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Collaborators: Ulrich Brose Carol Blanchette Jennifer Dunne Sonia Kefi Neo Martinez Bruce Menge Sergio Navarrete Owen Petchey Philip Stark Rich Williams …

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Predictability

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Predict Biodiversity

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Prediction Biodiversity Changes in Focal Species

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….add bit about yosemite toad or mt yellow legged frog

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How can we predict the consequences of species loss in complex ecosystems? Little Rock Lake Food Web (Martinez 1991)

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1 degree How can we predict the consequences of species loss in complex ecosystems? Little Rock Lake Food Web (Martinez 1991)

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2 degrees How can we predict the consequences of species loss in complex ecosystems? Little Rock Lake Food Web (Martinez 1991)

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3 degrees Williams et al. PNAS 2002 How can we predict the consequences of species loss in complex ecosystems? Little Rock Lake Food Web (Martinez 1991)

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Complex

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Complicated

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some hope

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metabolism

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everything needs energy to stay alive

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BIG things need more energy than small things

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BIG things need more energy than small things ( ) 3/4 allometric scaling of metabolism with body size

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Feeding is Universal

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Food Webs are the foundation of Ecological Networks

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Body Size should predict the strength of interactions in food webs

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Feeding is Universal

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Universal ≠ The Only Thing

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Ubiquitous ≠ The Only Thing

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non-metabolic interactions R. Donovan

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Question

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can we explain with body size (metabolism)? ALL interaction strengths

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can we explain with body size (metabolism)? ALL interaction strengths

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can we explain with body size (metabolism)? WHAT

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can we explain with body size (metabolism)? WHAT NOT

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.

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repeat it

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can we explain with body size (metabolism)? ALL interaction strengths

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can we explain with body size (metabolism)? WHAT

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can we explain with body size (metabolism)? WHAT NOT

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abundance, interaction strength, etc. ?

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abundance, interaction strength, etc. feeding, body size, metabolism, etc.

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abundance, interaction strength, etc. feeding, body size, metabolism, etc.

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can we describe a metabolic baseline of interactions in complex networks?

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can we detrend metabolism in complex networks?

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Brose et al. 2005 Ecology Brose et al. 2006 Ecology Petchey et al. 2008 PNAS Body Size also influences Food Web Structure

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if each link obeys allometric rules are those rules preserved at the network scale?

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if each link obeys allometric rules will body size predict the effect of species loss in the network?

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does more complex = more complicated?

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Approach

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Simulation Results

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Real World

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Approach: Simulate species dynamics in a wide variety of networks stochastic variation in structural and dynamic parameters

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Approach: all feeding links governed by (body size) ¾

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Approach: delete each species and measure effects on all others

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Approach: Track variation for each simulation interaction strengths network level structure neighborhood structure species attributes link attributes

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Approach: mine the variability for what best explains interaction strengths

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The Model

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The Models coupled

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Food Web Structure: Niche Model (Williams and Martinez 2000) Predator-Prey Interactions: Bio-energetic Model (Yodzis and Innes 1992, Brose et al. 2005, 2006 Eco Letts) Plant population dynamics: Plant-Nutrient Model (Tilman 1982, Huisman and Weissing 1999)

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Bioenergetic Predator-Prey Dynamics Biomass i at time t Biomass of each species (i) at time (t) is balance of 1. gain from consuming prey species 2. loss to being consumed by other species 3. loss to metabolism

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mass-specific metabolic rate max metabolic-specific ingestion rate Functional Response assimilation efficiency Bioenergetic Predator-Prey Dynamics x i, y i scale with body size (body size correlated with web structure) # Prey Consumption

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Nutrient-Dependent Growth of Plants Bioenergetic Predator-Prey Dynamics (Plants) mass-specific growth rate metabolic loss loss to herbivores r i, x j, y scale with body size

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Nutrient-Dependent Growth of Plants Growth determined by most limiting Nutrient plant growth rate Concentration of Nutrients determined by Supply Turnover Consumption Half saturation conc. for uptake of that Nutrient

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Generate a food web (Niche Model) Calculate trophic level for each species Apply plant-nutrient model to plants, predator-prey model to rest. Assign body sizes based on trophic level (mean pred: prey ratio = 10) Run simulation with each species deleted individually to generate a complete removal matrix Repeat for all species and for 600 Niche Model webs

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R T Removed Species Target Species

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R T X +

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R T

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R T X - per capita I= (B T+ - B T- )/N R population I= B T+ - B T-

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R T X - per capita I= (B T+ - B T- )/N R population I= B T+ - B T-

