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Biological invasions are increasingly being considered important spatial processes that drive global changes, threatening biodiversity, regional economies, and ecosystem functions. A unifying conceptual model of the invasion dynamics could serve as a useful tool for comparison and classification of invasion processes involving different species across large geographic ranges. By dividing these geographic ranges that are subject to invasions into discrete spatial units, we here conceptualize the invasion process as the transition from pristine to invaded spatial units. We use California cities as the spatial units and a long-term database of invasive tropical tephritids to characterize the invasion patterns. A new life-table method based on insect demography, including the progression model of invasion stage transition and the species-specific partitioning model of multispecies invasions, was developed to analyze the invasion patterns. The progression model allows us to estimate the probability and rate of transition for individual cities from pristine to infested stages and subsequently differentiate the first year of detection from detection recurrences. Importantly, we show that the interval of invasive tephritid recurrence in a city declines with increasing invasion stages of the city. The species-specific partitioning model revealed profound differences in invasion outcome depending on which tephritid species was first detected (and then locally eradicated) in the early stage of invasion. Taken together, we discuss how these two life-table invasion models can cast new light on existing invasion concepts; in particular, on formulating invasion dynamics as the state transition of cities and partitioning species-specific roles during multispecies invasions. These models provide a new set of tools for predicting the spatiotemporal progression of invasion and providing early warnings of recurrent invasions for efficient management.