  Complementarity among species with different traits is one of the basic
processes affecting biodiversity, defined as the number of species in the
ecosystem. We present here a soluble model ecosystem in which the species are
characterized by binary traits and their pairwise interactions follow a
complementarity principle. Manipulation of the species composition, and so the
study of its effects on the species diversity is achieved through the
introduction of a bias parameter favoring one of the traits. Using statistical
mechanics tools we find explicit expressions for the allowed values of the
equilibrium species concentrations in terms of the control parameters of the
model.
