Globally, species ranges are shifting in response to climate change. For black mangrove (Avicennia germinans), fewer severe freeze events in a warming climate facilitate poleward range expansion into temperate coastal salt marshes, however propagules that disperse into marshes encounter biotic interactions (e.g., predation) that affect their survival and subsequent forest development. To better understand the relative roles of climate, predation, and propagule dispersal in shaping A. germinans range expansion, we developed a stage-based population model that tested forest stand establishment and survival under differing scenarios of freeze regime, predation pressure, and propagule dispersal. Predation parameters were developed from a field experiment that tested propagule density-predation intensity relationships for purple marsh crab (Sesarma reticulatum), which showed proportional propagule consumption decreased with increased propagule density. Model outcomes demonstrated all measures of mangrove stand development and regeneration decreased with increased freeze and predation intensities, modulated by propagule dispersal density and frequency. Regenerating stands were more likely to recover from freezes under a reduced freeze regime compared to a historical freeze regime, but moderate and high predation intensities hindered stand development and recovery across freeze regimes. Maintaining a regenerating stand generally required recurring dispersal events. While several studies have investigated the individual effects of freezes, predation pressure, and dispersal on mangrove ranges, our model is the first effort of which we are aware that quantifies the combined effects of all three controls. The model can thus serve as a tool for understanding patterns of A. germinans range expansion in the Big Bend and other regions under future warming.