Extinction models of robustness for weighted ecological networks

Abstract

O_LIAnalysis of ecological networks is a valuable approach to understanding the vulnerability of systems to environmental change. The tolerance of ecological networks to co-extinctions, resulting from sequences of primary extinctions, is a widely-used tool for modelling network robustness. Previously, these extinction models have been developed for and applied mostly to binary networks and recently used to predict cascades of co-extinctions in plant-pollinator networks. There is a need for robustness models that can make the most of the weighted data available and most importantly there is a need to understand how the structure of a network affects its robustness.\nC_LIO_LIHere, we developed a framework of extinction models for bipartite ecological networks (specifically plant-pollinator networks). In previous models co-extinctions occurred when nodes lost all their links, but by relaxing this rule (according to a set threshold) our models can be applied to binary and weighted networks, and can permit structurally correlated extinctions, i.e. the potential for avalanches of extinctions. We tested how the average and the range of robustness values is impacted by network structure and the impact of structurally-correlated extinctions sampling non-uniformly from the distribution of random extinction sequences.\nC_LIO_LIWe found that the way that structurally-correlated extinctions are modelled impacts the results; our two ecologically-plausible models produce opposing effects which shows the importance of understanding the model. We found that when applying the models to networks with weighted interactions, the effects are amplified and the variation in robustness increases. Variation in robustness is a key feature of these extinction models and is driven by the structural heterogeneity (i.e. the skewness of the degree distribution) of nodes (specifically, plant nodes) in the network.\nC_LIO_LIOur new framework of models enables us to calculate robustness with weighted, as well as binary, bipartite networks, and to make direct comparisons between models and between networks. This allows us to differentiate effects of the model and of the data (network structure) which is vital for those making ecological inferences from robustness models. The models can be applied to mutualistic and antagonistic networks, and can be extended to food webs.\nC_LI