Robustness of empirical food webs with varying consumer's sensitivities to loss of resources

•We study the robustness to random node loss of 10 food webs with empirical weightings.•We use extinction threshold v as an energetic criterion to define species extinction.•Robustness of food webs increases linearly with v.•Among food webs, sensitivity of robustness to v varies with complexity.

Food web responses to species loss have been mostly studied in binary food webs, thus without accounting for the amount of energy transferred in consumer-resource interactions.We introduce an energetic criterion, called extinction threshold, for which a species goes secondarily extinct when a certain fraction of its incoming energy is lost. We study the robustness to random node loss of 10 food webs based on empirically-derived weightings. We use different extinction scenarios (random removal and from most- to least-connected species), and we simulate 105 replicates for each extinction threshold to account for stochasticity of extinction dynamics.We quantified robustness on the basis of how many additional species (i.e. secondary extinctions) were lost after the direct removal of species (i.e. primary extinctions). For all food webs, the expected robustness linearly decreases with extinction threshold, although a large variance in robustness is observed. The sensitivity of robustness to variations in extinction threshold increases with food web species richness and quantitative unweighted link density, while we observed a nonlinear relationship when the predictor is food web connectance and no relationship with the proportion of autotrophs.