Part 3: Food-Web Robustness

In short, there is no comfortable theorem assuring thatincreasing diversity and complexity beget enhancedcommunity stability; rather, as a mathematical generalitythe opposite is true. The task, therefore, is to elucidatethe devious strategies which make for stability in enduringnatural systems.

Bob May (1973) Stability and Complexity in Model Ecosystems

Why might ecological network structure matter?

“Devious Strategies” for EcosystemStability, Robustness, Persistence

Robustness of small world, scale free networks

Albert, R., Jeong, H., and Barabási, A.-L. 2000. Error and attack tolerance of complex networks. Nature 406:378-382.

fraction of nodes removed

S = 6209, L = 12,2000, C = 0.003, scale free

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Internet Routers

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attack - highdegree nodesremoved

• Small-world, scale-free networks: -are tolerant of errors (random node losses) -are vulnerable to attacks (removal of hubs)

• Demonstrated for -WWW -Internet routers -yeast protein network -metabolic networks

• What about networks that lack small-world, scale-free topology? (like food webs!)

An ecological perspective

What is the potential for biodiversity loss to triggercascading extinctions in food webs? Loss of prey items can lead to secondary extinctions

Other dynamics can mitigate or exacerbate trophic effects Species richness/ecosystem function

Average effects of species loss vs. loss of particular types of species

Does complexity confer robustness to perturbation? Dynamical Stability of Communities – MacArthur, May, and beyond Structural Stability of Communities – a complementary approach

Remove 4 Grasses 15 Secondary Extinctions

S = 61, C = 0.03

UK Endophytic Grassland Web

S = 42, C = 0.04

UK Endophytic Grassland Web

Remove 4 Insects 10 Secondary Extinctions

S = 28, 4 sub-webs

Remove 2 Grasses, 2 Insects 19 Secondary Extinctions

UK Endophytic Grassland Web

S = 5, 2 food chains

Total: 12 Primary Removals 44 Secondary Extinctions

UK Endophytic Grassland Web

Systematically remove taxa from food webs

4 criteria for species removal sequences (based on degree centrality)1) Most-connected species2) Most-connected species, but protect basal taxa3) Random species4) Least-connected species

If a taxon loses all prey items, it goes extinct

Quantify secondary extinctions

“Robustness” = proportion of species removed that results in 50% total species loss (primary removals + 2° extinctions)

Simulated species loss & secondary extinctions

Species Deletion Sequences:

Most connected ; Most connected, no basal deletions ; R andom ; Least connected

Species Deletion Sequences:

Most connected ; Most connected, no basal deletions ; R andom ; Least connected

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Dark dashed line: 100% total species loss line

Red dashed line: 50% total species loss line

Robustness: Proportion ofprimary species loss toreach ≥ 50% total speciesloss for a particular foodweb and type of loss

species removed / S

2° extinctions in empirical food webs

Species Deletion Sequences:

Most connected ; Most connected, no basal deletions ; R andom ; Least connected

Species Deletion Sequences:

Most connected ; Most connected, no basal deletions ; R andom ; Least connected

Coachella

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Increasing connectance of food web

What types of food webs tend to be robust?

Robustness: Proportion of primary removals that results in ≥ 50% total species loss

Structural robustness increases with connectance

Loss of most-connected taxa

y = 0.15Ln(x) + 0.63; R2 = 0.74

Random extinctions

y = 0.06Ln(x) + 0.55; R2 = 0.56

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Robustness of 19 food webs

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• Different types of biodiversity loss lead to different levels of potential 2° extinctions in food webs.

Loss of highly connected species (high 2° extinctions, threshold effects) Loss of random species (lower 2° extinctions) Loss of minimally connected species (usually few 2° extinctions) Protecting basal species generally mitigates 2° extinctions

• Food web structure (empirical and model) displays increasing robustness to species loss with increasing connectance. Higher C (and less skewed degree distributions) results in:

Lower sensitivity to species loss Delayed thresholds of increased sensitivity Differences among different types of species loss

• Structural robustness doesn’t vary with S or omnivory in empirical webs; in model webs structural robustness increases slowly with S.

Robustness Summary