This is the first of two papers where we discuss the limits imposed by
competition to the biodiversity of species communities. In this first paper we
study the coexistence of competing species at the fixed point of population
dynamic equations. For many simple models, this imposes a limit on the width of
the productivity distribution, which is more severe the more diverse the
ecosystem is (Chesson, 1994). Here we review and generalize this analysis,
beyond the ``mean-field''-like approximation of the competition matrix used in
previous works, and extend it to structured food webs. In all cases analysed,
we obtain qualitatively similar relations between biodiversity and competition:
the narrower the productivity distribution is, the more species can stably
coexist. We discuss how this result, considered together with environmental
fluctuations, limits the maximal biodiversity that a trophic level can host
