  Niche and neutral theory are two prevailing, yet much debated, ideas in
ecology proposed to explain the patterns of biodiversity. Whereas niche theory
emphasizes selective differences between species and interspecific interactions
in shaping the community, neutral theory supposes functional equivalence
between species and points to stochasticity as the primary driver of ecological
dynamics. In this work, we draw a bridge between these two opposing theories.
Starting from a Lotka-Volterra (LV) model with demographic noise and random
symmetric interactions, we analytically derive the stationary population
statistics and species abundance distribution (SAD). Using these results, we
demonstrate that the model can exhibit three classes of SADs commonly found in
niche and neutral theories and found conditions that allow an ecosystem to
transition between these various regimes. Thus, we reconcile how neutral-like
statistics may arise from a diverse community with niche differentiation.
