Spatially explicit models that simulate the evolution of dispersal strategies have not considered colonial organisms. Here we develop the colony-based lattice model, in which a colony, rather than an individual, occupies each lattice site. With this model we investigate why invasive tramp ant species usually lack long-distance dispersal, despite living in frequently disturbed habitats. We assume a new trade-off between the dispersal distance and the offspring colony size in the competition between two extreme strategies: the short-distance dispersal strategy (the S strategy, simulating budding or fission), which splits a colony in half with one of the two halves moving to a neighboring site, and the long-distance dispersal strategy (the L strategy, assuming colony-founding by winged queens), which allocates a minimal resource to an offspring colony that disperses to a randomly chosen site. Mortality of a colony is assumed to depend on the size; the L strategy suffers from costs due to small initial colony size (i.e., high mortality and late colony maturity). Disturbance causes additional mortality to both types of colonies and is controlled by disturbance frequency, p, and a stochastic parameter determining the spatial autocorrelation of disturbance, q. Simulations show that the S strategy is favored under frequent but spatially small-scale disturbances (high p and low q), whereas large-scale disturbances (low p and high q) favor the L strategy. When mortality is generally high or particularly high in small colonies, the S strategy tends to be advantageous. In contrast, when colony mortality is generally low, the L strategy is favored. We discuss the importance of colony size dynamics and the trade-off between colony size and the dispersal distance in the evolution of dispersal strategies in ants and other more or less sessile organisms.