Abstract :
It is demonstrated that a Kolmogorov-type competition model featuring species allocation
and gain functions can possess multiple coexistence states. Two examples are constructed:
one in which the two competing species possess rectangular allocation functions but
distinct gain functions, and the other in which one species has a rectangular allocation
function, the second species has a bi-rectangular allocation function, and the two species
share a common gain function. In both examples, it is shown that the species nullclines
may intersect multiple times within the interior of the first quadrant, thus creating both
locally stable and unstable equilibrium points. These results have important applications in
the study of plant competition for sunlight, in which the allocation functions describe the
vertical placement of leaves for two competing species, and the gain functions represent
rates of photosynthesis performed by leaves at different heights when shaded by overlying
leaves belonging to either species.
