In order to set priorities in management of costly and ecosystem-damaging species, policymakers and managers need accurate predictions not only about where a specific invader may establish but also about its potential abundance at different geographical scales. This is because density or biomass per unit area of an invasive species is a key predictor of the magnitude of environmental and economic impact in the invaded habitat. Here, we present a physiologically based demographic model describing and explaining the population dynamics of a widespread freshwater invader, the golden apple snail Pomacea canaliculata, which is causing severe environmental and economic impacts in invaded wetlands and rice fields in Southeastern Asia and has also been introduced to North America and Europe. The model is based on bio-demographic functions for mortality, development and fecundity rates that are driven by water temperature for the aquatic stages (juveniles and adults) and by air temperature for the aerial egg masses. Our model has been validated against data on the current distribution in South America and Japan, and produced consistent and realistic patterns of reproduction, growth, maturation and mortality under different scenarios in accordance to what is known from real P. canaliculata populations in different regions and climates. The model further shows that P. canaliculata will use two different reproductive strategies (semelparity and iteroparity) within the potential area of establishment, a plasticity that may explain the high invasiveness of this species across a wide range of habitats with different climates. Our results also suggest that densities, and thus the magnitude of environmental and agricultural damage, will be largely different in locations with distinct climatic regimes within the potential area of establishment. We suggest that physiologically based demographic modelling of invasive species will become a valuable tool for invasive species managers.