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

Jennifer A. Dunne

Santa Fe Institute Pacific Ecoinformatics & Computational Ecology Lab

PEaCE Lab: www.foodwebs.org

Ecological Network Research

Circuit Boards Neurons Ecosystems Road Maps Proteins Support Network for a Homeless Woman Internet Connectivity The Kevin Bacon Game

Technological Networks Social Networks Biological Networks

Why is network anatomy so important to characterize? Because structure always affects function.

Strogatz 2001 Exploring complex networks. Nature

Nodes=taxa (S)

• primary producers
• herbivores
• detritivores
• carnivores
• parasites

Edges=trophic links (L)

• predation
• herbivory
• detritivory
• parasitism
• cannibalism

• G. Evelyn Hutchinson. 1959.

Homage to Santa Rosalia, or Why are There so Many Kinds of Animal? The American Naturalist 93: 145-159.

Why trophic (feeding) interactions?

1970’s Challenge:

Complex communities LESS stable than simple communities

(i.e., May 1972/1973)

1950’s Paradigm:

Complex communities MORE stable than simple communities

(i.e., MacArthur 1955)

Current & Future Research:

“Devious strategies” that promote stability and species coexistence

Why ecological networks?

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

Fishes Insects Zoo- plankton Algae Species = 92, Links = 997, L/S = 11, C (L/S2) = 0.12, TL = 2.40

Martinez 1991 Ecological Monographs

Food Web of Little Rock Lake, Wisconsin

Structure: Degree distributions 0.01 0.10 1.00 25 50 75

# links per species cumulative distribution Little Rock Lake Exponential, not Power Law!

Desert Rainforest Lake Estuary Marine

Apparent complexity

Raw data for 16 webs

Normalized data for 16 webs

0.001 0.010 0.100 1.000 1 10

# of trophic links / 2( L/S) cumulative distribution

0.001 0.010 0.100 1.000 1 10

# of trophic links / 2( L/S) cumulative distribution

0.001 0.010 0.100 1.000 1 10

# of trophic links / 2( L/S) cumulative distribution

0.001 0.010 0.100 1.000 1 10

# of trophic links / 2( L/S) cumulative distribution

Raw data for 16 webs

Apparent complexity Underlying simplicity

Desert Rainforest Lake Estuary Marine

Types of Organisms: % Top spp. = 1.1 % 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

Structure: Beyond degree distribution

Little Rock Lake

Characteristic path length Connectance

S = 20 S = 100 S = 1000

1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 0.04 0.06 0.08 0.10 0.30

Characteristic path length Connectance

S = 20 S = 100 S = 1000

1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 0.04 0.06 0.08 0.10 0.30 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 0.04 0.06 0.08 0.10 0.30

Characteristic path length Connectance

S = 20 S = 100 S = 1000

1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 0.04 0.06 0.08 0.10 0.30

Characteristic path length Connectance

S = 20 S = 100 S = 1000

1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 0.04 0.06 0.08 0.10 0.30 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 0.04 0.06 0.08 0.10 0.30

Mean Shortest Path Length Data from 7 Food Webs

Scale dependence with S & C

Williams et al. 2002 PNAS, Vermaat et al. 2009 Ecology

One Dimension Two Parameters (C,S) Simple Link Distribution Rules Predicts Network Structure across Habitats

(DD, metrics, motifs, maximum likelihood)

The Niche Model

Desert Rain- forest Lake Estuary Marine

Structure: Simple models for complex structure

Williams & Martinez 2000 Nature

Robustness: Response of networks to node loss

fraction nodes removed

10 5 15 20 0.01 0.02 0.03

path length

Internet Routers

Error Attack

• Many “real-world” networks are:
• tolerant of “errors” (random node loss)
• vulnerable to “attacks” (high degree node loss)
• Simulated for power-law networks:
• WWW
• Internet
• Protein networks
• Metabolic networks
• Ecological networks?
• not power-law
• extinction risk vs. information flow
• bottom-up effects vs. top-down effects

Albert et al. 2000 Nature

Pollination Web: Loss of most highly connected plants

Ecological network robustness

Robustness by degree…

Robustness (R50): Proportion of primary species loss to reach ≥ 50% total species loss for a particular food web and type of loss

• St. Marks

(S=48, C=0.10) 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 1

• St. Marks

(S=48, C=0.10)

• St. Marks

(S=48, C=0.10) 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 1

species removed / S cumulative secondary extinctions / S

• St. Marks Estuary (S = 48)

R50 R100

high degree random degree high (protect plants) low degree

Dunne et al. 2008 Ecology Letters

Coachella (S=29, C=0.31) 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 1 0.8 Coachella (S=29, C=0.31) 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 1 0.8

cumulative secondary extinctions / S species removed / S

Coachella (S=29, C=0.31) 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 1 0.8 Coachella (S=29, C=0.31) 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 1 0.8

cumulative secondary extinctions / S species removed / S cumulative secondary extinctions / S species removed / S cumulative secondary extinctions / S species removed / S

