Ecological Network Research Jennifer A. Dunne Santa Fe Institute - PowerPoint PPT Presentation

Ecological Network Research Jennifer A. Dunne Santa Fe Institute Pacific Ecoinformatics & Computational Ecology Lab PEaCE Lab: www.foodwebs.org

Why is network anatomy so important to characterize? Because structure always affects function. Technological Networks Social Networks Biological Networks Proteins Road Maps The Kevin Bacon Game Neurons Internet Connectivity Ecosystems Support Network for a Homeless Woman Circuit Boards Strogatz 2001 Exploring complex networks. Nature

Nodes=taxa (S) -primary producers -herbivores -detritivores -carnivores -parasites Edges=trophic links (L) -predation -herbivory -detritivory -parasitism -cannibalism

Why trophic (feeding) interactions? G. Evelyn Hutchinson. 1959. Homage to Santa Rosalia, or Why are There so Many Kinds of Animal? The American Naturalist 93: 145-159.

Why ecological networks? 1950’s Paradigm: Complex communities MORE stable than simple communities (i.e., MacArthur 1955) 1970’s Challenge: Complex communities LESS stable than simple communities (i.e., May 1972/1973) Current & Future Research: “Devious strategies” that promote stability and species coexistence

_ Ecological Network Structure _ Structural Robustness _ Ecological Network Dynamics _ New Directions

Food Web of Little Rock Lake, Wisconsin Fishes Insects Zoo- plankton Algae Species = 92, Links = 997, L/S = 11, C (L/S 2 ) = 0.12, TL = 2.40 Martinez 1991 Ecological Monographs

Structure: Degree distributions Little Rock Lake 1.00 cumulative distribution Exponential, not Power Law! 0.10 0.01 0 25 50 75 # links per species

Apparent complexity Raw data for 16 webs Marine Estuary Lake Rainforest Desert

Apparent complexity Underlying simplicity Raw data for 16 webs Normalized data for 16 webs 1.000 1.000 1.000 1.000 cumulative distribution cumulative distribution cumulative distribution cumulative distribution 0.100 0.100 0.100 0.100 0.010 0.010 0.010 0.010 0.001 0.001 0.001 0.001 0 0 0 0 1 1 1 1 10 10 10 10 # of trophic links / 2( L/S ) # of trophic links / 2( L/S ) # of trophic links / 2( L/S ) # of trophic links / 2( L/S ) Marine Estuary Lake Rainforest Desert

Structure: Beyond degree distribution Types of Organisms: % Top spp. = 1.1 Little Rock Lake % Intermediate spp. = 85.9 % Basal spp. = 13.0 % Cannibal spp. = 14.1 % Herbivore spp. = 37.0 % Omnivore sp. = 39.1 % Species in loops = 26.1 Linkage Metrics: Mean food chain length = 7.28 SD food chain length = 1.31 Log number of chains = 5.75 Mean trophic level = 2.40 Mean max. trophic simil. = 0.74 SD vulnerability (#pred.) = 0.60 SD generality (#prey) = 1.42 SD links (#total links) = 0.71 Mean shortest path = 1.91 Clustering coefficient = 0.18

Scale dependence with S & C Data from 7 Food Webs Characteristic path length Characteristic path length Characteristic path length Characteristic path length 2.8 2.8 2.8 2.8 2.8 2.8 Mean Shortest Path Length 2.6 2.6 2.6 2.6 2.6 2.6 2.4 2.4 2.4 2.4 2.4 2.4 2.2 2.2 2.2 2.2 2.2 2.2 2.0 2.0 2.0 2.0 2.0 2.0 1.8 1.8 1.8 1.8 1.8 1.8 1.6 1.6 1.6 1.6 1.6 1.6 S = 20 S = 20 S = 20 S = 20 S = 100 S = 100 S = 100 S = 100 1.4 1.4 1.4 1.4 1.4 1.4 S = 1000 S = 1000 S = 1000 S = 1000 1.2 1.2 1.2 1.2 1.2 1.2 0.04 0.04 0.04 0.04 0.04 0.04 0.06 0.08 0.10 0.06 0.08 0.10 0.06 0.08 0.10 0.06 0.08 0.10 0.06 0.08 0.10 0.06 0.08 0.10 0.30 0.30 0.30 0.30 0.30 0.30 Connectance Connectance Connectance Connectance Williams et al. 2002 PNAS , Vermaat et al. 2009 Ecology

