  Understanding the behaviors of ecological systems is challenging given their
multi-faceted complexity. To proceed, theoretical models such as Lotka-Volterra
dynamics with random interactions have been investigated by the dynamical
mean-field theory to provide insights into underlying principles such as how
biodiversity and stability depend on the randomness in interaction strength.
Yet the fully-connected structure assumed in these previous studies is not
realistic as revealed by a vast amount of empirical data. We derive a generic
formula for the abundance distribution under an arbitrary distribution of
degree, the number of interacting neighbors, which leads to degree-dependent
abundance patterns of species. Notably, in contrast to the well-mixed system,
the number of surviving species can be reduced as the community becomes
cooperative in heterogeneous interaction structures. Our study, therefore,
demonstrates that properly taking into account heterogeneity in the
interspecific interaction structure is indispensable to understanding the
diversity in large ecosystems, and our general theoretical framework can apply
to a much wider range of interacting many-body systems.
