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Understanding factors controlling the introduction and spread of species is crucial to improving the management of both natural populations and introduced species. The zebra mussel, Dreissena polymorpha, is considered the most aggressive freshwater invader in the Northern Hemisphere, and is a convenient model system for invasion biology, offering one of the best aquatic examples for examining the invasion process. We used data on 553 of the 1040 glacial lakes in the Republic of Belarus that were examined for the presence of zebra mussels. We used these data to build, test, and construct modified models to predict the spread of this invader, including selection of important parameters that could limit the spread of this invader. In spite of 200 years of continuous invasion, by 1996, zebra mussels were found in only 16.8% of all lakes studied. Of those lakes without zebra mussels in 1996, 66% were predicted to be susceptible to invasion by zebra mussels in the future, and 33% were predicted to be immune to successful invasion due to their water chemistry. Eighty lakes free of zebra mussels in 1996 were reexamined from 1997 to 2008. Of these, zebra mussels successfully invaded an additional 31 lakes, all of which were classified initially as suitable for zebra mussels; none of the lakes previously classified as unsuitable were invaded. We used the Random Forests classification algorithm with 16 environmental variables to determine the most important factors that differed between invaded lakes and those lakes suitable for invasion that have not yet been invaded. Distance to the nearest infested lakes was found to be the most important variable, followed by the lake area, color, average depth, and concentration of chloride, magnesium, and bicarbonate. This study provides a useful approach for predicting the spread of an invader across a landscape with variable habitat suitability that can be applied to a variety of species and systems. [ABSTRACT FROM AUTHOR]