Complexity promotes stability in mutualistic networks through weaker mutualistic dependencies: Insights from...

Mutualistic networks provide essential contributions to long-term ecosystem functioning and food security, but Anthropocene stressors continue to alter their structure and size. Previous theoretical approaches produce conflicting predictions for how network features influence dynamical stability, which is the ability to return to the original state after a disturbance. The main methods, which are random matrix models and conventional differential equation models, face certain limitations, including difficulties in incorporating some biological details or explicit parameterization. An alternative approach is given by Generalized Modelling, which combines both high efficiency with high biological realism, but has not been applied to plant-animal mutualistic networks prior to this study. Here, we develop a Generalized Model for mutualism that allows the mathematically rigorous and highly efficient analysis of dynamical stability for many network replicates ( $\sim {10}^5$ per data point). The model incorporates important biological mechanisms that are known to influence stability behaviour, such as animal competition for limited plant resources and saturating mutualistic benefits, without the need for explicit parameterization. Using simulated network structures we find increasing dynamical stability with increasing complexity as measured by the product of species richness and connectance. We are able to explain this effect mechanistically: While mutualistic interactions do represent destabilizing positive feedbacks, the strengths of those feedbacks weaken with increasing complexity because mutualistic dependencies as given by the Jacobian matrix elements in the off-diagonal blocks decrease. We further show that the effect of nestedness on the dynamical stability of simulated networks is negligible compared to the effect of connectance and species richness. Additionally, we find similar relationships between network features and dynamical stability for 160 empirical networks as an input for our model, highlighting the robustness of our findings. As Anthropocene stressors lead to species and interaction loss, our model results predict a corresponding loss in dynamical stability if network complexity is decreased, highlighting the urgency of conservation strategies that preserve network complexity.