Complexity and Fragility in Ecological Networks — TEI-tagged view

Ricard V. Solé, José M. Montoya · 2001 · ecology · doi:10.1098/rspb.2001.1767 · full text at the source · TEI xml · tagged edition · index · concepts · authors
Where this record's text came from. faceted 2026-08 by reading the locally held text (pdftext); every evidence string verified as an exact substring of that text before merging. Claim type is 'mechanism': the headline result ('robust against random removal but very fragile when selective attacks are used') is attributed throughout to the scale-free degree distribution, i.e. fragility happens because of topology; a reading as plain 'existence' is defensible and the abstract sentence stating the result verbatim is 'Our results suggest that ecological networks are extremely robust against random removal but very fragile when selective attacks are used.' The Montoya and Solé quote retains the PDF's mangled accent ('Sol´e') because the rule is character-for-character copying. The paper mentions unpublished corroboration ('Preliminary analysis of model ecosystems suggest that our results are robust (Sol´e and Montoya, unpublished)'), which is not a published replication, so replication status stays 'untested'. Figure-caption and table text in this extraction is heavily garbled by column interleaving, so no quotes were taken from it. 2026-08-12 and 2026-08-15 schema-0.3 passes: every quote verified as an exact substring of the staged text and anchored at merge time; concept terms verified present; every edge endpoint an existing node.
Some words in these quotes contain the wrong character. The PDF this text was extracted from substituted 10 characters inside a word — a currency sign or a stray accent where a letter pair belongs, as in signi¢cantly for significantly, or a single ligature glyph, as in confidence. They are valid characters in the wrong place, so they survive every encoding check. The quotes keep them for the same reason as above, and a search of this page will not find the affected words.
Other fields define these differently the same word, defined another way in another discipline
species 3 fields · robustness 3 fields · graph 2 fields · simulation 2 fields · homeostasis 2 fields · keystone species 2 fields · and 2 more →
Tags on this paper every tag the record carries, whether or not the words occur in the text below — a number is how many papers in the corpus carry that tag; a tag with no number is unique to this paper
food web2 ecological network robustness5 keystone species3 species10 node4 link4 scale-free6 small world6 random networks2 secondary extinctions homeostasis3 topology5 percolation2 simulation51

Our tag layer for this paper

Cross-disciplinary analysis
content-tags & facets: phenomenon · claim-type · cross-domain-transfer · mechanism · claim-relation · replication-status · limitation — grounded in the full text
phenomenonfood web robustness and fragility under species removal— “Here we analyse the response of these ecological graphs to both random and selective perturbations (directed to most connected species).”
claim-typemechanism— “This complex organization entails some keys for ecological fragility.”
method — evidence— “We have simulated two kinds of species removals: random and directed.”
object of study — evidence— “our study is limited to the three richest and best-described food webs available in the ecological literature”
research question — evidence— “How dependent is ecosystem fragility from graph architecture?”
contribution — evidence— “By using this method, it is the topology of the food web instead of the trophic position of species what determines which species are keystone.”
transferfrom network science / statistical physics: the robustness/fragility (error- vs attack-tolerance) framework from complex networks applied to ecological food webs— “which have been shown to display a very high homeostasis against random removals of nodes”transfers[0]
transferfrom statistical physics of complex networks: the error-and-attack-tolerance analysis of scale-free graphs, applied to species loss in ecological communities— “The trophic organization of species-rich communities is similar to other complex network topologies (Albert et al 2000, Jeong et al 2000).”transfers[1]
mechanismfood 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— “Our results suggest that ecological networks are extremely robust against random removal but very fragile when selective attacks are used”mechanisms[0]
mechanisma power-law degree distribution makes random removal almost always hit a sparsely connected species, so little follows from it— “Secondary extinctions remain at low values because the probability of being removed decreases with k according to P (k) ≈ k−γ, so it is unlikely that a highly connected species will be deleted.”mechanisms[1]
mechanismremoving the most connected species instead fragments the web into disconnected clusters at a percolation threshold— “if most-connected nodes are successively eliminated, the structure of the network reveals an intrinsic fragility that eventually leads to a breaking into many small subgraphs”mechanisms[2]
mechanismthe scale-free shape itself survives random loss but is destroyed by directed loss, so the web loses the property that protected it— “Our analysis shows that indeed, SF distributions are stable up to high values of f (more than 50% of species eliminated in the three food webs) when random removals occur, while those particular distributions quickly disappear under directed removal.”mechanisms[3]
builds-on scale-free network theory— “belonging to the SF class of networks”claim_relations[0]
builds-on network error-and-attack tolerance results— “Our results suggest that ecological networks are extremely robust against random removal but very fragile when selective attacks are used”claim_relations[1]
builds-on Montoya and Solé (2000), small-world and scale-free patterns in food webs— “In a previous study, we have shown that these networks display small-world properties (Montoya and Sol´e, 2000).”claim_relations[2]
extends Albert et al. (2000) and Jeong et al. (2000), error and attack tolerance of complex networks— “Previous studies have shown that the eventual effect of removal is network fragmentation, which takes place in very different ways depending on the type of removal used (Albert et al., 2000; Jeong et al., 2000).”claim_relations[3]
builds-on Bond (1993) and Davic (2000) on keystone species beyond top predators— “In this respect, not only top predators must be considered as keystone species but also other organisms from different trophic levels, in agreement with previous studies (Bond 1993; Davic 2000).”claim_relations[4]
builds-on Albert, Jeong and Barabasi (2000), error and attack tolerance of complex networksclaim_relations[5]
builds-on Jeong et al. 2000, the metabolic-network analysis in this same corpusclaim_relations[6]
extendsWITHDRAWN AND REPLACED (RETRACTED AND RE-ADDED WITH THE FINDING CORRECTED) · Montoya and Sole (2000), which showed food webs are scale-free
Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher.
