  We compute the typical number of equilibria of the Generalized Lotka-Volterra
equations describing species-rich ecosystems with random, non-reciprocal
interactions using the replicated Kac-Rice method. We characterize the
multiple-equilibria phase by determining the average abundance and
similaritybetween equilibria as a function of their diversity (i.e. of the
number of coexisting species) and of the variability of the interactions. We
show that linearly unstable equilibria are dominant, and that the typical
number of equilibria differs with respect to the average number.
