Complexity and Fragility in Ecological Networks

Complexity and Fragility in Ecological Networks Ricard V. Solé José M. Montoya

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Complexity and Fragility in Ecological Networks 2001 Proceedings of the Royal Society B / arXiv 10.1098/rspb.2001.1767 cond-mat/0011196 sole2001-ecological-networks sole2001-ecological-networks.txt, the project's staged copy 8ac7b7c22a6f1ec4404bea3799dec0f434a04d71 arxiv-open ecology

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0 spans located by searching the stored text for the quote's exact words, allowing any whitespace between them Three of the best-described food webs in the ecological literature - Ythan estuary, Silwood Park and Little Rock Lake - treated as graphs and subjected to simulated species loss. Quotation withheld because this record is not cleared for redistribution. How much of an ecosystem's fragility follows from the shape of its food web rather than from the ecology of the species in it? Quotation withheld because this record is not cleared for redistribution. Shows that food webs inherit the robust-yet-fragile signature of scale-free networks, and turns 'keystone species' from a qualitative label into a topological one that can be computed from the web. Quotation withheld because this record is not cleared for redistribution. mechanism Quotation withheld because this record is not cleared for redistribution. food web robustness and fragility under species removal Quotation withheld because this record is not cleared for redistribution. simulation simulation Quotation withheld because this record is not cleared for redistribution. mechanisms food webs are robust to random species loss but fragile to targeted removal of highly-connected (keystone) species - the error-tolerance / attack-vulnerability of heterogeneous networks Quotation withheld because this record is not cleared for redistribution. mechanisms a power-law degree distribution makes random removal almost always hit a sparsely connected species, so little follows from it Quotation withheld because this record is not cleared for redistribution. mechanisms removing the most connected species instead fragments the web into disconnected clusters at a percolation threshold Quotation withheld because this record is not cleared for redistribution. mechanisms the scale-free shape itself survives random loss but is destroyed by directed loss, so the web loses the property that protected it Quotation withheld because this record is not cleared for redistribution. The approach lacks population dynamics and is constrained by the taxonomic resolution of the webs. what this limits: every fragility estimate in the paper: THIS APPROXIMATION TO COMMUNITY FRAGILITY HAS OBVIOUS CAVEATS DERIVED FROM A LACK OF DYNAMICS AND TAXONOMIC LIMITATIONS Quotation withheld because this record is not cleared for redistribution. The analysis treats food webs as undirected, unweighted graphs. what this limits: any claim about who eats whom or how much: the analysis treats food webs as undirected, unweighted graphs - direction and magnitude are discarded before it begins Quotation withheld because this record is not cleared for redistribution. Only three food webs could be analysed, because of the scarcity of adequately resolved data. what this limits: the generality of the food-web results: OUR STUDY IS LIMITED TO THE THREE RICHEST AND BEST-DESCR[ibed webs], BECAUSE OF THE LIMITATIONS OF THE AVAILABLE DATA IN TERMS OF BOTH TAXONOMIC RESOLUTION AND SIZE Quotation withheld because this record is not cleared for redistribution. The analysis has no population dynamics in it at all - only the graph. what this limits: every fragility result: the analysis has no population dynamics in it, only the graph Quotation withheld because this record is not cleared for redistribution. Interactions are treated as undirected and unweighted, so who eats whom and how strongly are both discarded. what this limits: any claim about interaction direction or strength: OUR FINDINGS ARE BASED ON A NON-DIRECTED, AND NON-WEIGHTED GRAPH Quotation withheld because this record is not cleared for redistribution. Three food webs, chosen because they are the only ones well enough described - the sample is the whole available population, not a random draw from it. what this limits: the generality of the conclusion: Quotation withheld - three because three is all there was Quotation withheld because this record is not cleared for redistribution. One of the three webs resolves only 31% of its nodes to species, so its degree distribution is partly an artefact of taxonomy. what this limits: the degree distribution of that web: ONLY 31% OF NODES ARE REAL SPECIES, BEING MOST OF THE NODES GENERA-LEVEL (63%) AND THE REST CORRESPONDING TO HIGHER TAXA - connectivity depends partly on how finely each group was resolved Quotation withheld because this record is not cleared for redistribution. the robustness/fragility (error- vs attack-tolerance) framework from complex networks applied to ecological food webs Quotation withheld because this record is not cleared for redistribution. the error-and-attack-tolerance analysis of scale-free graphs, applied to species loss in ecological