claim_relations[7]
extends Montoya and Sole (2000), which showed these networks display small-world properties
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claim_relations[8]
sensenetwork - a food web, whose nodes are species and whose links are trophic relations
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senses[0]
sensenetwork - biological and technological networks generally, sharing one graph of interaction and one response to node removal
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senses[1]
sensefragility - in ecology, how a community responds to losing species, which the paper reads as the graph's response to losing nodes
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senses[2]
controlthe ecological graphs subjected to RANDOM node removal as well as to selective removal aimed at the most connected species — held — rules out 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
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controls[0]
controlthe behaviour compared against purely random networks, where the degree distribution is Poissonian — held — rules out 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
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controls[1]
retractedWITHDRAWN AND REPLACED (RETRACTED AND RE-ADDED WITH THE FINDING CORRECTED) · Montoya and Sole (2000), which showed food webs are scale-free — 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 — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher.
Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher.
claim_relations[7]
auditkeystone species —operationalised-as→ topology — 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 — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher.
concept_edges[0]
auditfood web —is-a→ scale-free — 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.
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concept_edges[2]
auditfood web —is-a→ small world — 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.
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concept_edges[3]
auditEVIDENCE CORRECTED (RE-GROUNDED) · keystone species —causes→ secondary extinctions — 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.
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concept_edges[5]
retractedEVIDENCE CORRECTED (RE-GROUNDED) · keystone species —causes→ secondary extinctions — 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.
Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher.
Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher.
concept_edges[5]
outcome (stated by the tagger, no quotation)control — heldcontrols[0]
outcome (stated by the tagger, no quotation)control — heldcontrols[1]
for which uselimitation — every fragility estimate in the paper: THIS APPROXIMATION TO COMMUNITY FRAGILITY HAS OBVIOUS CAVEATS DERIVED FROM A LACK OF DYNAMICS AND TAXONOMIC LIMITATIONS
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limitations[0]
for which uselimitation — 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
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limitations[1]
for which uselimitation — 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
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limitations[2]
for which uselimitation — every fragility result: the analysis has no population dynamics in it, only the graph
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limitations[3]
for which uselimitation — any claim about interaction direction or strength: OUR FINDINGS ARE BASED ON A NON-DIRECTED, AND NON-WEIGHTED GRAPH
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limitations[4]
for which uselimitation — the generality of the conclusion: OUR STUDY IS LIMITED TO THE THREE RICHEST AND BEST-DESCRIBED FOOD WEBS AVAILABLE IN THE ECOLOGICAL LITERATURE - three because three is all there was
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limitations[5]
for which uselimitation — 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
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limitations[6]
replicationuntested
limitationThe approach lacks population dynamics and is constrained by the taxonomic resolution of the webs.
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limitations[0]
limitationThe analysis treats food webs as undirected, unweighted graphs.
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limitations[1]
limitationOnly three food webs could be analysed, because of the scarcity of adequately resolved data.
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limitations[2]
limitationThe analysis has no population dynamics in it at all - only the graph.
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limitations[3]
limitationInteractions are treated as undirected and unweighted, so who eats whom and how strongly are both discarded.
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limitations[4]
limitationThree 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.
