Functional Robustness of Food Webs: A Dynamic Biomass Framework with Vital Species Sets and Cluster Influence
1. Species loss can erode food-web functioning not only through secondary extinctions, but also through biomass redistribution, weakened energy pathways, and threshold-like functional collapse. Common topology-, connectivity-, and extinction-based robustness metrics provide valuable summaries of structural disassembly and cascade risk, but they are not designed to quantify continuous biomass retention, collapse-associated species sets, and non-additive group-level effects within a single dynamic framework. 2. We develop a dynamic biomass-based framework for assessing food-web robustness under progressive species removal. The framework introduces Dynamic Area-based Robustness (DAR), which quantifies the weighted area between slow- and fast-collapse reference trajectories of total ecosystem biomass retention. Building on these trajectories, we operationally define the Minimal Vital Species Set (MVSS) as the smallest fast-collapse-prefix species set whose removal first drives biomass below a predefined functional-collapse threshold. We further propose Cluster Influence (CI), which compares the biomass effect of simultaneous group removal with the mean effect of removing the same species individually. 3. We evaluated the framework using 120 niche-model virtual food webs spanning controlled gradients of species richness and connectance, and further demonstrated its applicability on 16 empirical stream food webs. We compared DAR with AUC- and secondary-extinction-based robustness metrics and assessed the sensitivity of DAR, MVSS, and CI to key bioenergetic parameters and parameter uncertainty. 4. DAR captured biomass-based robustness patterns that were only partly aligned with structural and extinction-based metrics, indicating that dynamic functional degradation provides complementary information. In virtual food webs, MVSS subsets were strongly enriched in basal species or basal resource nodes, and smaller MVSS proportions were associated with stronger positive CI under fast-collapse trajectories. Together, DAR, MVSS, and CI provide a reproducible framework for linking food-web structure, biomass dynamics, collapse thresholds, and non-additive species-set effects, offering a practical tool for dynamic robustness assessment in theoretical and empirical food webs.