We developed a simulation model of monogyne red imported fire ant,Solenopsis invicta, populations that operates by competitive interactions of individual colony territories. This model describes six major aspects of colony lite history: nest founding, brood raiding, territory expansion, queen death, possible requeening, and colony death. Individual colony territories are represented by rectangles, whose sides change independently depending upon the presence and size of neighboring colonies. Growing colonies try to occupy free space, while retaining square territorial dimensions whenever possible. The growth of fire ant populations in the model compared well with available field data. The model predicted that competitive exclusion caused by territorial interactions should occur when areas reach 70–90% territory coverage. Several computer experiments were conducted with the model to examine the importance of colony growth rate, brood raiding activity, and other parameters on the relative success of sequentially founding colony cohorts. A 1-wk advantage in founding generally increased the long-term survival of young colonies by 40–80%. We also examined the factors affecting average coverage of an area by colony territories. Maximum coverage was achieved under a continuous influx of 50 queens/(ha·wk) or a single settlement of 1000 queens/ha; both values were much less than actual magnitudes of queen influx observed in the field.