The Community Matrix and the Number of Species in a Community

In this paper I am concerned with the number of species that will be held in stable equilibrium in a community of competing organisms, using the general form of the Lotka-Volterra competition equations for m species. Defining Ki as the saturation density for the ith species and αij as the competition coefficient between species i and j, and Ni as the equilibrium density of species i, the number of species will be determined by N̄, K̄, $$overline{alpha}$$ , var (K), the covariances among the α's, and the covariance between α and N. In particular, the number of species increases as K̄ increases but as N̄, $$overline{alpha}$$ , cov (α), cov (α,N) and variance of K decrease.