• St. Marks

(S=48, C=0.10) 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 1

• St. Marks

(S=48, C=0.10)

• St. Marks

(S=48, C=0.10) 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 1

cumulative secondary extinctions / S species removed / S cumulative secondary extinctions / S species removed / S

• St. Marks

(S=48, C=0.10) 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 1

• St. Marks

(S=48, C=0.10)

• St. Marks

(S=48, C=0.10) 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 1 El Verde (S=155, C=0.06) 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 1 El Verde (S=155, C=0.06) 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 1

cumulative secondary extinctions / S species removed / S

El Verde (S=155, C=0.06) 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 1 El Verde (S=155, C=0.06) 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 1

cumulative secondary extinctions / S species removed / S cumulative secondary extinctions / S species removed / S

Grassland (S=61, C=0.03) 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 1 Grassland (S=61, C=0.03) 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 1

cumulative secondary extinctions / S species removed / S

Grassland (S=61, C=0.03) 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 1 Grassland (S=61, C=0.03) 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2 1

cumulative secondary extinctions / S species removed / S cumulative secondary extinctions / S species removed / S

Increasing Connectance of Food Web W

Loss of most-connected taxa y = 0.15Ln(x) + 0.63; R

2 = 0.74

Random extinctions y = 0.06Ln(x) + 0.55; R

2 = 0.56

0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4

Shelf Benguela Reef

Robustness (R50) as ƒ(C) for 19 food webs*

*No relationship between S & R50

Dunne et al. 2002 PNAS, Dunne et al. 2004 Mar Ecol Prog Ser

Robustness to natural extinctions…

Ecologically plausible (“natural”) extinction sequences derived from lake-specific rankings based on species’ geographic prevalences, corroborated by pH tolerances

Geographic Nestedness of 210 Species in 50 Adirondack Lakes

# species removed / S

# cum. secondary extinctions / S

Natural Extinctions Random Extinctions Reverse Natural

Natural Random Reverse

\

R25: 0.250 0.230 0.203 R50: 0.500 0.450 0.339 R75: 0.724 0.665 0.578

Why Robust to Natural Extinctions?

 Specialist (low-degree) consumers tend to eat geographically widespread taxa  Generalist (high-degree) consumers tend to eat more geographically restricted taxa

Srinivasan et al. 2007 Ecology

• ‘Complex’ food webs aren’t intractably complex, nor are they random: they share

underlying scale-dependent structure.

• The Niche model and its variants do a good job of predicting many aspects of

empirical web structure.

 Hierarchical Feeding + Beta/Exponential Distribution + Intervality + Cycles

• Evaluation of models largely indifferent to inference method.



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



Food-web structural robustness increases with C in empirical webs, and with C and S in model webs.



Food-web structure is very robust to “natural” extinction sequences through an interplay of geographic distribution and local food-web structure.



Structural analyses give the minimum potential secondary extinctions.

Ecological network structure & robustness summary

? ?

?

n j =1

Bi'(t) = Gi (B) – xi Bi (t) +

(xi yij ?ij Fij (B) Bi (t) – xj yji ?ji Fji (B) Bj (t)) / eji

Rate of change = Production rate – Loss of biomass + Gain of biomass – Loss of biomass to in biomass

• f basal spp. to metabolism from

resource spp. consumer spp.

? ?

?

n j =1

Bi'(t) = Gi (B) – xi Bi (t) +

(xi yij ?ij Fij (B) Bi (t) – xj yji ?ji Fji (B) Bj (t)) / eji

? ?

?

n j =1

Bi'(t) = Gi (B) – xi Bi (t) +

(xi yij ?ij Fij (B) Bi (t) – xj yji ?ji Fji (B) Bj (t)) / eji

Rate of change = Production rate – Loss of biomass + Gain of biomass – Loss of biomass to in biomass

• f basal spp. to metabolism from

resource spp. consumer spp. Rate of change = Production rate – Loss of biomass + Gain of biomass – Loss of biomass to in biomass

• f basal spp. to metabolism from

resource spp. consumer spp.

Time evolution of species’ biomasses in a food web result from:

• Basal species grow to a carrying capacity, resource competition, or other models
• Other species grow according to feeding rates and assimilation efficiencies
• All species lose energy due to metabolism and consumption
• Functional responses determine how feeding rates vary with consumer/resource abundances
• Biological rates of production, metabolism, and maximum consumption scale with body size

Dynamics: Bioenergetic model

Network3D

400 600 800 1000 1200 1400 1600 Number of observations a) Invertebrates 100 200 300 400 500 600 Number of observations b) Ectotherm vertebrates 400 600 800 1000 1200 1400 1600 Number of observations a) Invertebrates 100 200 300 400 500 600 Number of observations b) Ectotherm vertebrates

