The architecture of mutualistic networks facilitates coexistence of individual participants by minimizing competition relative to facilitation1,2. However, it is not known whether this benefit is received by each participant node in proportion to its overall contribution to network persistence. This issue is critical to understanding the trade-offs faced by individual nodes in a network3,4,5. We address this question by applying a suite of structural and dynamic methods to an ensemble of flowering plant/insect pollinator networks. Here we report two main results. First, nodes contribute heterogeneously to the overall nested architecture of the network. From simulations, we confirm that the removal of a strong contributor tends to decrease overall network persistence more than the removal of a weak contributor. Second, strong contributors to collective persistence do not gain individual survival benefits but are in fact the nodes most vulnerable to extinction. We explore the generality of these results to other cooperative networks by analysing a 15-year time series of the interactions between designer and contractor firms in the New York City garment industry. As with the ecological networks, a firm's survival probability decreases as its individual nestedness contribution increases. Our results, therefore, introduce a new paradox into the study of the persistence of cooperative networks, and potentially address questions about the impact of invasive species in ecological systems and new competitors in economic systems.
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Funding was provided by the Kellogg School of Management, Northwestern University, the Northwestern University Institute on Complex Systems (NICO; to S.S. and B.U.), NUCATS grant UL1RR025741 (to S.S.), a CSIC-JAE postdoctoral fellowship (to D.B.S.), the Army Research Laboratory (under cooperative agreement W911NF-09-2-0053 to B.U.), and the European Research Council under the European Community's Seventh Framework Programme (FP7/2007-2013) through an Advanced Grant (grant agreement 268543 to J.B.). Figures were generated with PyGrace (http://pygrace.sourceforge.net).
The authors declare no competing financial interests.
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Saavedra, S., Stouffer, D., Uzzi, B. et al. Strong contributors to network persistence are the most vulnerable to extinction. Nature 478, 233–235 (2011). https://doi.org/10.1038/nature10433
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