Stability of biological cooperation against the invasion of selfish strategies is a major evolutionary question that has remained largely unsolved. In the parthenogenetic ant Pristomyrmex punctatus, all nestmates are involved in both reproduction and altruistic behavior such as nursing and foraging. Socially parasitic cheaters have been found in some field populations of this species, and are known to have detrimental effect on the whole colony. Molecular data suggest that cheaters are genetically distinct from altruists and that these two have coexisted for relatively a long period. To investigate conditions for this coexistence, we developed a spatio-temporal dynamics model for altruists and cheaters in this species. We applied the colony-based lattice model, in which a colony can exist in each lattice site. Altruists increase logistically in number within a colony, and reproduction at the colony-level occurs solely by fission. We assumed that an invasion of a cheater always leads the colony to extinction. Cheaters can coexist with altruists in the following conditions: (1) when they invade other colonies, (2) when the invasion is spatially restricted, and, somewhat paradoxically, (3) when they are far more fecund than altruists, i.e. behaving extremely selfishly. This coexistence can be explained in the context of meta-population dynamics theory. Vacant sites formed by rapid extinction of parasitized colonies are reoccupied by non-parasitized colonies, accelerating coexistence through "local extinction & recolonization process" in the spatially structured population.