Abstract
Analysis of ecological networks is a valuable approach to understanding the vulnerability of systems to disturbance. The tolerance of ecological networks to coextinctions, resulting from sequences of primary extinctions (here termed “knockout extinction models”, in contrast with other dynamic approaches), is a widely used tool for modeling network “robustness”. Currently, there is an emphasis to increase biological realism in these models, but less attention has been given to the effect of model choices and network structure on robustness measures. Here, we present a suite of knockout extinction models for bipartite ecological networks (specifically plant–pollinator networks) that can all be analyzed on the same terms, enabling us to test the effects of extinction rules, interaction weights, and network structure on robustness. We include two simple ecologically plausible models of propagating extinctions, one new and one adapted from existing models. All models can be used with weighted or binary interaction data. We found that the choice of extinction rules impacts robustness; our two propagating models produce opposing effects in all tests on observed plant–pollinator networks. Adding weights to the interactions tends to amplify the opposing effects and increase the variation in robustness. Variation in robustness is a key feature of these extinction models and is driven by the structural heterogeneity of nodes (specifically, the skewness of the plant degree distribution) in the network. Our analysis therefore reveals the mechanisms and fundamental network properties that drive observed trends in robustness.
Highlights
Network analysis has become an important tool for ecologists seeking to understand the vulnerability of ecosystems to environmental change
3.1 Varying the value of the threshold for secondary extinctions Median robustness Rm increases non-linearly with T, and the least robust of our three networks at low T becomes the most robust at high T (Fig. 3a). This appears to be an artefact of the relationship between T and Teff, the nodeaveraged effective threshold (Fig. 3b), because Rm increases linearly with Teff and the three networks are increasingly robust in order of increased connectance, as found by Dunne, Williams and Martinez (2002), at all values of Teff (Fig 3c)
3.2 Robustness Distributions The distributions f(R) produced by each of the 3 models for binary and weighted data (Fig. 4) are all rather broad, suggesting a strong dependence of R on the order in which plants are made extinct; the computed values span the range generated by primary extinction sequences in bSO with plants removed in increasing and decreasing order of degree (R=0.178 and R=0.812 respectively)
Summary
Network analysis has become an important tool for ecologists seeking to understand the vulnerability of ecosystems to environmental change. Recent research has centred on network approaches for improving our understanding of plant-pollinator communities and extinctions, especially in the light of the widely documented recent declines in key insect pollinators such as honeybees, bumblebees and butterflies (Biesmeijer et al, 2006; Senapathi et al, 2015; Goulson, Lye & Darvill, 2008; Benton, 2006). These trends are concerning for biodiversity, ecosystem function and food security (Potts et al, 2010) as insect pollinators are known to play a vital role in providing ecosystem services (Bailes et al, 2015). The dynamics are typically run to fixation, and the populations at fixation used to determine community robustness, and how it relates to overall network structure
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