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limitations[5]
limitationOne of the three webs resolves only 31% of its nodes to species, so its degree distribution is partly an artefact of taxonomy.
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limitations[6]
Content tags
content-observations: finding · quantity · variable · definition · key-term — grounded in the full text
findingEcological networks are extremely robust against random removal but very fragile under selective attacks.
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content_tags.findings[0]
findingThis robust-yet-fragile structure bears on biodiversity dynamics, extinction-rate estimates, and the definition of keystone species.
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content_tags.findings[1]
findingThe food webs show high homeostasis under random species removal, with a slow, linear decrease in the fraction of species in the largest cluster.
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content_tags.findings[2]
findingDirected removal of the most connected species is catastrophic - extinction rates run up to 95 times higher than under random removal.
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content_tags.findings[3]
findingThe scale-free distribution itself is stable under random loss of more than half the species, and collapses after only a few directed removals.
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content_tags.findings[4]
findingThe topology of the food web, rather than the trophic position of species, determines which species are keystone.
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content_tags.findings[5]
quantitythree food webs — number of species-rich ecosystem food webs analysed
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content_tags.quantities[0]
quantityP(k) ≈ k^-γ — scale-free power-law degree distribution of the food webs
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content_tags.quantities[1]
evidence status notequantity — 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.content_tags.quantities[1]
quantityNs = 134 species — size of the Ythan estuary food web
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content_tags.quantities[2]
quantity<k> = 4.75 — average links per species in the Silwood Park web
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content_tags.quantities[3]
quantity<k> = 26.05 — average links per species in the Little Rock Lake web
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content_tags.quantities[4]
quantity95 times higher — ratio of extinction rate under directed removal to random removal
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content_tags.quantities[5]
quantity88% real species — taxonomic resolution of the Ythan estuary web
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content_tags.quantities[6]
variablesize of the largest species cluster (dependent)
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content_tags.variables[3]
definitionsecondary extinctions
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content_tags.definitions[2]
definitionkeystone species
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content_tags.definitions[3]
definitionpower law distribution
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content_tags.definitions[5]
key-termsnetwork, species, scale-free, robust, fragile, extinction, nodes, connections, trophic, food web, keystone species, node, link, small world, secondary extinctions, homeostasis, random networks, power law, topology, percolation, graph
Concepts
terms this paper carries, each with the sentence it was cut from — the layer that joins one paper to another. Terms with no quote yet are on CONCEPTS.html.
conceptfood web
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concepts[0]
conceptkeystone species
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concepts[3]
conceptspecies — not defined in this paper's own words; the ecological unit that serves as a node of the food web
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concepts[4]
conceptnode — not defined in this paper's own words; an element of the graph; here a species, or a genus where the taxonomy is coarser
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concepts[5]
conceptlink — not defined in this paper's own words; a connection between two nodes; here a trophic relation between two species
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concepts[6]
conceptscale-free — not defined in this paper's own words; a network whose link distribution follows a power law, so most nodes have few links and very few have many
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concepts[7]
conceptsmall world — not defined in this paper's own words; a topology in which nodes are highly clustered while the path between any two remains short
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concepts[8]
conceptrandom networks — not defined in this paper's own words; a network with a Poisson link distribution, which is equally fragile whichever way its nodes are removed
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concepts[9]
conceptsecondary extinctions — not defined in this paper's own words; species lost not by being removed but by being isolated when the species they depend on are removed
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concepts[10]
concepthomeostasis — not defined in this paper's own words; the network's capacity to absorb random removal of its nodes without fragmenting
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concepts[11]
concepttopology — not defined in this paper's own words; the shape of the graph, taken here as the thing that determines fragility - as against the trophic position of a species
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concepts[12]
conceptpercolation — not defined in this paper's own words; the critical fraction of removed species at which the web breaks into many disconnected sub-webs
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concepts[13]
Statistics — cross-field join keys
field-invariant statistical terms, used in their statistical sense (gated on a number / symbol / test). A p-value or a standard deviation means the SAME thing in physics, biology, psychology and sociology — so these are the strongest cross-field join keys. Grounded verbatim.
p-value p as written: p < 0.01
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content_tags.statistics[0]
power-law P(k) ~ k^-γ
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content_tags.statistics[1]
poisson-distribution Poissonian
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content_tags.statistics[2]
mean <k>
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content_tags.statistics[3]
Second readings
a facet read a second time, independently, from its own sentence — and whether the two readings agree
claim typemechanism — a second reading reaching the same value; recorded: mechanism
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alternatives.claim_type
phenomenonrobustness 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
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alternatives.phenomenon

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