Ecological networks of viable species with degree-dependent interaction
The generalized Lotka-Volterra (GLV) framework, recently advanced by dynamical mean-field theory, enables the systematic analysis of large ecological networks. When combined with structured interaction topologies, previous studies have shown that the viability of species, defined by having a positive stationary abundance, depends on the number of their interacting neighbors or the "degree." While such model studies usually assume that interaction strengths follow an identical distribution across all connected pairs, real ecological communities often exhibit correlations between interaction strength and a species' degree. To capture this overlooked feature, we introduce degree-dependent interaction strengths into a generalized random LV model. We identify two distinct regimes: a hub-favored phase, where highly connected species survive preferentially, and a hub-suppressed phase, where they face higher extinction risks. We analytically derive the phase boundary where these degree-dependent strengths precisely balance the connectivity effect, leaving all species equally susceptible. Crucially, these phases induce opposing shifts in the degree-degree correlation or "assortativity" of the network of viable species: the hub-favored phase enhances disassortativity by selectively removing the interactions between low-degree species, whereas the hub-suppressed phase reduces it as the interactions involving hub species tend to disappear. Ultimately, our findings demonstrate that degree-dependent interactions are a fundamental mechanism not only for shaping species survival, but for naturally reproducing the wide range of assortativity values observed in real ecological networks.