The volterra competition equations with resource - Independent growth coefficients and discussion on their biological and biophysical implications

Abstract

Analysis of the biophysical conditions for a correct application of the Volterra Competition Equations with resource-independent coefficients reveals the following: The traditional, mathematical formalism with the two equations representing two straight lines at the condition of zero growth applies. As a directly resource-limited situation does not permit for stable equilibrium (One-line or K-system, Walker [18]; Ceiling model, Pollard [11]), the combined equilibrium density represented by the intersect of the two lines (Two-line system or S-system; Equilibrium model; lit. ref. see above) is by necessity smaller than the carrying capacity of shared resources would permit. The physical determinant is density in space as a result of behavioural/physiological interaction between organisms. The traditional inequality conditions then mean that coexistence of species sharing the same space is possible provided density-dependent reduction of growth relative to the intrinsic growth rate is more effective within species than between species. The distance of the intersect from the line linking the specific population densities of single species on the axes is a measure for the overlap in the use of space by the two species; thus, overlap of the spatial niche results in stability. This biophysical system allows for coexistence of species in identical space/resource niches. Food-jealous behaviour is a direct function of density in space; it is only indirectly and inconsistently influenced by resource availability. © 1984 Martinus Nijhoff/Dr W. Junk Publishers.