Species Packing in Two Dimensions

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Abstract
The 2-dimensional case for invasion by a species into a resource space occupied by 2 resident species is considered. Numerical solutions for the condition for invasion were obtained, and invasibility spaces constructed for certain sets of values for the parameters of the system. The configuration of the invasibility spaces varies for different values of k/K (the invader-to-resident ratio of carrying capacities) and dx (1/2 the inter-resident distance). In general, stable 3 spp. systems result when invasion occurs somewhere between the 2 residents. Penetration by the invader between the residents can effectively occur if the residents are far enough apart or 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 3 spp. systems formed as a consequence of invasion are stable systems follows from the requirement that all 3 spp. satisfy the increase-when-rare criterion. It is argued that, for the cases considered here, this criterion is sufficient to insure stability of the system. It is also shown that the increase in dimensionality (from 1 to 2) of the resource space allows species to achieve configurations in which they are closer together than is possible when only 1 resource dimension is available.

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