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R T X - per capita I= (B T+ - B T- )/N R population I= B T+ - B T-

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R T X - per capita I= (B T+ - B T- )/N R population I= B T+ - B T-

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R T X ? T per capita I= (B T+ - B T- )/N R population I= B T+ - B T-

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R T X 1° Consumers 2° Consumers 3° Consumers 1° Prey 2° Prey 3° Prey ? T per capita I= (B T+ - B T- )/N R population I= B T+ - B T-

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R T X 1° Consumers 2° Consumers 3° Consumers 1° Prey 2° Prey 3° Prey ? T per capita I= (B T+ - B T- )/N R population I= B T+ - B T-

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K D S1S1 NK 1 K = Keystone consumer NK = Non-Keystone consumer D = Dominant basal species S = Subordinate basal species R = Resource R1R1 R2R2

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S1S1 S2S2 K D S1S1 NK 1 + Keystone Present R1R1 R2R2 Consumption Resource competition Indirect Facilitation

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S1S1 S2S2 K D S1S1 NK 1 + Keystone Present R1R1 R2R2 Increased Resources Consumption Resource competition Indirect Facilitation

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S1S1 S2S2 K D S1S1 NK 1 SnSn Other Competitors + Keystone Present R1R1 R2R2 Consumption Resource competition Indirect Facilitation

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S1S1 K D S1S1 NK 1 Secondary Consumers + R1R1 R2R2 NK 2n Consumption Resource competition Indirect Facilitation

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S1S1 S2S2 K D S1S1 NK 1 NK 3n Tertiary Consumers + Secondary Consumers R1R1 R2R2 NK 2n Consumption Resource competition Indirect Facilitation

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S1S1 S2S2 K D S1S1 NK 1 NK 2n NK 3n Tertiary Consumers + Secondary Consumers R1R1 R2R2 and so on… NK 4n

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S1S1 K D S1S1 + S2S2 Bottom up Top down Horizontal

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add noise

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track the consequences of that noise

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add noise: Web Structure size, connectance, architecture

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add noise: Animal Attributes metabolic and max consumption rate, pred-prey body size ratio functional response type predator interference

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add noise: Plant Attributes growth rate half saturation concentrations

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track: 90 predictors to explain variation in the strengths of 254,032 interactions among 12,116 species in 600 webs

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track: Global network structure Species attributes of R and T Local network structure around each R and T Attributes of the interaction

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preypredator prey + - R T R T attributes of the interaction + -

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shortest path = 2 degrees 2 degree paths: +, +, - preypredator prey + - R T R T + - attributes of the interaction

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shortest path = 2 degrees 2 degree paths: +, +, - 3 degree paths: +, +, +, - preypredator prey + - R T R T + - attributes of the interaction

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shortest path = 2 degrees 2 degree paths: +, +, - 3 degree paths: +, +, +, - 4 degree paths: - preypredator prey + - R T R T + - sign shortest path = +1 sign next shortest path = +2 un-weighted sum (shortest + next shortest) = +3 weighted sum (shortest + (next shortest / 2)) = +2 attributes of the interaction

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Body Size and Food Web Structure

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R 2 = 0.90 Slope = 0.74 Log (per capita consumption) Log (R body mass) Each Feeding Interaction Scales with (Body Size) 3/4 R T

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R 2 = 0.90 Slope = 0.74 Log (per capita consumption) Per Capita Linear Interaction Strength Log (R body mass) R T = Per Capita Removal Interaction Strength?

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Log |per capita I| R 2 = 0.32 Slope = 0.74 Log (R body mass) Per Capita Removal Interaction Strength R T

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Log |per capita I| R 2 = 0.14 Slope = 1.3 Log (R body mass) Per Capita Removal Interaction Strength R T

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Log (R body mass) Log |per capita I| R 2 = 0.45 Slope = 1.4 Per Capita Removal Interaction Strength R T

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Log (R body mass) Log |per capita I| Per Capita Interaction Strength Low R Biomass High R Biomass Residuals Log (T biomass) Per Capita Removal Interaction Strength R T

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Predicted by: Log (T biomass) + Log (R biomass) + Log (R body mass) Log |per capita I| Per Capita Interaction Strength R 2 = 0.88 R T

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population I (population interaction strength)

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population I (total effect on T of removing R)

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Classification and Regression Trees (CART) on log transformed |Interaction Strengths| best predictors of absolute magnitude of log(population I) T biomass R biomass (Degrees Separated) of the 90 variables tracked R 2 = 0.65

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Log |population I| Log (T biomass)

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Low R Biomass High R Biomass Log (T biomass) Log |population I| R 2 = 0.65

