A Kolmogorov-type Competition Model with Finitely Supported Allocation Profiles and its Applications to Plant Competition for Sunlight Dedicated to Avner Friedman on the occasion of his 75th birthday

A Kolmogorov-type competition model featuring species allocation profiles, gain functions, and cost parameters is examined. For plant species that compete for sunlight according to the Canopy Partitioning Model (R.R. Vance and A.L. Nevai, J. Theor. Biol. 245 (2007) 210–219), the allocation profiles describe vertical leaf placement, the gain functions represent rates of leaf photosynthesis at different heights, and the cost parameters signify the energetic expense of maintaining tall stems necessary for gaining a competitive advantage in the light gradient. The allocation profiles studied here, being supported on three alternating intervals, determine an “interior” species and an “exterior” species. It is shown that when the allocation profile of the interior species is singular (i.e., a Dirac-delta function) then either competitive exclusion or coexistence at a single globally attracting equilibrium point occurs. However, if the allocation profile of the interior species is piecewise continuous or multi-singular (i.e., a weighted sum of Dirac-delta functions) then multiple coexistence states may also occur. These results have important implications for big-leaf plants that compete for sunlight.