyzing the extant and potential range expansion of invasive species. Previous modeling efforts for D. suzukii include a degree-day model, a MaxEnt ecological niche model, a demographic model incorporating the effects of temperature, and a preliminary mechanistic physiologically-based demographic model (PBDM). In the present analysis, we refine the PBDM for D. suzukii based on biological data reported in the literature. The PBDM is used to assess the effects of temperature and relative humidity from a recently published global climate dataset (AgMERRA) on the prospective geographic distribution and relative abundance of the pest in the USA and Mexico, and in Europe and the Mediterranean Basin. Our focus is on areas of recent invasion and of predicted higher invasiveness in these areas. Although the species is native to Asia and is of putative temperate origins, it has established in subtropical to north temperate zones worldwide where it infests a wide range of wild and domesticated berries and stone fruits. The model captures the observed phenology of D. suzukii at specific locations, as well as the potential geographic distribution and relative favorability across larger regions. The main limiting factor is cold winter temperature in northern areas, though high temperatures and low relative humidity may be limiting in arid areas. The effect of greater cold tolerance in winter morph adults is explored.