The two-dimensional case for invasion by a species into a resource space occupied by two resident species is considered. Numerical solutions for the condition for invasion were obtained, and invisibility spaces constructed for certain sets of values for the parameters of the system. The configuration of the invisibility spaces varies for different values of k/K (the invader-to-resident ratio of carrying capacities) and dx (one-half the inter-resident distance). In general, stable three-species systems result when invasion occurs somewhere between the two residents. Penetration by the invader between the residents can effectively occur if (a) the residents are far enough apart or (b) the residents are very close together and the invader's carrying capacity is equal to or larger than the common carrying capacity of the residents. That the three-species systems formed as a consequence of invasion are stable systems follows from the requirement that all three species satisfy the increase when-rare criterion. ...