Empirical Body Size Ratios

~101 ~102

Dynamics 1: Factors underlying persistence

persistence (S

persistent / S initial )

log10 consumer-resource body-size ratio persistence (S

persistent / S initial )

log10 consumer-resource body-size ratio

400 600 800 1000 1200 1400 1600 Number of observations a) Invertebrates 100 200 300 400 500 600 Number of observations b) Ectotherm vertebrates 400 600 800 1000 1200 1400 1600 Number of observations a) Invertebrates 100 200 300 400 500 600 Number of observations b) Ectotherm vertebrates

Model: Persistence as ƒ (Body-Size Ratios)

~101 ~102

Brose et al. 2006 Ecology Letters Data: Body Size Ratios

solid lines- observations dashed line- model predictions

Dynamics 2: Predicting interaction strength

1 species knockouts, measure change in biomass of all other species. That “interaction strength” is simple function of

 body mass of the removed species (MR )  biomass of target species with removed species present (B+

T )

 biomass of the removed species (Br )

log10|pcI| = -1.14 + 0.88 log10 (MR ) + 0.71 log10 (B+

T ) – 0.79 log10 (Br ) [R2 = 0.88]

Empirical Test: Whelks, Mussels, & Barnacles

Berlow et al. 2009 PNAS

Barnacles Absent Barnacles Present

Dynamics 3: Robustness to invasion by single species

47% of invaders successfully establish in dynamical model food webs Degree of secondary extinctions related to connectance

Ecological network dynamics summary

• The trophic dynamics of complex food webs can be modeled using a relatively

simple, non-linear, bioenergetic model combined with niche model structure.

• We use this approach to explore the conditions and constraints that support or

inhibit the coexistence and persistence of species in complex networks.

• Empirical validation is very hard; coarse-grained measures like body size ratios

have provided support.



Such models can be used to explore a wide variety of important issues such as simple prediction of interaction strength, impacts of keystone species, robustness to invasion, etc.

New directions 1: Enriched, highly resolved data

Taxa = 492

62 autotrophs 4 mixotrophs 345 invertebrates 48 ectotherm vertebrates 29 endotherm vertebrates 3 detritus 1 bacteria

Trophic Species Web S = 290 L = 7200 L/S = 24.8 C = 0.086 Mean TL = 3.79 Antarctic Weddell Sea Food Web

No Par Par, no IP Par, with IP

Bahia San Quintin Carpinteria Estero de Punta Banda

New directions 2: Parasites

Lagerstätten: Fossil assemblages with exceptional soft-tissue preservation

Geologic Time Scale

Messel Shale (49 Ma)

New directions 3: Ancient ecosystems

Burgess Shale (505 Ma) Chengjiang Shale (520 Ma)

Burgess Shale Biota

Wiwaxia Waptia Marella Anomalocaris Hallucigenia Opabinia Ollenoides Pikaia Ottoia



Gut contents



Body size



By analogy with associated taxa



Damage patterns



Environmental deposition



Functional morphology



Stable isotopes



Trace fossils



Coprolites



The occasional smoking gun…

Certainty: 1 = possible 2 = probable 3 = certain

Every link is a hypothesis based on inferences

Lines of evidence for feeding interactions

predator prey predator prey

Burgess Shale Food Web

S = 85, L = 559, L/S = 6.6, C = 0.08, TL = 2.99

Desert Rain- forest Lake Estuary Marine

ri

1 i

ni ci ri

1 i

ni ci

Chengjiang-520 Ma Burgess-505 Ma

Habitat Deep Time

Messel Shale Biota

Propalaeotherium Ailuravus Amphiperca Laurophyllum

leaf mining

Damselfly

eggs

Buprestidae

pollen in gut

Macrocranion

Jumping hedgehog stomach contents leaf cuticle grape seeds predator prey fur teeth (hard seeds)

Fish & Crocodile

coprolites

Terrestrial

• Ter. + Lake

Lake

S = 700, L ~ 7000

Messel Shale Food Web

 Sanak Aleut: ~6000 years of sustainable culture & habitation  A local economy tied directly to ecosystem goods & services  How did their roles as hunter-gatherers affect ‘sustainability’?

Sanak Archipelago, Western Gulf of Alaska New directions 4: Coupled natural-human systems

Aleut (Homo sapiens)

Topology: Sanak Island Intertidal Food Web

 164 species, 725 feeding links  Aleut fed directly on 40 taxa  Aleut topped chains linked to 92 more taxa  Humans are strongest generalists & omnivores

0.0 0.2 0.5 0.8 1.0

STRENGTH 0.0 0.2 0.4 0.6 0.8 1.0 PERSISTENCE Basal HighTL LowTL RandomTL

Dynamics: Impact of Super-Generalists on Species Persistence

 High species persistence can occur if super-generalist feeds strongly on only a few species at any given time.  Aleut switched prey across habitats & seasons.

www.FoodWebs.org

Eric Berlow

• U. of California, Merced

Ulrich Brose

Georg-August-U. Göttingen

Jennifer Dunne

Santa Fe Institute

Neo Martinez

Pacific Ecoinformatics & Computational Ecology Lab

Tamara Romanuk

Dalhousie University

Rich Williams

Microsoft Research