communities Quotation withheld because this record is not cleared for redistribution. the ecological graphs subjected to RANDOM node removal as well as to selective removal aimed at the most connected species eliminates: the fragility being a property of removing nodes at all rather than of removing the RIGHT nodes - random removal is the same operation without the targeting · outcome (stated by the tagger, no quotation): held Quotation withheld because this record is not cleared for redistribution. the behaviour compared against purely random networks, where the degree distribution is Poissonian eliminates: a robustness property that any network would show - the random graph is the object the claim must beat, and it has to be constructed rather than observed · outcome (stated by the tagger, no quotation): held Quotation withheld because this record is not cleared for redistribution. food web food web Quotation withheld because this record is not cleared for redistribution. keystone species keystone species Quotation withheld because this record is not cleared for redistribution. species species Quotation withheld because this record is not cleared for redistribution. node node Quotation withheld because this record is not cleared for redistribution. link link Quotation withheld because this record is not cleared for redistribution. scale-free scale-free Quotation withheld because this record is not cleared for redistribution. small world small world Quotation withheld because this record is not cleared for redistribution. random networks random networks Quotation withheld because this record is not cleared for redistribution. secondary extinctions secondary extinctions Quotation withheld because this record is not cleared for redistribution. homeostasis homeostasis Quotation withheld because this record is not cleared for redistribution. topology topology Quotation withheld because this record is not cleared for redistribution. percolation percolation Quotation withheld because this record is not cleared for redistribution. network - a food web, whose nodes are species and whose links are trophic relations Quotation withheld because this record is not cleared for redistribution. network - biological and technological networks generally, sharing one graph of interaction and one response to node removal Quotation withheld because this record is not cleared for redistribution. fragility - in ecology, how a community responds to losing species, which the paper reads as the graph's response to losing nodes Quotation withheld because this record is not cleared for redistribution. claim_type: mechanism a second reading reaching the same value. Recorded: mechanism — note: a second reading reaching the same value from a different sentence. Not applied - a person decides. Quotation withheld because this record is not cleared for redistribution. phenomenon: robustness of food webs to random species loss and fragility to loss of the most connected species a second reading DIFFERING from the recorded value. Recorded: food web robustness and fragility under species removal — note: a second reading, verbatim-verified, disagreeing with the value on the record. Not applied - a person decides. Quotation withheld because this record is not cleared for redistribution. builds-on → scale-free network theory Quotation withheld because this record is not cleared for redistribution. builds-on → network error-and-attack tolerance results Quotation withheld because this record is not cleared for redistribution. builds-on → Montoya and Solé (2000), small-world and scale-free patterns in food webs Quotation withheld because this record is not cleared for redistribution. extends → Albert et al. (2000) and Jeong et al. (2000), error and attack tolerance of complex networks Quotation withheld because this record is not cleared for redistribution. builds-on → Bond (1993) and Davic (2000) on keystone species beyond top predators Quotation withheld because this record is not cleared for redistribution. builds-on → Albert, Jeong and Barabasi (2000), error and attack tolerance of complex networks Quotation withheld because this record is not cleared for redistribution. builds-on → Jeong et al. 2000, the metabolic-network analysis in this same corpus Quotation withheld because this record is not cleared for redistribution. WITHDRAWN AND REPLACED (RETRACTED AND RE-ADDED WITH THE FINDING CORRECTED) · extends → Montoya and Sole (2000), which showed food webs are scale-free WITHDRAWN AND REPLACED: RETRACTED AND RE-ADDED WITH THE FINDING CORRECTED. The target said the cited paper 'SHOWED FOOD WEBS ARE SCALE-FREE'. The span says '…DISPLAY SMALL-WORLD PROPERTIES (Montoya and Sole, 2000)…' SMALL-WORLD IS NOT SCALE-FREE - they are distinct properties and the difference is exactly what this literature argues about. The quote was exact, the anchor resolved and the endpoints were attested throughout: 'target' is the one field of the pair that nothing checks, and it is the fold key. Quotation withheld because this record is not cleared for redistribution. extends → Montoya and Sole (2000), which showed these networks display small-world properties Quotation withheld because this record is not cleared for redistribution. keystone