Cross-scale persistence analysis in mutualistic networks unifies extinction thresholds and invasibility

Cross-scale integration remains a persistent challenge in ecology. Mechanistic network models have advanced this integration by linking individual behavior to community dynamics. Their complexity, however, often limits exploration to numerical simulations, which tend to be insufficient for fully unveiling the fundamental rules governing system behavior. Extracting these rules requires moving beyond numerical observation to establish exact, analytical constraints. Here, a complete mathematical analysis of a mechanistically detailed plant-pollinator model is presented. This cross-scale analysis decouples transient and equilibrium dynamics, proving that pollination strictly gates plant persistence while recruitment competition caps equilibrium abundance. The precise behavioral mechanisms scaling up to determine network stability are determined: nestedness stabilizes communities by generating floral reward gradients that guide adaptive foraging, whereas connectance destabilizes by eroding these rescue pathways. Additionally, native community persistence and biological invasions are conceptually unified; a single, multi-scale reward threshold (R*) is shown to govern both native survival and alien establishment. These analytical derivations are distilled into conceptual frameworks and visual summaries accessible for empiricists interested in theory and conceptual unification. By translating numerical observations into rigorous, trait-grounded proofs, this analysis demonstrates that complex, cross-scale networks are tractable, revealing the precise conditions under which communities assemble, persist, and collapse.