Structure: Simple models for complex structure Marine The Niche Model Estuary Lake One Dimension Rain- forest Two Parameters (C,S) Simple Link Distribution Rules Predicts Network Structure across Habitats Desert (DD, metrics, motifs, maximum likelihood) Williams & Martinez 2000 Nature

Robustness: Response of networks to node loss Internet Routers • Many “real-world” networks are: 20 - tolerant of “errors” (random node loss) - vulnerable to “attacks” (high degree node loss) Attack 15 path length • Simulated for power-law networks: 10 - WWW - Internet 5 - Protein networks - Metabolic networks Error 0 • Ecological networks? 0 0.01 0.02 0.03 - not power-law fraction nodes removed - extinction risk vs. information flow - bottom-up effects vs. top-down effects Albert et al. 2000 Nature

Ecological network robustness Pollination Web: Loss of most highly connected plants

Robustness by degree… St. Marks Estuary ( S = 48) 1 1 1 1 St. Marks St. Marks St. Marks cumulative secondary extinctions / S R 100 ( S =48, C =0.10) ( S =48, C =0.10) ( S =48, C =0.10) 0.8 0.8 0.8 0.8 high degree 0.6 0.6 0.6 0.6 R 50 high (protect plants) 0.4 0.4 0.4 0.4 Robustness (R 50 ): random degree Proportion of primary species low degree 0.2 0.2 0.2 0.2 loss to reach ≥ 50% total species loss for a particular food web and type of loss 0 0 0 0 0 0 0 0 0.2 0.2 0.2 0.2 0.4 0.4 0.4 0.4 0.6 0.6 0.6 0.6 0.8 0.8 0.8 0.8 1 1 1 1 species removed / S Dunne et al. 2008 Ecology Letters

Increasing Connectance of Food Web W cumulative secondary extinctions / S cumulative secondary extinctions / S cumulative secondary extinctions / S cumulative secondary extinctions / S cumulative secondary extinctions / S cumulative secondary extinctions / S cumulative secondary extinctions / S cumulative secondary extinctions / S cumulative secondary extinctions / S cumulative secondary extinctions / S cumulative secondary extinctions / S cumulative secondary extinctions / S 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 St. Marks St. Marks St. Marks St. Marks St. Marks St. Marks Grassland Grassland Grassland Grassland El Verde El Verde El Verde El Verde Coachella Coachella Coachella Coachella 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 ( S =61, C =0.03) ( S =61, C =0.03) ( S =61, C =0.03) ( S =61, C =0.03) ( S =155, C =0.06) ( S =155, C =0.06) ( S =155, C =0.06) ( S =155, C =0.06) 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 ( S =48, C =0.10) ( S =48, C =0.10) ( S =48, C =0.10) ( S =48, C =0.10) ( S =48, C =0.10) ( S =48, C =0.10) ( S =29, C =0.31) ( S =29, C =0.31) ( S =29, C =0.31) ( S =29, C =0.31) 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 1 1 1 1 1 1 1 1 species removed / S species removed / S species removed / S species removed / S species removed / S species removed / S species removed / S species removed / S species removed / S species removed / S species removed / S species removed / S Robustness (R 50 ) as ƒ(C) for 19 food webs* 0.5 Shelf 0.4 Reef *No relationship 0.3 between S & R 50 Benguela 0.2 Random extinctions 2 = 0.56 y = 0.06Ln(x) + 0.55; R 0.1 Loss of most-connected taxa 2 = 0.74 y = 0.15Ln(x) + 0.63; R 0.0 0.0 0.1 0.2 0.3 0.4 Dunne et al. 2002 PNAS , Dunne et al. 2004 Mar Ecol Prog Ser

Robustness to natural extinctions… Geographic Nestedness of 210 Species in 50 Adirondack Lakes Ecologically plausible (“natural”) extinction sequences derived from lake-specific rankings based on species’ geographic prevalences, corroborated by pH tolerances

Natural Extinctions Random Extinctions Reverse Natural # cum. secondary extinctions / S # species removed / S Why Robust to Natural Extinctions? Natural Random Reverse \ R 25 : 0.250 0.230 0.203  Specialist (low-degree) consumers tend R 50 : 0.500 0.450 0.339 to eat geographically widespread taxa R 75 : 0.724 0.665 0.578  Generalist (high-degree) consumers tend to eat more geographically restricted taxa Srinivasan et al. 2007 Ecology