species —operationalised-as→ topology keystone species topology strength of the relation: 1 Audit 2026-09-28: DOUBTFUL - read against its span and kept, but the span says topology rather than trophic position determines which species are keystone; operationalised-as is loose. Quotation withheld because this record is not cleared for redistribution. food web —is-a→ scale-free food web scale-free strength of the relation: 1 Audit 2026-09-28: DOUBTFUL - read against its full span and kept, but the span writes 'scalefree distributions of connections'; endpoint variant, is-a loose. Quotation withheld because this record is not cleared for redistribution. food web —is-a→ small world food web small world strength of the relation: 1 Audit 2026-09-28: DOUBTFUL - read against its full span and kept, but endpoint by anaphora: 'these networks' = the three food webs (previous sentences); is-a is loose. Quotation withheld because this record is not cleared for redistribution. EVIDENCE CORRECTED (RE-GROUNDED) · keystone species —causes→ secondary extinctions keystone species secondary extinctions EVIDENCE CORRECTED: RE-GROUNDED. The old span named neither endpoint. This sentence names both and states the causal link the edge asserts - removal of keystone species producing secondary extinctions. — strength of the relation: 1 Audit 2026-09-28: DOUBTFUL - read against its full span and kept, but the span reports extinction rates up to 95 times higher when keystone species are removed; 'secondary extinctions' is a variant. Quotation withheld because this record is not cleared for redistribution. three — number of species-rich ecosystem food webs analysed Quotation withheld because this record is not cleared for redistribution. P(k) ≈ k^-γ — scale-free power-law degree distribution of the food webs about this quote: QUOTE REPAIRED: the extractor split a hyphen-space and the quote was recorded faithfully with the damage in it, which made it unanchorable. The repaired string is an EXACT SUBSTRING of the staged text - that is why it was accepted, not because a rule produced it. The text as originally recorded is kept in evidence as extracted. Quotation withheld because this record is not cleared for redistribution. Ns = 134 species — size of the Ythan estuary food web Quotation withheld because this record is not cleared for redistribution. <k> = 4.75 — average links per species in the Silwood Park web Quotation withheld because this record is not cleared for redistribution. <k> = 26.05 — average links per species in the Little Rock Lake web Quotation withheld because this record is not cleared for redistribution. 95 times higher — ratio of extinction rate under directed removal to random removal Quotation withheld because this record is not cleared for redistribution. 88% real species — taxonomic resolution of the Ythan estuary web Quotation withheld because this record is not cleared for redistribution. Ecological networks are extremely robust against random removal but very fragile under selective attacks. Quotation withheld because this record is not cleared for redistribution. This robust-yet-fragile structure bears on biodiversity dynamics, extinction-rate estimates, and the definition of keystone species. Quotation withheld because this record is not cleared for redistribution. The food webs show high homeostasis under random species removal, with a slow, linear decrease in the fraction of species in the largest cluster. Quotation withheld because this record is not cleared for redistribution. Directed removal of the most connected species is catastrophic - extinction rates run up to 95 times higher than under random removal. Quotation withheld because this record is not cleared for redistribution. The scale-free distribution itself is stable under random loss of more than half the species, and collapses after only a few directed removals. Quotation withheld because this record is not cleared for redistribution. The topology of the food web, rather than the trophic position of species, determines which species are keystone. Quotation withheld because this record is not cleared for redistribution. size of the largest species cluster size of the largest species cluster Quotation withheld because this record is not cleared for redistribution. secondary extinctions secondary extinctions Quotation withheld because this record is not cleared for redistribution. keystone species keystone species Quotation withheld because this record is not cleared for redistribution. power law distribution power law distribution Quotation withheld because this record is not cleared for redistribution. p-value p-value Quotation withheld because this record is not cleared for redistribution. power-law power-law Quotation withheld because this record is not cleared for redistribution. poisson-distribution poisson-distribution Quotation withheld because this record is not cleared for redistribution. mean mean Quotation withheld because this record is not cleared for redistribution.

The full text of this article is not redistributable, so it is not included here. The evidence sentences are withheld with it; the tag layer and its grounding status remain. The article itself is at https://doi.org/10.1098/rspb.2001.1767.