  We investigate the replicator dynamics with "sparse" symmetric interactions
which represent specialist-specialist interactions in ecological communities.
By considering a large self interaction $u$, we conduct a perturbative
expansion which manifests that the nature of the interactions has a direct
impact on the species abundance distribution. The central results are all
species coexistence in a realistic range of the model parameters and that a
certain discrete nature of the interactions induces multiple peaks in the
species abundance distribution, providing the possibility of theoretically
explaining multiple peaks observed in various field studies. To get more
quantitative information, we also construct a non-perturbative theory which
becomes exact on tree-like networks if all the species coexist, providing exact
critical values of $u$ below which extinct species emerge. Numerical
simulations in various different situations are conducted and they clarify the
robustness of the presented mechanism of all species coexistence and multiple
peaks in the species abundance distributions.