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Sign (strong interactions) ≤ -1 ≥ 1 Weighted Sum Path Signs Proportion Observed Sign (weak interactions) ≤ -1 ≥ 1 Weighted Sum Path Signs positive negative

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Log (|per capita I|) Log (|population I|) Residuals from (a) Log (T biomass) Log (R Body Mass) Log (|population I|) (a) 2. strongest per capita I: large bodied, low biomass R effects on high biomass T R 2 = 0.88 3. strongest population I: high biomass R effects on high biomass T R 2 = 0.65 Summary: 1. 3/4 scaling disappears in complex networks Low R Biomass High R Biomass Log (per capita linear I)

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Strong per capita effects

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Strong population effects

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How can it be so simple?

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Is it circular? Log (T biomass) Log (|population I|) predicting: (B T+ - B T- ) using: B T+ Log (B T+ ) B T+ = T biomass (R present) B T- = T biomass (R removed)

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Is it circular? Log (T biomass) Log (|population I|) predicting: ( B T+ - B T- ) 2 ° extinction of T Log (T biomass) reshuffled interactions using: B T+ Log (B T+ ) R 2 = 0.59 R 2 = 0.19

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population I Degrees Separated Chains of interactions tend to dampen with distance

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Proportion of Variation Explained R 2 = 0.88 Number of Species R 2 = 0.73 More Complex is More Simple per capita I population I

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What about the real world?

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Predictions: Purely metabolic interactions should be well predicted by simple attributes of R and T.

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Predictions: Deviations from simple metabolic predictions should point to strong non-metabolic influences.

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Goal: De-trend the "metabolic baseline" of complex systems to gain insight into other important ecological processes.

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Successfully Predict

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Fail Predictably

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Berlow 1999 Nature 398:330

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R T Whelks Mussels Barnacles Space

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R T Whelks Mussels Barnacles Space Field Experiment Conditions

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R T Whelks Mussels Barnacles Space

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R T Whelks Mussels Barnacles Space + - + - - - - Metabolic

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R T Whelks Mussels Barnacles Space + - + - - - - Metabolic + Non-Metabolic

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R T Whelks Mussels Barnacles + - Metabolic + Non-Metabolic R T R T + - + - - T + - + - - R T R T - T - Metabolic Experimental Design Whelks Excluded Low Whelk Biomass High Whelk Biomass Natural Variation in Mussels and Barnacles 4 blocks x 3 start dates x 1-3 yrs

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Log (|per capita I|) Log (T biomass) Log (|population I|) Simulation Results Low R Biomass High R Biomass

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Log (Mussel biomass) Low Whelk Biomass High Whelk Biomass Central Tendency Predicted by Simulations predicted Log (|per capita I|) Log (|population I|)

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R T - Metabolic predicted Log (Mussel biomass) Log (|per capita I|) Log (|population I|) Low Whelk Biomass High Whelk Biomass

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R T R T + + - - - R 2 = 0.49 R 2 = 0.43 Metabolic predicted observed Log (Mussel biomass) Log (|per capita I|) Log (|population I|) Low Whelk Biomass High Whelk Biomass Low Whelk Biomass High Whelk Biomass

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R T R T + + - - - R 2 = 0.49 R 2 = 0.43 Metabolic + Non-Metabolic Log (Mussel biomass) predicted observed Log (|per capita I|) Log (|population I|)

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Summary ¾ power law signal disappears and new simple patterns emerge in a network context. magnitude of per capita and population I explained by 2-3 simple species attributes (of 90) effects dampen with distance more complex = more simple predictable fit and lack-of-fit in field experiment

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Conclusions metabolic "webbiness" of life not necessarily a big source of uncertainty.

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Conclusions “module” approaches may work best when embedded in complexity

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Conclusions metabolic "null model" may describe a universal baseline of species interactions in a complex network.

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Conclusions "de-trend" metabolism in ecological networks to better understand non-metabolic interactions and processes

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"I would not give a fig for simplicity on this side of complexity, but I'd give my life for the simplicity on the other side of complexity" Oliver Wendell Holmes, Jr.

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Acknowledgements Alexander von Humboldt Foundation

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R 2 = 0.96 slope = -1.05 High Biomass R 2 = 0.36 slope = -1.17 Low Biomass R 2 = 0.59 slope = -1.4 All Points

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Positive Effects Negative Effects Probability 0.10 0.05 0.15 0.10 0.05 0.15 Log (|population I|)

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n = 5 random subsamples of 10,000 interactions (a) + + - -

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Chains of interactions tend to dampen with distance

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