  The random Lotka-Volterra model is widely used to describe the dynamical and
thermodynamic features of ecological communities. In this work, we consider
random symmetric interactions between species and analyze the strongly
competitive interaction case. We investigate different scalings for the
distribution of the interactions with the number of species and try to bridge
the gap with previous works. Our results show two different behaviors for the
mean abundance at zero and finite temperature respectively, with a continuous
crossover between the two. We confirm and extend previous results obtained for
weak interactions: at zero temperature, even in the strong competitive
interaction limit, the system is in a multiple-equilibria phase, whereas at
finite temperature only a unique stable equilibrium can exist. Finally, we
establish the qualitative phase diagrams in both cases and compare the two
species abundance distributions.
