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

Predictability

Predict Biodiversity

Prediction Biodiversity Changes in Focal Species

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

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

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

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

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)

Complex

Complicated

some hope

metabolism

everything needs energy to stay alive

BIG things need more energy than small things

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

Feeding is Universal

Food Webs are the foundation of Ecological Networks

Body Size should predict the strength of interactions in food webs

Feeding is Universal

Universal ≠ The Only Thing

Ubiquitous ≠ The Only Thing

non-metabolic interactions R. Donovan

Question

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

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

can we explain with body size (metabolism)? WHAT

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

.

repeat it

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

can we explain with body size (metabolism)? WHAT

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

abundance, interaction strength, etc. ?

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

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

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

can we detrend metabolism in complex networks?

Brose et al Ecology Brose et al Ecology Petchey et al PNAS Body Size also influences Food Web Structure

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

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

does more complex = more complicated?

Approach

Simulation Results

Real World

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

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

Approach: delete each species and measure effects on all others

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

Approach: mine the variability for what best explains interaction strengths

The Model

The Models coupled

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)

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

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

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

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

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

R T Removed Species Target Species

R T X +

R T

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

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

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

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

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

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-

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-

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

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

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

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

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

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

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

S1S1 K D S1S1 + S2S2 Bottom up Top down Horizontal

add noise

track the consequences of that noise

add noise: Web Structure size, connectance, architecture

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

add noise: Plant Attributes growth rate half saturation concentrations

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

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

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

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

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

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

Body Size and Food Web Structure

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

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?

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

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

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

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

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

population I (population interaction strength)

population I (total effect on T of removing R)

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

Log |population I| Log (T biomass)

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

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

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 = 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)

Strong per capita effects

Strong population effects

How can it be so simple?

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)

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

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

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

What about the real world?

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

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

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

Successfully Predict

Fail Predictably

Berlow 1999 Nature 398:330

R T Whelks Mussels Barnacles Space

R T Whelks Mussels Barnacles Space Field Experiment Conditions

R T Whelks Mussels Barnacles Space

R T Whelks Mussels Barnacles Space Metabolic

R T Whelks Mussels Barnacles Space Metabolic + Non-Metabolic

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

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

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

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

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

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|)

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

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

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

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

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

"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.

Acknowledgements Alexander von Humboldt Foundation

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

Positive Effects Negative Effects Probability Log (|population I|)

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

Chains of interactions tend to dampen with distance